Paper 14
Paper 14
Paper 14
STRATEGIC FINANCIAL
MANAGEMENT
FINAL
GROUP – III
PAPER – 14
Published By :
Directorate of Studies
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FINAL
GROUP – III
PAPER – 14
INDEX
3 Leasing Decisions 36 – 48
6 Capital Markets 66 – 70
7 Commodity Exchange 71 – 74
9 Financial Risks 93 – 95
Directorate of Studies, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament)
Suggested Marks Distribution from Examination Point of View
Only for Practice Purpose
MCQ = 20 Marks
Total 100 Marks 3 Hours
Others = 80 Marks
Objective Question
Practical Problem
Study Note – 1
Learning Objective: After studying this chapter, the students will be able to:
• Calculate, interpret, and evaluate problems on investment
decisions under different methods of appraisal.
(i) If the cost of an investment is `25000 and it results in a net cash inflow of `1800 per annum forever, the
Net Profitability Index of the investment is ___________(assume a discount rate of 8%)
(a) 0.9
(c) 1.11
(d) 0.8
Year 0 1 2 3
Cash Flow (` Lakh) -25 30 -15 40
(a) 11.75
(b) 12.34
(c) 12.74
(d) 11.50
(iii) A project with an initial investment of ` 100 lakhs and life of 10 years generates cash flows after tax
(CFAT) of ` 20 lakh per annum. The Payback Reciprocal is ___________
(a) 25%
(b) 20%
(c) 10%
(d) 30%
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(iv) The NPV of a 5 year project is ` 250 lakh and PVIFA at 10% for 5 years is 3.79. The Equivalent Annual
Benefit of the project is ___________
(a) ` 65.96 lakh
(b) ` 947.5lakh
(c) ` 56.96 lakh
(d) ` 96.65 lakh
(vii) The Profitability Index of a project is 1.28 and its cost of investment is ` 250000. The NPV of the project is
___________
(a) ` 75000
(b) ` 80000
(c) ` 70000
(d) ` 65000
(viii) From the following information calculate the MIRR of the project.
Initial Outlay ` 50000, cost of capital 12% p.a., Life of the project 4 years, Aggregate future value of
cash flows ` 104896.50.
(a) 20.35%
(b) 21.53%
(c) 31.25%
(d) 12.25%
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(ix) The IRR of a project is 10%. If the annual cash flow after tax is ` 130000 and project duration is 4 years,
what is the initial investment in the project?
(a) ` 4,10,000
(b) ` 4,12,100
(c) ` 3,90,000
(d) ` 4,05,000
(x) The NPV of a 4 year project is ` 220 lakh and PVIFA at 12% for 4 years is 3.037. The Equivalent Annual
Benefit of the project is ___________
(b) ` 94.74lakh
(xi) The Gross Profitability Index of a project is 1.52 and its NPV is ` 52000, The cost of investment of the
project is ___________
(a) ` 110000
(b) ` 100000
(c) ` 95000
(d) ` 105000
(xii) If Annual CFAT is ` 540000, Project life is 4 years and initial cost is ` 1980000, what is the Payback
Profitability of the project?
(a) ` 160000
(b) ` 195000
(c) ` 180000
(d) ` 120000
Answer:
Question. (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) (xi) (xii)
Answer: (b) (c) (b) (a) (a) (b) (c) (a) (b) (a) (b) (c)
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The management plan to introduce more mechanisation in the department at a capital cost of `16,000. As
an effect of this the number of employees will be reduced from the existing strength of 160 nos. to 120 nos.
but the output of individual employee will increase by 60%. As an incentive to achieve the extra output, the
management propose to offer an one per cent increase in the existing piece work price of Re. 0.10 per
article for every 2% increase in the individual output achieved, hi order to sell the increased output, it will
be necessary to reduce the sale price by 4%.
You are required to calculate extra weekly contribution resulting from the proposed changes, as above,
and give your recommendation.
Answer:
Current output per employee per week 48,000 units,/160 Nos. = 300 units
Output per employee per week after mechanisation 300 units × 160/100 = 480 units
Total production after mechanisation 480 units × 120 employees = 57,600 units
Current selling price ` 60,000/48,000 units - ` 1.25
Revised selling price ` 1.25 × 96/100 = ` 1.20
Variable cost {excluding wages) p.u. = ` 31,200/48,000 units = Re. 0.65 p.u.
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3. An oil company proposes to install a pipeline for transport of crude from wells to refinery. Investments and
operating costs of the pipeline vary for different sizes of pipelines (diameter). The following details have
been conducted:
The estimated life of the installation is 10 years. The oil company’s tax rate is 50%. There is no salvage value
and straight line rate of depreciation is followed.
Calculate the net savings after tax and cash flow generation and recommend therefrom, the largest
pipeline to be installed, if the company desires a 15% post-tax return. Also indicate which pipeline will have
the shortest payback. The annuity PV factor at 15% for 10 years is 5.019.
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Answer:
(` lakhs)
Suggestion: Pipeline of 6 inches diameter has highest NPV and it is recommended for installation.
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4. GFM produces two products - a main product Cp and a co-product Dg. For their main product Cp there is
a 100% buy back arrangement with their foreign collaborators. Recently GFM doubled their capacity and
with this their production capacity for the co-product Dg increased to 10,000 MT per annum. Fortunately,
there was an unprecedented increase in demand for Dg and price too has increased significantly to ` 1000
per tonne.
However with delicensing and liberalisation, more and more units for manufacturing Cp and Dg are being
set up in the country. GFM, therefore, anticipates stiff competition for Dg from next financial year. For
maintaining sales at current level (i.e., 10,000 MT per year) GFM will have to drop the price by ` 50 per MT
every year for the next 5 years when prices are likely to stabilise at pre-boom level of ` 750 per MT.
The Vice-President (Marketing) who, sensing this situation, has just completed a market study, suggests that
the Company revive and earlier project for converting Dg into Dp grade and starting with 1,000 MT from
next year increase production of Dp in stages of 1,000 MT every year by correspondingly reducing Dg. The
Production Manger estimates that the additional variable cost for Dp will be ` 200 per MT. V.P. (Marketing)
feels that Dp can be sold at ` 1,500 per MT but in the first two years a discounted price of ` 1,400 in year 1
and `1,450 in year 2 will have to be fixed. With partial conversion into Dp, the drop in price of Dg can also
be contained at ` 25 MT instead of ` 50 envisaged. Production facilities for Dp involves a capital outlay of
` 50 lakhs.
Present the projected sales volume and price of products Dg and Dp for the next 5 years under two
alternatives.
If GEM normally appraises investments @ 12% p.a. and if cash beyond 5 years from investment are ignored,
advise whether Dp should be produced.
Answer:
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Part II: For the revival of the earlier project for converting Dg partially into Dp the PV of the expected additional
contribution, if any, from Alternative II over that from Alternative I has to be considered.
Working Notes:
** Incremental selling price - Incremental variable cost = (1,400 - 950) - 200 = ` 250 and so on.
Calculation of total PV
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5. A particular project has a four-year life with yearly projected net profit of ` 10,000 after charging yearly
depreciation of ` 8,000 in order to write-off the capital cost of ` 32,000. Out of the capital cost ` 20,000 is
payable immediately (Year 0) arid balance in the next year (which will be the year 1 for evaluation). Stock
amounting to ` 6,000 (to be invested in year 0} will be required throughout the project and for debtors a
further sum of ` 8,000 will have to be invested in year 1. The working capital will be recouped in year 5. It is
expected that the machinery will fetch a residual value of ` 2,000 at the end of 4th year. Income tax is
payable @ 40% and the Depreciation equals the taxation writing down allowances of 25% per annum.
Income tax is paid after 9 months after the end of the year when profit is made. The residual value of `
2,000 will also bear tax (a 40%. Although the project is for 4 years, for computation of tax and realisation of
working capital, the computation will be required up to 5 years.
Taking discount factor of 10%, calculate NPV of the project and give your comments regarding its
acceptability.
Answer:
Particulars Year
0 1 2 3 4 5
Capital expenditure (20,000) (12,000) - - - -
Working capital (6,000) (8,000 - - - -
Net profit - 10,000 10,000 10,000 10,000 -
Depreciation add back - 8,000 8,000 8,000 8,000 -
Tax - - (4,000) (4,000) (4,000) (4,800)
Salvage value - - - - 2,000 -
Recovery of working capital - - - - - 14,000
Net cash inflow (26,000) (2,000) 14,000 14,000 16,000 9,200
Discount factor (a 10% 1.000 0.9091 0.8264 0.7513 0.6830 0.6209
Present values (26,000) (1,818) 11,570 10,518 10,928 5,712
0 1 2 3 4 5
Working Capital Stock 0 6000 6000 6000 6000
Working Capital Stock Investment - 6000 0 0 0
Working Capital Debtor 0 8000 8000 8000
Working Capital Debtor Investment - 8000 0 0
Salvage Working Capital 14000
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6. T Ltd. has specialised in the manufacture of a particular type of transistors. Recently, it has developed a
new model and is confident of selling all the 8,000 units (new product) that would be manufactured in a
year. The required capital equipment would cost ` 25 lakhs and that would have an economic life of 4
years with no significant salvage value at the end of such period. During the first four years, the promotional
expenses would be as planned below:
(`)
Year 1 2 3 4
Expenses
Advertisement 1,00,000 75,000 60,000 30,000
Others 50,000 75,000 90,000 1,20,000
Variable costs of producing and selling a unit would be ` 250. Additional fixed operating costs to be
incurred because of this new product are budgeted at ` 75,000 per year. The management expects a
discounted return of 15% (after tax) on investments in the new product. You are required to work out an
initial selling price per unit of the new product that may be fixed with a view to obtaining the desired return
on investment. Assume a tax rate of 40% and use of straight line method of depreciation for tax purpose.
Note: The present value of annuity of Re. 1 received or paid in a steady stream throughout the period of four
years in the future at 15% is 3.0079.
Answer:
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14,438x = 57,63,571.50
x = 57,63,571.50/14,438 = ` 399.20
Hence, the initial selling price of new product is ` 399.20 per unit.
7. Modern Enterprises is considering the purchase of a new Computer System at a cost of ` 35 lakhs for its
Research and Development (R & D) Division. The cost of operation and maintenance (excluding
depreciation) will be ` 7 lakhs per annum. The useful life of the system will be 6 years after which it will have
a disposal value of ` 1 lakh. With the installation of the system there will be a reduction in running cost of ` 1
lakh per month in the R & D Division.
Moreover, the company is expected to receive ` 9 lakh immediately by disposal of some existing
equipments and furniture.
Capital expenditure in R & D will attract 100% write off for tax purpose. The effective tax rate of the
company may be taken as 50%. The gains arising from disposal of equipments and furniture are to be
considered as free of tax.
Taking the average cost of capital of the company as 12%, you are required to advise financial viability of
the proposal.
Answer: (`)
5.00
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Statement showing the present value of cash flow of the proposal (` lakhs)
8. A company is considering a cost saving project. This involves purchasing a machine costing ` 7,000, which
will result in annual savings on wage costs of ` 1,000 and on material costs of ` 400.
The following forecasts are made of the rates of inflation each year for the next 5 years:
Wages costs 10%, Material costs 5%, General prices 6%
The cost of capital of the company, in monetary terms, is 15%.
Evaluate the project, assuming that the machine has a life of 5 years and no scrap value.
Answer:
Year Labour cost savings Material Costs Savings. Total DCF Present values
(`) (`) savings (`) @ 15% (`)
1 1000 X (1.1) = 1,100 400 X (l.05) = 420 1,520 0.870 1,322
2 1000 X (l.l)2 = 1,210 400 X(l.05)2 = 441 1,651 0.756 1,255
3 1000 X (1.1)3 = 1,331 400 X(l.05)3 = 463 1,794 0.658 1,184
4 1000X (1.1)4 = 1,464 400 X(l.05)4 = 486 1,950 0.572 1,112
5 1000X (1.1)5 = 1,610 400 X(l.05)5 = 510 2,120 0.497 1,060
Present value of total savings 5,933
Less. Initial cash outflow 7,000
NPV (-) 1,067
Suggestion: Since the present value of cost of project exceeds the cost of savings from it and hence it is not
suggested to purchase the machine.
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9. ABC Enterprises Ltd. is evaluating an option to computerise their distribution system. The total capital cost
for the system is `100 lakhs. The operation and maintenance costs (excluding depreciation) per annum is
expected to be ` 10 lakhs. The computer system is expected to have an useful life of 5 years after which it
is expected to become obsolete and would require replacement. It would have negligible salvage value
at that time. The depreciation rate is 10 per cent on written down value method. There would a cost savings
of `10 lakhs due to reduction in clerical numbers, `20 lakhs due to space released and `10 lakhs on
account of inventory reduction. Previous trends indicate that costs are inflating at 10% per annum. The tax
rate for the firm is 50%. Advice whether the company should invest in the Computer system.
Answer:
Year 1 2 3 4 5
WDV at the beginning 100 90 81 72.9 65.61
Less: Depreciation 10 9 8.1 7.29 6.561
WDV at the end 90 81 72.9 65.61 59.049
Year 1 2 3 4 5
Savings:
Reduction in labour cost 10.00 11.00 12.10 13.31 14.64
Reduction in space 20.00 22.00 24.20 26.62 29.28
Savings in inventory 10.00 11.00 12.10 13.31 14.64
40.00 44.00 48.40 53.24 58.56
Costs:
Operation and maintenance 10.00 11.00 12.10 13.31 14.64
Depreciation 10.00 9.00 8.10 7.29 6.56
20.00 20.00 20.20 20.60 21.20
Net savings 20.00 24.00 28.20 32.64 37.36
Less : Tax @50% 10.00 12.00 14.10 16.32 18.68
10.00 12.00 14.10 16.32 18.68
Add: Depreciation 10.00 9.00
Cash inflow after tax 20.00 21.00 22.20 23.61 25.24
Discount factor 0.909 0.826 0.751 0.683 0.621
Present values 18.18 17.35
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10. Apex Enterprises is interested in assessing the cash flows associated with the replacement of the old
machine by a new machine. The old machine has a book value of ` 90,000 which can be sold for the
same amount. It has a remaining life of 5 years, after which the salvage value is expected to be ‘nil’. It is
being depreciated annually @ 10% using the written down value method.
The new machine costs ` 4 lakhs, and has a resale value of ` 2.5 lakhs at the end of 5 years. The new
machine is expected to save manufacturing costs of ` 1 lakh p,a. Investment in working capital remains
same. The tax rate applicable to the firm is 50%.
You, as a Project Analyst, are required to work out the incremental cashflows associated with the
replacement of the old machine and to prepare a statement to be presented to the management for
consideration.
Answer:
Statement Showing Incremental Cashflows and CFAT associated with Replacement of Old Machine with a New
Machine
(` lakhs)
Incremental earning after tax (EAT) 0.3450 0.3605 0.3745 0.3870 0.3983
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Add : Salvage value - - - - 2.5000
Suggestion: In view of positive incremental net cash flows, it is suggested to replace the existing machine.
REPLACEMENT DECISION:
11. A machine used on a production line must be replaced at least every four years. The costs incurred in
running the machine according to its age are:
(`)
Age of machine (years) 0 1 2 3 4
Purchase price 3,000
Maintenance 800 900 1,000 1,000
Repairs 200 400 800
Net Realisable value 1,600 1,200 800 400
Future replacement will be identical machines with the same costs. Revenue is unaffected by the age of
the machine. Assume there is no inflation and ignore tax. The cost of capital is 15%. Determine the optimum
replacement cycle.
Answer:
The possible replacement options of the machine are every one, two, three and four years. The annual
equivalent cost of each of these replacement policies are as follows:
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Year 0 1 2
Cost (3000) - -
Maintenance - (800) (900)
Repairs - - (200)
Resale value - - 1200
Total (3000) (800) 100
DCF @ 15% 1.0 0.8696 0.7561
Present value of cash flows (3000) (696) 76
Years 0 1 2 3
Cost (3,000) - - - -
Maintenance - (800) (900) (1,000) (1000)
Repairs - - (200) (400) (800)
Net realisable value - - - - 400
Total (3,000) (800) (1,100) (1400) (1400)
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Suggestion: Since, annual equivalent cost is the minimum in three years, the machine is suggested to be
replaced every three years.
12. Company has to replace one of its machines which has become unserviceable. Two options are available:
(i) A more expensive machine (EM) with 12 years of life, (ii) A less expensive machine (LM) with 6 years of
life.
If machine LM is chosen, it will be replaced at the end of 6 years by another LM machine. The pattern of
maintenance, running costs and prices are as under:
(`)
Particulars EM LM
You are required to recommend with supporting calculations which of the machines should be purchased.
Present Value factors are:
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Answer:
Annualized value
Since annualised value is less for more expensive machine, it is suggested to replace existing machine with
machine EM.
13. Five Projects M, N, O, P and Q are available to a company for consideration. The investment required for
each project and the cash flows it yields are tabulated below. Projects N and Q are mutually exclusive.
Taking the cost of capital @ 10%, which combination of projects should be taken up for a total capital
outlay not exceeding `3 lakhs on the basis of NPV and Benefit-Cost Ratio (BCR)?
(`)
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Answer:
Computation of Net Present Value and Benefit-Cost Ratio for five Projects
(`)
Project Investment Cash flow No. of P.V. @ P.V. NPV BCR
p.a. years. 10% (PV/Investment
M 50,000 18,000 10 6.145 1,10,610 60,160 2.212
N 1,00,000 50,000 4 3.170 1,58,500 58,500 1.585
O 1,20,000 30,000 8 5.335 1,60,050 40,050 1.334
P 1,50,000 40,000 16 7.824 3,12,960 1,62,960 2.086
Q 2,00,000 30,000 25 9.077 2,72,310 72,310 1.362
Comment - The optimum combination of projects, is Projects M, N and P with total investment of ` 3.00 lakhs
since it has highest NPV & BCR of ` 2,82,070 and 1.940 respectively. Hence, the same should be taken up.
14. S Ltd. has ` 20,00,000 allocated for capital budgeting purposes. The following proposals and associated
profitability indexes have been determined:
Which of the above investments should be undertaken? Assume that projects are indivisible and there. Is
no alternative use of the money allocated for capital budgeting.
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Answer:
Selection of projects: Under NPV method (assuming the projects are indivisible and there is no alternative use of
unutilized amount), projects 3, 4 and 5 which will give a combined NPV of ` 382000 with no unutilized amount,
should be selected. (Detailed calculation of different alternative combinations must be given as per the
previous problem.)
15. XYZ Ltd., an infrastructure company is evaluating a proposal to build, operate and transfer a section of 35
km. of road at a project cost of ` 200 crores to be financed as follows:
Equity share capital ` 50 crores, loans at the rate of interest of 15% p.a. from financial institutions ` 150
crores. The project after completion will be opened to traffic and a toll will be collected for a period of 15
years from the vehicles using the road. The company is also required to maintain the road during the
above 15 years and after the completion of that period, it will be handed over to the Highway Authorities at
zero value. It is estimated that the toll revenue will be ` 50 crores per annum and the annual toll collection
expenses including maintenance of the roads will amount to 5% of the project cost. The company
considers to write off the total cost of the project in 15 years on a straight line basis. For corporate Income-
tax purposes the company is allowed to take depreciation @ 10% on WDV basis. The financial institutions
are agreeable for the repayment of the loan in 15 equal annual instalments - consisting of principal and
interest.
Calculate Project IRR and Equity IRR. Ignore corporate taxation. Explain the difference in Project IRR and
Equity IRR.
Answer:
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The present value annuity factor appearing nearest to 5.092 for 15 years @ 18%.
3.68
IRR = 18% + 3.68 − (−4.96) ×1% = 18.43%
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Study Note – 2
Learning Objective: After studying this chapter, the students will be able to:
• Solve numerical problems on different ways of evaluating risk in
investment proposals.
(i) If the cash flows over the life of the project are perfectly correlated, the Standard Deviation is
determined using the formula ________
Σσ 2
(a) SD =
(1+ i)2
Σσ
(b) SD =
(1+ i)2
Σσ 2
(c) SD = (i + i)
σt
(d) SD = ∑ (1+ i) t
(ii) If nominal discounting rate is 15%, inflation rate is 5%, then real discounting rate will be ___________
(a) 9.52%
(b) 9.25%
(c) 10.25%
(d) 10.52%
(iii) If project cost = ` 12,000, Annual cash flow = ` 4,500 Cost of capital = 14%, life = 4 years, PVIFA (14%, 4)
= 2.9137, then the sensitivity with respect to the project cost is
(a) 9.27%
(b) 10.27%
(c) 9.72%
(d) 10.72%
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(a) ` 1,00,000
(b) ` 75,000
(c) ` 90,000
(d) ` 1,20,000
(v) If expected NPV = ` 1,20,000 and S.D = ` 30,000, then coefficient of variation will be _____________
(a) 25%
(b) 20%
(c) 30%
(d) 50%
(vi) Given, expected value of profit without perfect information = ` 1,600 and expected value of perfect
information = ` 300, then expected value of profit with perfect information will be ________
(a) ` 1300
(b) ` 1900
(c) ` 950
Answer:
It has assumed that the sales price of ` 6 per unit, marginal cost ` 3.50 per unit, and fixed costs ` 34,000.
What is the probability that: (a) the company will break-even in the period? (b) the company will make a
profit of at least ` 10,000?
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Answer:
To break-even, the company must earn enough total contribution to cover its fixed costs. The contribution to
fixed costs and profit is ` 2.50 per unit (i.e. 6 - 3.5).
The probability that sales will equal or exceed 13,600 units is the probability that sales will be 14,000, 16,000 or
18,000 units, which is (0.25 + 0.30 + 0.20) = 0.75 or 75%
To earn profit of ` 10,000, the company must earn enough contribution to cover its fixed costs (` 34,000) and
then make the profit, so total contribution must be ` 44,000. To earn this contribution, sales must be as follows:
` 44,000/2.50 = 17,600 units
The probability that sales will equal or exceed 17,600 units is the probability of sales being 18,000 units, which is
0.20 or 20%.
3. A company has estimated the unit variable cost of a Product to be ` 10, and the selling price is ` 15 per
unit. Budgeted sales for the year are 20,000 units. Estimated fixed costs are as follows:
What is the probability that the company will equal or exceed its target profit of ` 25,000 for the year.
Answer:
The different outcomes for fixed cost are mutually exclusive events. If fixed costs are ` 50,000 for example, they
can’t be anything else as well.
= 0.7 or 70%
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4. The following table presents the proposed cash flows for projects M and N with their associated
probabilities. Which project has a higher preference for acceptance?
Project M Project N
Possibilities Cash flow Probability Cash flow Probability
(` lakhs) (` lakhs) (` lakhs) (` lakhs)
1 7,000 0.10 12,000 0.10
2 8,000 0.20 8,000 0.10
3 9,000 0.30 6,000 0.10
4 10,000 0.20 4,000 0.20
5 11,000 0.20 2,000 0.50
Answer:
Possibilities Cash flow Probability Expected Cash flow Probability Expected value
value
1 7,000 0.1 700 12,000 0.10 1,200
2 8,000 0.2 1,600 8,000 0.10 800
3 9,000 0.3 2,700 6,000 0.10 600
4 10,000 0.2 2,000 4,000 0.20 800
5 11,000 0.2 2,200 2,000 0.50 1,000
1.0 EV = 9200 1.00 EV = 4400
Analysis: The expected monetary value of Project M is greater than Project N. Therefore, Project Mhas a higher
preference for acceptance.
5. The Managing Director of Y Ltd. has evolved some decision making to the operating division of the firm. He
is anxious to extend this process but first wishes to be assured that decisions are being taken properly in
accordance with group policy.
As a check on existing practice, he has asked for an investigation to be made into a recent decision to
increase the price of the sole product of Z division to ` 14.50 per unit but to rising costs.
The following information and estimates were available for the management of Z division:
Last year 75,000 units were sold at ` 12 each with total units cost of ` 9 of which ` 6 were variablecosts.
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For the year ahead the following cost and demand estimates have been made:
(Unit variable costs, fixed costs and demand estimates are statistically independent)
For this type of decision the group has decided that the option should be chosen which has the highest
expected outcome with at least an 80% chance of breaking even.
You are required:
(a) to assess whether the decision was made in accordance with group guidelines,
(b) to obtain what is the group attitude to risk as evidenced by the guidelines.
Answer:
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Selling Price ` 14.50
35,000 0.3 7.50 0.15 2,62,500 0.045 0.045
8.00 0.65 2,80,000 0.195 0.240
8.30 0.20 2,90,500 0.060 0.300
55,000 0.5 7.50 0.15 4,12,500 0.075 0.375
8.00 0.65 4,40,000 0.325 0.700
8.30 0.20 4,56,500 0.100 0.800
68,000 0.2 7.50 0.15 5,10,000 0.030 0.830
8.00 0.65 5,44,000 0.130 0.960
8.30 0.20 5,64,400 0.040 1.000
To break-even the contribution must be greater than ` 291375. It is noticed from the above tables iat at
selling price of ` 13.50 there is 100% chance to break-even. However, at selling price of ` 14.50 there is 70%
(0.075 + 0.325 + 0.1 + 0.03 + 0.13 + 0.04) chance of break-even. The selling price of ` 14.50, therefore,
contravenes group guidelines.
Attitude to Risk - The group seeks to minimise the downside risk whilst maximising its return. It is to some
extent risk averse, but it is prepared to take some risk i.e., 20% risk of loss. It is always sought maximise its
returns, ignoring the probability of failure, it would be risk neutral.
6. (a) A Ltd. has a choice between three projects X, Y and Z. The following information has been estimated:
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Answer:
In order to obtain perfect information about future states of demand from market researchers, a company
has to pay for the information. The maximum value of this perfect information will be equal the EV with the
information less the EV without information.
D2 Y 200 0.2 40
D3 Y 160 0.2 32
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7. Pioneer Projects Ltd. is considering accepting one of two mutually exclusive projects X & Y. The cash flow
and probabilities are estimated as under:
Project X Project Y
Probability Cash flow Probability Cash flow
0.10 12,000 0.10 8,000
0.20 14,000 0.25 12,000
0.40 16,000 0.30 16,000
0.20 18,000 0.25 20,000
0.10 20,000 0.10 24,000
Answer:
P X EV = P*X (x-x) (x - x )2 P (x - x )2
(‘000)
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Analysis - Project Y is more risky as it is more susceptible to wider degree of variation around the most likely
outcome than Project X. Therefore, Project X should be preferred.
8. A company is trying to choose between two investment proposals A and B. Project A has a standard
deviation of ` 6,500 while Project B has a standard deviation of ` 7,200. The finance manager wishes to
know which investment to choose, given each of the following combinations of the expected values;
(i) Project A and Project B both have expected net present value of ` 15,000.
(ii) Project A has expected NPV of ` 18,000 while for Project B it is ` 22,000.
Answer:
(i) If Project A and Project B both have expected net present value of ` 15,000, the Finance Manager should
select Project A since its Standard Deviation is lesser than that of Project B. The lesser Standard Deviation
represents lesser risk.
(ii) If Project A has expected NPV of ` 18,000 while for Project B is ` 22,000, then selection of Project will be
done with the help of Coefficient of Variation.
Analysis - Investment in Project B should be chosen, since its Coefficient of Variation is lower.
9. M Ltd. is attempting to decide whether or not to invest in a project that requires an initial outlay of ` 4 lakhs.
The cash flows of the project are known to be madeup of two parts, one of which varies independently
over time and the other one which display perfect positive correlation. The cash flows of the six year life of
the project are:
(`)
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(i) Find out the expected value of the NPV and its standard deviation, using a discount rate of 10%.
(ii) Also find the probability that the project will be successful, i.e. P (NPV > 0) and state the assumptions
under which this probability can be determined.
Answer:
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Variance = 5,71,80,546
= ` 34,26,28,329
0 − 27285
(ii) P (NPV ≥ 0) = P (z ≥ ) = P (z ≥ –1.47) = 0.5 + 0.4292 (from normal table) = 0.9292
18510
Hence, the probability that the project will be successful is 92.92%. The assumption made under which this
probability can be determined is that the cash flows follow normal distribution with mean (M) is 27,285 and
standard deviation (a) is 18,510 as calculated above.
10. From the following project details calculate the sensitivity of the (a) Project cost, (b) Annual cashflow, and
(c) Cost of capital. Which variable is the most sensitive?
The annuity factor at 14% for 4 years is 2.9137 and at 18% for 4 years is 2.6667.
Answer:
Particulars `
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If the project cost is increased by ` 1112, the NPV of the project will become zero. Therefore, the sensitivity
for project cost is = 1,112/12000 × 100 = 9.27%
If the present value of annual cash inflow is lower by ` 1112, the NPV of the project will become zero.
Therefore, the sensitivity for annual cash flow is = 1112/13112 × 100 = 8.48%
Let ‘x’ be the annuity factor which gives a zero NPV i.e. ‘x’ is the IRR
– 12,000 + 4,500x = 0
Hence, x = 2.6667 and at 18% for 4 years, the annuity factor is 2.6667.
Analysis: The cash inflow is more sensitive, since only 8.5% change in cash inflow will make the NPV of the
project zero.
11. Determine the risk adjusted net present value of the following projects:
Particulars A B C
Net cash outlay (Rs.) 1,00,000 1,20,000 2,10,000
Project life 5 years 5 years 5 years
Annual cash inflow (Rs.) 30,000 42,000 70,000
Coefficient of variation 0.4 0.8 1.2
The company selects the risk-adjusted rate of discount on the basis of the co-efficient of variation:
Coefficient of variation Risk adjusted rate of Present value factor 1 to 5years at risk
discount adjustedrate of discount
0.0 10% 3.791
0.4 12% 3.605
0.8 14% 3.433
1.2 16% 3.274
1.6 18% 3.127
2.0 22% 2.864
More than 2.0 25% 2.689
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Answer:
Project A B C
Present value factor 1 to 5 years at risk adjusted rate of discount (iii) 3.605 3.433 3.274
12. A company is considering the purchase of a new machine for ` 3,50,000. It feels quite confident that it can
sell the goods produced by the machine so as to yield an annual cash surplus of ` 1,00,000. There is,
however, some uncertainty as to the machine’s working life. A recently published trade association survey
shows that members of the association have between them owned 250 of these machines and have found
the lives of the machines vary as under:
3 20
4 50
5 100
6 70
7 10
250
Assuming a discount rate of 10% the net present value for each different machine life is as follows:
You are required to advise whether the company should purchase a new machine or not.
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Answer:
Analysis: The expected NPV is ` 26,480 positive. Hence, the company should take up the project.
13. Given the following information, find out which project is more risky - A or B.
Answer:
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Study Note – 3
LEASING DECISIONS
Learning Objective: After studying this chapter, the students will be able to:
• Solve problems on investment decisions under ‘Lease’ or ‘Buy’
options.
1. A factory needs an equipment for use. It has the option of outright purchase or leasing the equipment. Data
are given below. Recommend the best option that the factory should choose.
Option 1
Purchase outright for a cost of ` 80 lakhs. It is to be entirely financed by a term loan @18%p.a. interest on
outstanding payable on a yearly basis. The term loan to be repaid in eight equal instalments of ` 10 lakhs
each, beginning from second year-end. The economic life of the equipment is assessed to be ten year. The
equipment will be depreciated @ 10% p.a. on straight line basis, with insignificant salvage value at the end
of the economic life? The estimated maintenance expenses would be as detailed below:
Year 1 2 3 4 5 6 7 8 9 10
MC* 4.00 4.40 4.88 5.47 6.18 7.05 8.11 9.41 11.01 13.00
Option 2
The equipment may be leased for a ten-year period. The maintenance of the equipment will be done by
the lessor. The lessee has to pay ` 18 lakhs annual rental at the beginning of each year over the lease
period.
Note - Assume that the lessee is in a tax bracket of 50% and average cost of capital of the lessee firm as
14% p.a.
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Answer:
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Suggestion: The present value of net cash flows is lowest for lease option, hence it is suggested to take
equipment on lease basis.
2. A firm has the choice of buying a piece of equipment at a cost of ` 1,00,000 with borrowed funds at a cost
of 18% p.a. repayable in five annual instalments of ` 32,000, or to take on lease the same on an annual
rental of ` 32,000. The firm is in the tax-bracket of 40%.
Assume:
(i) The salvage value of the equipment at the end of the period is zero.
Answer:
= 18% (0.60)
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One or two sample computation may be helpful for better understanding this problem
Suggestion: It is advantageous to purchase the asset on borrowed funds, as the present value of advantages is
positive.
3. PQR. Ltd. is considering the possibility of purchasing a multipurpose machine which cost ` 10 lakhs. The
machine has an expected life of 5 years. The machine generates ` 6 lakhs per year before depreciation
and tax, and the management wishes to dispose the machine at the end of 5 years which will fetch `1
lakh. The depreciation allowable for the machine is 25% on written down value and the company’s tax rate
is 50%. The company approached a NBFC for a five year lease for financing the asset which quoted a rate
of ` 28 per thousand per month. The company wants you to evaluate the proposal with purchase option.
The cost of capital of the company is 12% and for lease option it wants you to consider a discount rate of
16%.
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Answer:
Particulars 0 1 2 3 4 5
Present value factor @ 12% 1.00 0.893 0.797 0.712 0.636 0.567
Particulars 1 2 3 4 5
Suggestion: From the analysis of the above we can observe that NPV of lease option is more than that of
purchase option. Hence, lease of machine is recommended.
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4. XYZ Ltd. is considering a proposal to acquire an equipment costing ` 5,00,000. The expected effective life
of the equipment is 5 years. The company has two options - either to acquire it by obtaining a loan of ` 5
lakhs at 12% interest p.a. or by lease. The following additional information is available:
(i) the principal amount of loan will be repaid in 5 equal yearly instalments.
(ii) the full cost of the equipment will be written off over a period of 5 years on straight line basis and it is to
be assumed that such depreciation charge will be allowed for tax purpose.
(iii) the effective tax rate for the company is 40% and the after tax cost of capital is 10%.
(iv) the interest charge, repayment of principal and the lease rentals are to be paid on the last day of
each year.
You are required to work out the amount of lease rental to be paid annually, which will match the loan
option.
Answer:
Year Repayment Interest Total Tax on Tax on Total Net Discount NPV
of principal on loan (1)+(2) depreciation Interest (a)+(b) outflow factor
(3)-(c)
Annual lease rental which will be indifferent to loan option = ` 82,966/1 - 0.40 = ` 1,38,277
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5. N Ltd. is a hire purchase and leasing company. It has been approached by a small business firm interested
in acquiring a machine through leasing. The quoted price of the machine is ` 5,00,000. 10% sale tax is
extra. The lease will be for a primary lease period of 5 years.
The finance company wants 8% post-tax return on the outlay. Its effective tax rate is 35%. The income tax
rate of depreciation on the machine is 25% (WDV). Lease rents are payable in arrear at the end of each
year.
Answer:
3.993 1,22,284
2.59545x = 4,27,716
x = 4,27,716/2.59545 = 1,64,795
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6. S Ltd. is faced with a decision to purchase or acquire on lease a mini car. The cost of the mini car is
`1,26,965. It has a life of 5 years. The mini car can be obtained on lease by paying equal lease rentals
annually. The leasing company desires a return of 10% on the gross value of the asset. S Limited can also
obtain 100% finance from its regular banking channel. The rate of interest will be 15% p.a. and the loan will
be paid in five annual equal instalments, inclusive of interest. The effective tax rate of the company is 40%.
For the purpose of taxation it is to be assumed that the asset will be written off over a period of 5 years on a
straight line basis.
(b) What should be the annual lease rental to be charged by the leasing company to match the loan
option?
Answer:
(a) Annual loan repayment = Loan amount/ Annuity factor of 15% = 126965/3.86 = ` 32,892
Note: Annuity factor is based on the assumption that loan instalment is repaid at the beginning of the year to
be at par with lease rentals. Such annuity factor at 15% works out to be 3.86.
Year 0 1 2 3 4
*Difference between the instalment amount and opening balance of 4th year.
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End of Loan Interest Depreciation Tax. shield Net cash PV factor P.V. of cash
re-payment @15% [(2) + (3) × 0.40] outflows - (4) @ 9% outflows
(1) (2) (3) (4) (5) (6) (7)
0 32,892 - - - 32,892 1.00 32.892
1 32,892 14,111 25,393 15,802 17,090 0.92 15,723
2 32,892 11,294 25,393 14,675 18,217 0.84 15,302
3 32,892 8,054 25.393 13,379 19,513 0.77 15,025
4 32,892 4,036 25,393 11,772 21,120 0.71 14,995
5 - 25,393 10,157 (10,157) 0.65 (6,602)
Total present valueof cash outflows 87,335
Annual lease rental = Cost of the asset/Annuity factor of 10%= 126965/4.17 = ` 30447
End of the year Lease Tax After tax PV factors Present value
payment shield cash at 9% of cash outflows
outflows
0 30,447 - 30,447 1.00 30,447
1-4 30,447 12,179 18,268 3.24 59,188
5 12,179 (12,179) 0.65 (7,916)
Total present value of cash outflows ` 81,719
Decision - The present value of cash outflows under lease financing is ` 81,719 while that of debt financing (i.e.,
owning the asset) is ` 87,335. Thus leasing has an advantage over ownership in this case.
Therefore, the lease rental should be ` 34,906 to match the loan option.
7. XYZ Ltd. is considering a proposal to acquire a machine costing ` 1,10,000 payable ` 10,000 down and
balance payable in 10 annual equal instalments at the end of each year inclusive of interest chargeable at
15%. Another option before it is to acquire the asset on a lease rental of ` 15,000 per annun payable at the
end of each year for 10 years. The following information is also available :
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(ii) The company provides 10% depreciation on straight line method on the original cost.
You are required to compute and analyse cash flows and to advise as to which option is better.
Answer:
Particulars (`)
The annual instalments are payable at the end of each year inclusive of interest chargeable at 15%.
Directorate of Studies, The Institute of Cost Accountants of India (Statutory Body under an Act of Parliament) Page 45
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Year Instalment Interest Depreciation Tax shield Net cash P.V. Present
@ 50% flow factor values
[(3)+(4)]* 50/100 (2) -(5)
53,806
Lease rent payable at the end of each year for 10 years = ` 15,000 p.a.
Net cash outflow p.a. on lease rentals after taking into consideration tax savings = ` 7,500 p.a.
Suggestion - The present value of cash outflows is less in case of lease option. Hence, it is suggested to acquire
the machine on lease basis.
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8. ABC Limited has decided to go in for a new model of Mercedes Car. The cost of the vehicle is ` 40 lakhs.
The company has two alternatives: (i) taking the car on finance lease, or (ii) borrowing and purchasing the
car.
PQR Limited is willing to provide the car on finance lease to ABC Limited for five years at an annual rental of
` 8.75 lakhs, payable at the end of the year.
The vehicle is expected to have useful life of 5 years, and it will fetch a net salvage value ` 10 lakhs at the
end of year five. The depreciation rate for tax purpose is 40% on written-down value basis. The applicable
tax rate for the company is 35%. The applicable before tax borrowing rate for the company is 13.8462%.
The values of present value interest factor at different rates of discount are as under:
Rate of Discount 1 2 3 4 5
Answer:
Year Lease Tax shield gained Tax, shield lost on Net cash Discount P.V.of cash.
rentals on lease rental depreciation outflow factor @ outflows
@ 35% 9%
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Year 1 2 3 4 5
WDV at the beginning of the year 40,00,000 24,00,000 14,40,000 8,64,000 5,18,400
Suggestion - Since the NPV of leasing is lower than the cost of purchase, it is suggested to acquire the car on
finance lease basis.
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Study Note – 4
Learning Objective: After studying this chapter, the students will be able to:
• Understand structure of financial markets and different institutions
operating in India.
Answer:
Answer:
(i) Mobilise and allocate savings: The financial system links the savers and investors to mobilise and allocate
the savings efficiently and effectively.
(ii) Monitor corporate performance: The operators of the financial system not only select the projects that are
to be funded but also monitor the performance of the investment carefully.
(iii) Provide payment and settlement systems: The financial system provides adequate payment and
settlement system to its investors for exchange of goods and services and transfer of economic resources
through time and across geographic regions and industries. The depositories and clearing houses are in
charge of the clearing and settlement mechanism of the stock markets.
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(iv) Optimum allocation of risk-bearing and reduction: The financial system provides various option of risk-
reduction to its investors such as diversified portfolios and also by framing rules governing the operation of
the system.
(v) Disseminate price-related information: The financial system helps in disseminating the price related
information so that the investors can take well informed decisions regarding the investment,
disinvestment, reinvestment or holding of any particular asset.
(vi) Offer portfolio adjustment facility–The financial system also provides portfolio adjustment facility by
providing the options of buying and selling a wide variety of financial assets in a quick, cheap and
reliable way.
(vii) Lower the cost of transactions: The transactions done with in the financial system are smooth, effective
and have lower costs.
(viii) Promote the process of financial deepening and broadening –Financial deepening refers to an increase
of financial assets as a percentage of GDP. Financial depth is an important measure of financial system
development as it measures the size of the financial intermediary sector. Financial broadening refers to
building an increasing number of varieties of participants and instruments. The financial system thus
promotes the process of financial deepening and broadening.
3. What are the tools and techniques used by RBI to maintain financial stability?
Answer:
The following tools and techniques used by RBI to maintain financial stability:
(i) Financial Stress Indicator: It is a contemporaneous indicator of conditions in financial markets and in the
banking sector.
(ii) Systemic Liquidity Indicator: This is used for assessing stresses in availability of systemic liquidity.
(iii) Fiscal Stress Indicator: This indicator used for assessing buildup of risks from the fiscal.
(iv) Network Model: This model used for the bilateral exposures in the financial system for assessing the inter-
connectedness in the system.
(v) Banking Stability Indicator: This indicator issued for assessing risk factors having a bearing on the stability of
the banking sector.
(vi) A series of Banking Stability Measures for assessing the systemic importance of individual banks.
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4. What are the direct instruments used by the RBI to formulate and implement monetary policy?
Answer:
There are several direct instruments that are used in the formulation and implementation of monetary policy.
These are as follows:
(i) Cash Reserve Ratio (CRR): The share of net demand and time liabilities that banks must maintain as cash
balance with the Reserve Bank. The Reserve Bank requires banks to maintain a certain amount of cash in
reserve as percentage of their deposits to ensure that banks have sufficient cash to cover customer
withdrawals. The adjustment of this ratio, is done as an instrument of monetary policy, depending on
prevailing conditions. Our centralized and computerized system allows for efficient and accurate
monitoring of the balances maintained by banks with the Reserve Bank of India.
(ii) Statutory Liquidity Ratio (SLR): The share of net demand and time liabilities that banks must maintain in
safe and liquid assets, such as government securities, cash and gold.
(iii) Refinance Facilities: Sector-specific refinance facilities (e.g., against lending to export sector) provided to
banks exchange or other commercial papers. It also signals the medium-term stance of monetary policy.
Answer:
Some of the important regulations relating to acceptance of deposits by NBFCs are as under:
(i) The NBFCs are all owed to accept/renew public deposits for a minimum period of 12 months and
maximum period of 60 months. They cannot accept deposits repayable on demand.
(ii) NBFCs cannot offer interest rates higher than the ceiling rate prescribed by RBI from time to time. The
Present ceiling is 12.5 percent per annum. The interest may be paid or compounded at rests not shorter
than monthly rests.
(iii) NBFCs cannot offer gifts/incentives or any other additional benefit to the depositors.
(iv) NBFCs (except certain AFCs) should have minimum investment grade credit rating.
(vii) Certain mandatory disclosures are to be made about the company in the Application Form issued by the
company soliciting deposits.
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Answer:
Banks and NBFCs are the financial institutions of a Financial System. NBFCs lend and make Investments and
hence their activities are akin to that of banks; however there are a few differences as given below:
(ii) NBFCs do not form part of the payment and settlement system and cannot issue cheques drawn on itself;
(iii) Deposit insurance facility of Deposit Insurance and Credit Guarantee Corporation is not available
depositors of NBFCs, unlike in case of banks.
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Study Note – 5
Learning Objective: After studying this chapter, the students will be able to:
• Understand different types of financial instruments in financial
markets and calculate returns on mutual fund schemes.
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Receivables ` 1 Lakhs
Liabilities ` 50,000
(a) ` 145.00
(b) ` 145.90
(c) ` 146.60
(d) ` 147.00
(v) In case of an open ended Mutual Fund scheme the market price (ex-dividend) was ` 70. A dividend of
` 10 has just been paid and ex-divided price now is ` 82. The return has earned over the past year by
the mutual fund is-
(a) 30.30%
(b) 30.90%
(c) 31.00%
(d) 31.43%
(vi) Money Plant mutual fund had a Net Asset Value (NAV) of ` 60 at the beginning of the year. During the
year a sum of ` 6 was distributed as dividend besides ` 2 as capital gains distribution. At the end of the
year NAV was ` 72.The total return for the year-
(a) 33.33%
(b) 33.95%
(c) 34.23%
(d) 34.78%
(vii) Suppose the aforesaid mutual fund [question(iv)] in the next year gives a dividend of ` 4 and no
capital gains distribution and NAV at the end of second year is ` 66. So,the return for the second year
would be-
(a) 15.96%
(b) 16.66%
(c) 16.98%
(d) 17.16%
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Return 13%
Risk (S.D. i.e. σ) 15%
Beta (ß) 0.90
Risk Free Rate 10%
(a) 0.20
(b) 0.25
(c) 0.30
(d) 0.35
Answer:
2. Mr. Sinha made an investment in a Mutual Fund when the Net Asset Value was ` 14.50. 90 Days later the
Asset Value per unit of the fund becomes ` 14.25. Moreover, in the meantime, Mr. Sinha received a cash
dividend of ` 0.60 and a Capital Gain distribution of ` 0.40. Compute the monthly return.
Answer:
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3. The following portfolio details of a mutual fund scheme are given below:
The scheme has accrued expenses towards portfolio managers of ` 6 Lakh. There are 80 lakh shares
outstanding. Find out the NAV (Net Asset Value) per unit of the scheme.
Answer:
4. Vibrant Mutual Fund company made an issue of 10,00,000 units of `10 each on 01.01.2018. No entry load
was charged. It made the following investments:
Particulars
Total ` 96,00,000
During the year, dividends of ` 10,00,000 were received on equity shares. Besides, interest on all types of
debt securities was received on due time. At the end of the year equity shares and 10% debentures are
quoted at 200% and 90% respectively. Other investments are quoted at par.
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Find out the Net Asset Value (NAV) per unit given that the operating expenses during the year amounted to
` 6,00,000. Also find out the NAV, if the Mutual Fund had distributed a dividend of ` 1 per unit during the
year to the unit holders.
Answer:
Given the Total initial investments is ` 96,00,000, out of issue proceeds of ` 1,00,00,000. Therefore, the balance of
` 4,00,000 is considered as issue expenses.
5. ABC Company Limited as the Asset Management Company (Commencing its functions from 1st May, 2017)
under a trust deed with T.P Mutual Funds Limited managing solely equity schemes of 8 years (with effect
from 1st June, 2017). Information relating to its expenses incurred during the year 2018-19 is as follows.
(` in Crores)
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If accounts are intended to be closed on 31st March, 2019 and on that date the AMC is expected to hold
Net Assets worth ` 1,500 crores (For operational year 2018-19).
What would be the eligible amount of expense chargeable by the AMC for its operations?
Answer:
From the given problem it is clear that ABC Company Limited as AMC is engaged in issuance of a close ended
scheme (As the maturity period of the fund lies between 3 – 15 years). Expenses related to issue of units are to
be amortized over the period of the scheme on weekly basis.
The total number of weeks within which the scheme remains effective is of (8 years × 12 months × 4 weeks) =
384 weeks. The financial year (i.e. 2018-19) comprise of (1 year × 12 months × 4 weeks) = 48 weeks.
Issue Expenses eligible for amortization in the year 2018-19 is of ` (48 × 112.5) / 384
Maximum Limit of charging expenses for management by any AMC is 1.5% of the average weekly net assets
held up to the ceiling of ` 100 crores (excluding amortized part of expenses on issue and redemption). For
financial year 2018-19 assets held by the AMC is of ` 1,500 crores, therefore average weekly net assets held =
`1,500 / 48 = ` 31.25 crores.
Maximum permissible expenses for management by ABC Company Ltd. is of ` (31.25 × 1.5%)
= ` 0.46875 crores.
Total threshold or simply total of maximum eligible expense for management = ` (14.0625 + 0.46875) crores =
`14.53125 crores.
Table showing actual expenses claimed from AMC‘s part from T.P Mutual Funds Limited.
(` in Crores)
Therefore eligible amount of expenses to be charged against management of scheme by ABC Company
Limited is ` 14.53125 crores.
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6. Goodluck Mutual Funds Limited registered in Mumbai issues equity oriented Mutual Fund Schemes mostly
traded in BSE as well as in CSE. The trade being in operations found to cease on 8th February, 2018 in the
respective exchanges.
Additional Information:
• Uncertain Mutual Funds Limited having a more or less similar portfolio of risk-return manages to offer a
dividend yield of 5.46% at a payout ratio of 60% holding a Market Price of ` 110 per unit.
• Number of units issued by Goodluck Mutual Funds Limited are 1, 00,000 at an average cost of raising
funds of 10%.
Required:
b. Whether the value changes if valuation had been made on 9th April, 2018. - Explain
c. If values change what is the value of the scheme on 9th April, 2018?
Answer:
(a) Valuation of the Equity oriented Mutual Fund Scheme on 10th April, 2018
Since, 60 days have been passed since the last trade took place units are to be valued as a non-trade
scrip.
A proxy needs to be identified for computing the value of the scheme. Here in the problem Uncertain
Mutual Funds Limited having a market price of ` 110, and paying a dividend yield of 5.46% that means
paying a dividend of ` 110 × 5.46% = ` 6 per unit best fits the place of proxy. If dividend of Rs. 6 is paid out
at a Dividend Payout Ratio of 0.6, then Earnings per Unit is of ` 6 / 0.6 = ` 10.
Value of the Units on 10th April, 2018 of Goodluck Mutual Funds Limited will be ` 10 / 0.1 = ` 100 Value of the
Mutual Fund Scheme: ` (100 × 1, 00,000 units) = ` 1, 00, 00,000
(b) The value of units changes if valuation is made on 9th April, 2018 (The previous day), As on 9th April, 2018,
the time span of 60 days not expires and therefore we can use the closing price of the units as listed in its
principal stock exchange for valuation purpose.
(c) Value of the scheme on 9th April, 2018: ` (110.8 × 1,00,000 units) = ` 1,10,80,000
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7. PQ Limited contemplating to issue shares at ` 120 each (Face Value of ` 100 each) bearing floatation costs
of 5% on the issue price.
Expected return on capital employed is 20%, with an anticipated payment of dividend per share of ` 11.40.
MX Mutual Funds Limited investing in the same industry manages to yield a return similar to the expectation
of PQ Limited, bearing a floatation cost of 1.5% and management expenses (other than floatation costs) of
1.7% of yield.
Required:
Answer:
(a) Net sale proceeds from each share = ` 120 × (1 – 0.05) = ` 114
Return on Capital Employed = ` 114 × 20% = ` 22.80, out of which dividend payable ` 11.40 Cost of Equity
Capital (Ke) = D1 / P0 = ` 11.40 / ` 120 = 9.5%
Expected Market Price per Equity Share at the end of 1st year = ` 22.80 / 9.5% = ` 240 Number of Equity
shares to be issued = 1,00,000
Expected Market Capitalization of PQ Limited at the end of 1st year = ` 240 × 1,00,000 = ` 2,40,00,000
(b) Investor Expectation on Returns from units of MX Mutual Funds Limited will be as follows:
Returns from Mutual Funds = (Investors’ Expectation / 100 – Issue Expenses) + Annual Recurring Expenses
If returns from MX Mutual Funds Limited becomes equal to the expectation of PQ Limited regarding their
return on capital employed, since they both are in operations within the same sectors.
Then, Investors Expectation = {20% - (20% × 1.7%)} × (100 – 1.5) % = (19.66 × 0.985) = 19.3651%
8. Risk-Return Combinations relating to asset-mix of MFK and MFP are provided below.
MFK MFP
Securities Expected Total Risk Investment Expected Total Risk Investment
Return Return (`)
Equity Shares
Ambuja Cement - - - 15% 14% 8,00,000
Tata Steel 12% 13% 1000000 - - -
Ashok Leyland 10% 15% 600000 - - -
Preferential Shares
J.K Tyre - - - 10% 8% 5,00,000
Debentures
Essar Steel - - - 9% 8% 7,00,000
ACC 8% 5% 400000 - - -
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Company Name Tata Steel Ashok Leyland AC C Ambuja Cement Essar Steel J.K Tyre
Answer:
Risk associated with returns of Mutual Funds (σMF) = √ (wI2 × σI2) + (wJ2 × σJ2) + (wL2 × σL2) + 2
Where, ‘I’, ‘J’, and ‘L’ are the securities with which the mutual fund institution has constructed its portfolio.
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(b)
■ Risk associated with returns of Mutual Funds ‘K’ (σMF) = √ (wT2 × σT2) + (wA2 × σA2) + (wA’2 × σA’2) + {2 × wT ×
wA × σT ×σA × r(T,A)} + {2 × wA × wA’ × σA ×σA’ × r(A,A’)}+ {2 × wT × wA’ × σT ×σA’ × r(T,A’)}
Or, (σMF) = √ (0.52 × 13%2) + (0.32 × 15%2) + (0.22 × 5%2) + (2 × 0.5 × 0.3 × 13% × 15% × 0.67) + (2 × 0.3 × 0.2 ×
15% × 5% × -0.5) + (2 × 0.5 × 0.2 × 13% × 5% × -0.4)
■ Risk associated with returns of Mutual Funds ‘P’ (σMF) = √ (wA2 × σA2) + (wE2 × σE2) + (wJ2 × σJ2) + {2 × wA ×
wE × σA ×σE × r(A,E)} + {2 × wE × wJ × σE ×σJ × r(E,J)}+ {2 × wA × wJ × σA ×σJ × r(A,J)}
Or, (σMF) = √ (0.42 × 14%2) + (0.352 × 8%) + (0.252 × 8%) + (2 × 0.4 × 0.35 × 14% × 8% × -0.8) + (2 × 0.35 × 0.25 ×
8% × 8% × 0.7) + (2 × 0.4 × 0.25 × 14% × 8% × -0.6) Or, (σMF) = 3.54%
(c) It is very much clear from the above computations that MFP is providing higher returns (11.65%) on account
of a lower risk association (3.54%) than that of provided by MFK.
Result: The Sharpe ratio recommends investment in MFP because it provides a higher risk premium for each
unit of risk (Total Risk) association in comparison to MFK.
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9. The following information is available of Mutual Fund A, Mutual B and Market Portfolio for the past six
months:
Fund/Month April 2017 May 2017 June 2017 July 2017 August September
(Return %) 2017 2017
Fund A 3.00 1.75 (1.00) 3.50 1.50 0.00
Fund B 2.25 (1.25) 0.00 3.00 2.50 1.00
Market Portfolio 1.00 (0.75) 2.00 1.50 0.25 3.50
The 6 Month Treasury Bills carry an interest rate of 6% p.a. You are requested to evaluate performance of
Funds A, B and Market Portfolio under Morning Star Index.
Answer:
Computation of Factors
*Monthly Risk free return = 6%/12 = 0.50 p.m. Computation of Morning Star Index (MSI)
Morning Star Index (MSI) (i.e. excess return) [(I)-(II)] 1.33 0.87 1.00
Ranking 1 2 3
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Evaluation: Fund A has performed better than the market portfolio, while Fund B has not performed as good as
the market portfolio despite having the equivalent average return during the period.
10. A Mutual Fund Scheme having 400,000 units has shown NAV of ` 9.25 and ` 9.95 at the beginning and at
the end of the year respectively. The Scheme has given two options:
(a) Pay ` 0.85 per unit as dividend and ` 0.70 per unit as capital gain, or
(b) These distributions are to be reinvested at an average NAV of ` 9.15 per unit.
You are required to find out what difference it would make in terms of return available and which option is
preferable?
Answer:
Option 1: Returns are distributed to the mutual fund holders Balance Sheet
Liabilities ` Assets `
NAV of Closing Date [`9.95*400,000] 3,980,000 Fund Assets 4,600,000
Dividend Payable [`0.85*400,000] 340,000
Capital Gain Distribution [`0.70*400,000] 280,000
4,600,000 4,600,000
= [4,600,000-3,700,000]/3,700,000 = 24.324%
Option 2: The distributions are reinvested at an average NAV of ` 9.15 Distributions reinvested
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Balance Sheet
Liabilities ` Assets `
4,600,000 4,600,000
Comment: Holding period return is the same from investor’s view point irrespective of whether the return
is reinvested or distributed in the form of capital gains or dividends.
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Study Note – 6
CAPITAL MARKETS
Learning Objective: After studying this chapter, the students will be able to:
• Understand money market, capital market and its instruments.
Answer:
The process of buy-back of shares was not permitted in India till 1988, which became permissible after changes
being done in the Companies Act 1956. Government of India and SEBI has issued certain guidelines which are
to be followed at the time of buy-back of shares. Buy back of shares is a corporate financial strategy in which
the shares of the company are bought by the company itself. Reliance, Bajaj, and Ashok Leyland etc. are the
few companies in India which have opted for buy-back of shares. There are generally two methods that are
applied in the corporate sector while buying-back of shares i.e. the tender method or the open market
purchase method. The company, under the tender method, offers to buy back shares at a specific price
during a specified period which is usually one month. Under the open market purchase method, a company
buys shares from the secondary market over a period of one year subject to a maximum price fixed by the
management. The open market purchase method is mostly preferred by the companies due to the advantage
of time and price flexibility.
The buy-back method has a huge impact on the P/E ratio of the company. The P/E ratio may rise if investors
view buyback positively or it may fall if the investors regard buyback negatively.
However, the share prices can also be manipulated by the promoters, speculators or collusive-traders through
the buy-back of shares, which can be counted as a disadvantage of this process.
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Answer:
The securities such as shares, debentures, bonds, Government Securities, MF units etc. are now kept in
electronic form instead of physical form through the process of dematerialization. This speeds up the process of
sale, purchase and transmission of securities. The services of dematerialization, re-materialization, transfer, sale
etc. are provided by depositories registered under SEBI. The Depository Participant, thus, is an agent of the
depository which acts as an intermediary between the depository and the investors. The investors can avail the
depository related services by opening a Depository account, also known as Demat a/c, with any of the
Depository Participants. The shares and securities are converted into electronic form and separate numbers are
allotted to them. All the corporate benefits like bonus, stock splits, dividend etc are also managed by the
depositories and its agent i.e. Depository Participants.
Answer:
There are various advantages of the depository system to different stakeholders which are as follows:-
(ii) It eliminates voluminous paper work and the time and money related with it;
(iii) It is time saving as it reduces settlement time and ensures quick settlement;
(iv) There is no odd lot problem of shares when the shares are kept with the depositories;
(i) It reduces the risks associated with the loss or theft of documents and securities and eliminates forgery;
(ii) It ensures liquidity as the process is automated and by speedy settlement of shares;
(iii) The depository holds the shares in electronic form so the investors are free from the physical holding of
shares;
(iv) It reduces costs such as stamp duty, transaction cost and brokerage; and
(i) It provides updated information of the shareholders and investors like names and addresses, etc.;
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(iv) It increases the efficiency of registrars and transfer agents; and
Answer:
Optionally Convertible Debentures (OCDs) are the debentures that include the option to get converted into
equity. The investor has the option to either convert these debentures into shares at price decided by the
issuer/agreed upon at the time of issue.
(i) Quasi-Equity: Dependence of Financial Institutions is reduced because of the inherent option for
conversion (i.e. since these are converted into equity, they need not be repaid in the near future.)
(ii) High Equity Line: It is possible to maintain Equity Price at a high level, by issuing odd-lot shares
consequent to conversion of the debentures, and hence lower floating stocks.
(iii) Dispensing Ownership: Optionally Convertible Debentures enable to achieve wide dispersal of equity
ownership in small lots pursuant to conversion.
(iv) Marketability: The marketability of the issue will become significantly easier, and issue expenses can be
expected to come down with the amounts raised becoming more.
(b) Investor
(i) Assured Interest: Investor gets assured interest during gestation periods of the project, and starts
receiving dividends once the project is functional and they choose to convert their debentures.
Thereby, it brings down the effective gestation period at the investor’s end to zero.
(ii) Secured Investment: The investment is secured against the assets of the Company, as against
Company deposits which are unsecured.
(iii) Capital Gains: There is a possibility of Capital Gains associated with conversion, which compensates for
the lower interest rate on debentures.
(b) Government
(i) Debentures helped in mobilizing significant resources from the public and help in spreading the Equity
Investors, thereby reducing the pressure on Financial Institutions (which are managed by Government)
for their resources.
(ii) By making suitable tax amendments, benefits are extended to promote these instruments, to safeguard
the funds of Financial Institutions and encouraging more equity participation, which will also require a
higher compliance under Corporate Laws, whereby organisations can be monitored more effectively.
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5. Explain the concept of Net Asset Value (NAV) of a Mutual Fund Scheme.
Answer:
Net Asset Value (NAV) can be considered as the summation of the total asset value (net of expenses) per unit
of the fund calculated by the Asset Management Company (AMC) at the end of every business day. The
realizable value that an investor holding the fund might get on the day the scheme is liquidated can be
reflected as the Net Asset Value for each unit of the scheme on that particular date. It can be deduced to the
statement that Net Asset Value (NAV) denotes the performance of a particular mutual fund scheme and the
day of valuation of NAV is called the valuation day. The NAV can also be defined as the value of joining a
particular mutual fund scheme by the new investors. It is the value of net assets of the fund. The subscription
made by the investors is noted as the capital in the balance sheet of the fund, and their investments are
treated as assets. The NAV is calculated individually for every mutual fund scheme and the aggregate value of
all other investment is taken as the portfolio’s value.
The Net Asset Value (NAV) = Net Asset of the Mutual Fund Scheme/ Number of the Units Outstanding
The NAV will always be computed at market value since the investment of the mutual funds are always marked
at market value only. The computation of NAV for traded and non-traded schemes of Mutual Fund are to be
done as per the separate valuation norms specified by the Securities and Exchange Board of India (SEBI). The
SEBI has also notified that the mutual funds are obligated to compute Net Asset Value (NAV) of each scheme
and to disclose them on a regular basis – daily or weekly (depending on scheme’s type) and publish them in
atleast two daily newspapers, as per the Regulation 48 of SEBI (Mutual Funds) Regulations.
The computation of NAV plays an important part in the decision of an investors whether to enter or to exit a MF
scheme. The NAV also helps the analyst in determination of the yield of the mutual fund schemes.
Answer:
(a) Instruments that are traded: Money market is a collection of instruments like Certificate of Deposits , Inter-
Bank Participation Certificates, Commercial Bills, Treasury Bills, Call money, Notice money, Repos, Term
money, Commercial Papers, Inter Corporate Deposits, Swaps, etc.
(b) Large number of Participants: The main participants of Money market are — (i) Large lenders, (ii) Mutual
funds companies and investors, (iii) Financial institutions such as the RBI, Scheduled commercial Banks,
Discount and Finance House of India and (iv) Large Borrowers. There exists a large network of such
participants in the money market which ultimately adds to the increase in the depth of the market. This
network can be generally categorised as follows:
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Organized Sector:
2. Co-operative Banks
Unorganized Sector
1. Indigenous Bankers
(c) Zone centric activities: Activities in the money market have a tendency to to concentrate in some centre
serving as a region or an area. The width of such area varies due to its size and the needs and demands of
the market.
(d) Pure competition: There exists a pure and healthy competition among the participants of the money
market as they generally tend to be impersonal in character.
(e) Price Difference are low: The Price difference for similar type assets gets eradicated by the interplay
between the demand and supply of the asset.
(f) Flexibility in Regulations: Certain degree of flexibility remains in the regulatory framework and continuous
endeavours are undertaken for introduction of new instruments / innovative techniques in dealing and
trading.
(g) Size of the Money market: The money market is considered a wholesale market as the size and volume of
funds or financial assets that are traded in the market are very large amounting to crores of rupees.
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Study Note – 7
COMMODITY EXCHANGE
Learning Objective: After studying this chapter, the students will be able to:
• Understand commodity derivatives and commodity exchanges.
Answer:
Commodity derivatives play an important role in risk management. We know that prices of commodities,
metals, shares and currencies fluctuate over time. The possibility of adverse price changes in future creates risk
for businesses. Commodity derivatives are used to reduce or eliminate price risk arising from unforeseen price
changes of commodities. Two important commodity derivatives are futures and options which are traded in
commodity exchanges.
(i) Commodity Futures Contracts: A futures contract is an agreement for buying or selling a commodity for a
predetermined delivery price at a specific future time. Futures are standardized contracts that are traded
on organized futures exchanges that ensure performance of the contracts and thus remove the default
risk.
(ii) Commodity Options contracts: Like futures, options are also financial instruments used for hedging and
speculation. The commodity option holder has the right, but not the obligation, to buy (or sell) a specific
quantity of a commodity at a specified price on or before a specified date.
Answer:
(i) The units are inter-changeable and no value adding processes are performed on them. This allows the
units to be traded on exchanges without prior inspection.
(ii) Every commodity has a unique supply factor and as they are produced “naturally”.
(iii) Commodities are subject to cycles in demand from both intermediate players and end users. High prices
usually lead to a boost in resource investments causing excess supply in the future which eventually pushes
down commodity prices.
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(iv) The commodities from different groups may be negatively correlated at a point of time. For example, the
prices of wheat and aluminum can move in the opposite direction as they are affected by a different set
of factors.
(v) There is a positive correlation between commodity prices and growth measures, although there may be a
significant lag between a pickup in industrial production and commodity prices.
(vi) A positive correlation is often seen between commodities and inflation indicators. In particular,
commodities tend to react to an early stage of inflation as raw material price appreciation generally tends
to precede, and quite often exceed consumer price inflation growth. While true over the very long term,
the relationship between inflation and commodity prices has been considerably weaker over the last 10
years, which has been characterized by disinflation/low inflation.
The above characteristics may not be true for all commodities taken individually; however they are true for
diversified indices of industrial commodities and agricultural commodities.
Answer:
(i) Price Discovery: Based on inputs regarding specific market information, the demand and supply
equilibrium, weather forecasts, expert views and comments, inflation rates, Government policies, market
dynamics, hopes and fears, buyers and sellers conduct trading at futures exchanges. This transforms into
continuous price discovery mechanism. The execution of trade between buyers and sellers leads to
assessment of fair value of a particular commodity that is immediately disseminated on the trading
terminal.
(ii) Price Risk Management: Hedging is the most common method of price risk management. It is strategy of
offering price risk that is inherent in spot market by taking an equal but opposite position in the futures
market. Futures markets are used as a mode by hedgers to protect their business from adverse price
change. Hedging benefits who are involved in trading of commodities like farmers, processors,
merchandisers, manufacturers, exporters, importers etc.
(iii) Improved product quality: The existence of warehouses for facilitating delivery with grading facilities along
with other related benefits provides a very strong reason to upgrade and enhance the quality of the
commodity to grade that is acceptable by the exchange. It ensures uniform standardization of commodity
trade, including the terms of quality standard: the quality certificates that are issued by the exchange-
certified warehouses have the potential to become the norm for physical trade.
(iv) Import- Export competitiveness: The exporters can hedge their price risk and improve their competitiveness
by making use of futures market. A majority of traders which are involved in physical trade internationally
intend to buy forwards. The purchases made from the physical market might expose them to the risk of
price risk resulting to losses. The existence of futures market would allow the exporters to hedge their
proposed purchase by temporarily substituting for actual purchase till the time is ripe to buy in physical
market. In the absence of futures market it will be meticulous, time consuming and costly physical
transactions.
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Answer:
Forward Markets Commission provides regulatory oversight in order to ensure financial integrity (i.e. to prevent
systematic risk of default by one major operator or group of operators), market integrity (i.e. to ensure that
futures prices are truly aligned with the prospective demand and supply conditions) and to protect and
promote interest of customers/ non-members. It prescribes the following regulatory measures:
(i) Limit on net open position as on the close of the trading hours. Sometimes limit is also imposed on intra-day
net open position. The limit is imposed operator-wise and in some cases, also member- wise.
(ii) Circuit-filters or limit on price fluctuations to allow cooling of market in the event of abrupt upswing or
downswing in prices.
(iii) Special margin deposit to be collected on outstanding purchases or sales when price moves up or down
sharply above or below the previous day closing price. By making further purchases/sales relatively costly,
the price rise or fall is sobered down. This measure is imposed only on the request of the exchange.
Answer:
A commodities exchange is an exchange where various commodities and derivatives products are traded.
Most commodity markets across the world trade in agricultural products and other raw materials (like wheat,
barley, sugar, maize, cotton, cocoa, coffee, milk products, pork bellies, oil, metals, etc.) and contracts based
on them. These contracts can include spot, forwards, futures and options on futures. Other sophisticated
products may include interest rates, environmental instruments, swaps, or ocean freight contracts.
Commodities exchanges usually trade futures contracts on commodities, such as trading contracts to receive
something, say corn, in a certain month. A farmer raising corn can sell a future contract on his corn, which will
not be harvested for several months, and guarantee the price he will be paid when he delivers; a breakfast
cereal producer buys the contract now and guarantees the price will not go up when it is delivered. This
protects the farmer from price drops and the buyer from price rises.
Speculators and investors also buy and sell the futures contracts in attempt to make a profit and provide
liquidity to the system. However, due to the financial leverage provided to traders by the exchange,
commodity futures traders face a substantial risk.
A commodity exchange provides the rules, procedures, and physical for commodity trading, oversees trading
practices, and gathers and disseminates marketplace information. Commodity exchange transactions take
place on the commodity exchange floor, in what is called a pit, and must be effected within certain time limits.
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6. Write short notes on Long Hedge and Short Hedge in Commodity Future Market.
Answer:
Hedging strategy with futures revolves around compensating anticipated losses in the spot market with the
equivalent gains in the futures market. This is done by taking a position on the futures market that is opposite to
the position in the spot market.
Long Hedge: A long hedge is one that requires taking a long position in the futures. It issued by those who are
short on the asset. For example, consider a petro chemical plant that needs to process 10,000 barrels of oil in
three month time. To hedge against the rising price the plant needs to go long on the futures contract of crude
oil. The spot price of crude oil is ` 1,950 per barrel, while futures contract expiring three months from now is selling
for ` 2,200 per barrel. By going long on the futures the petro chemical plant can lock-in the procurement at
`2,200 per barrel.
Short Hedge: A short hedge means a short position in futures. It is used by those who are long on the underlying
asset. In order to hedge the long position on asset one would require taking short position in the futures market.
For example, consider a sugar mill in Uttar Pradesh. It is expected to produce100MTof sugar in the month of
April. The current price today (the month of February) is ` 22 per kg. April futures contract in sugar due on 20th
April is trading at ` 25 per kg. The sugar mill apprehends that the price lesser than ` 25 per kg will prevail in April
due to excessive supply then. To execute the hedging strategy the sugar mill has to take the opposite position
in the futures market. The sugar mill is long on the asset in April. Therefore, it needs to sell the futures contract
today. The number of contracts that needs to be sold is dependent upon the exposure in the physical asset
and the value one needs to cover.
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Study Note – 8
Learning Objective: After studying this chapter, the students will be able to:
• Understand the concept of systematic risk, security market line,
etc.
• Calculate expected Rate of Return from securities, Standard
Deviation of returns, Systematic and unsystematic risk, re-
purchase price of share, etc.
• Recommend for investment from different alternatives and too
manage the portfolio for investors.
If the variance of the portfolio is 122, what is the coefficient of correlation between the stocks
approximately?
(a) 0.45
(b) −0.48
(c) 0.56
(d) 0.67
(ii) An investor owns a stock portfolio consisting of four stocks. He invested in stock 20% in stock A; 25% in
stock B; 30% in stock C and 25% in stock D. The betas of these four portfolios are :0.9; 1.3; 1.2 and 1.7
respectively. The beta of portfolio is-
(a) 1.12
(b) 1.29
(c) 1.45
(d) 1.76
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(iii) Security Market Line (SML) shows the relationship between return on the stock and
(iv) Historically, when the market return changed by 10%, the return on the stock of A Ltd. changed by
16%. If the variance of the market return is 257.81, what would be the systematic risk for A Ltd.?
(a) 320%
(b) 480%
(c) 660%
(d) 720%
(a) E(Rm) – Rf
(c) Rf - E(Rm)
(d) Rf
(vii) Securities A and B have a standard deviation of 10% and 15% respectively. The respective average
returns are 12% and 20%. Investor X has limited funds. Which is safer security for investment?
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(viii) Which of the following is on the horizontal axis of the Security Market Line?
(a) Beta
(ix) The beta of stock of A Ltd. is 2.00 and is currently in equilibrium. The required rate of return on the stock
is 12% and expected return on the stock is 10%. Suddenly, due to change in the economic conditions,
the expected return on the market increases to 12%. Other things remaining the same, what would be
new required rate of return on the stock?
(a) 15.0%
(b) 16.0%
(c) 20.0%
(d) 22.5%
(x) If you invest 60% of your money in B Ltd. and 40% in T Ltd.. Assume that the standard deviation of B Ltd.
is 80% and standard deviation of T Ltd. is 30%. The correlation coefficient between B Ltd. and T Ltd. is
0.2. What is the standard deviation of the portfolio?
(a) 41.33%
(b) 49.50%
(c) 51.75%
(d) 54.34%
Answer:
Question (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x)
Answer: (b) (b) (c) (c) (d) (b) (b) (a) (b) (c)
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2. (a) Calculate the expected rate of return for each security from the figures below.
Security A B C D E
β – values 1.3 1.6 1 1.5 0
Actual Return (Rp) 21 23.6 16 20 4.8
Investments (In ` Lacks.) 1.25 1.5 1.25 1.45 0.8
(b) Further if Mr. Anup Ahuja wants to form a portfolio with the above investible funds in respective
securities what would be his expected return on such asset-mix?
Security A B C
Beta coefficient 1.4 1.5 1.6
Standard Deviation of Market Return 0.5 0.5 0.5
Total Risk 0.6 0.8 0.85
For which of these securities the systematic component explains the largest share of total risk?
Answer:
(a) Since Value of Beta (β) for security C is 1, the market rate of return is equal to the return as reflected by
security C (i.e. 16%).
Similarly the risk free rate of return is equal to the return as provided by security E (i.e. 4.8%).
Therefore, Risk premium awarded by market is equal to (RM-RF), i.e. (16-4.8) % or, 11.2%.
Security A B C D E
Risk free Rate of Return (RF) 4.8% 4.8% 4.8% 4.8% 4.8%
Risk premium from Market (RM - RF) 11.2% 11.2% 11.2% 11.2% 11.2%
Effective Risk Premium [βi (RM - RF)] 14.56% 17.92% 11.2% 16.8% 0%
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In computation of the expected return from portfolio of the above securities weighted beta will be used as
a proxy to evaluate effective risk premium.
Securities A B C
Therefore, among all the securities the largest share of systematic risk explained out of total risk is been
followed in case of security A.
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3. Mr. Abinash has invested his fund in two securities of the same company, details of which has been laid in
the following section.
Compute:
(c) Minimum commitment of funds in securities to mitigate the exposure to risks at the given value of
correlation coefficient.
Answer:
Where, ‘i’ runs from 1 to ‘n’, ‘n’ is the number of securities in the portfolio.
Expected Return from portfolio [E (RP)] = {(0.4 × 14%) + (0.6 × 11%)} = 12.2%.
(b) Measure of Portfolio Risk (σP) = √ (wE2 × σE2) + (wP’2 × σP’2) + 2 × wE × wP’ × σE ×σP’ × r(E,P’)
Correlation Coefficient (r(E,P’)) = Cov. (E,P’)/ σE ×σP’ = 120 / (12 × 15) = 0.67
Portfolio Risk (σP) = √ {(0.4)2 × (12%) 2} + {(0.6)2 × (15%) 2} + {2 × (0.4 × 0.6) × (12 × 15 × 0.67)} = 12.73%.
(c) Minimum Investment required to mitigate risks in Equity (wE (Min.)) and in Preference Shares (wP’ (Min.))
Mr. Abinash is expected to invest his available funds in Equity Share @ 81.69% and in Preferential Share @
18.31% to make his portfolio bearing with minimum risk. At present his portfolio bears a combination of 40%
and 60% on equity and preferential share investments respectively, which is not the optimum one.
Therefore he is advised to try a different combination of securities.
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4. Return on asset mix of Sambhavana Limited and Bhavana Limited at different stages of economy with
respective chances of taking place is provided in the following.
(b) Volatility in expected return of the companies expressed in terms of Standard Deviation.
As an Investment Advisor in which of the above companies you would recommend to invest funds –
Establish a ground supporting your recommendation.
Answer:
(a) Expected Return on Investment [E (Ri)] = ∑pi × Ri , where, ‘i’ runs from ‘1’ to ‘n’.
Expected Return from Sambhavana Limited = {(20% × 0.1) + (15% × 0.5) + (10% × 0.3) + (5% × 0.1)} = 13%,
Expected Return from Bhavana Limited = {(26% × 0.1) + (18% × 0.5) + (8% × 0.3) + (0% × 0.1)} = 14%.
(b) Volatility in expected return of the companies (σ) = √ ∑pi × {Ri – E (Ri)} 2
Return and Risk from securities of Sambhavana Limited is denoted as RS’ and σS’ respectively.
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Return and Risk from securities of Bhavana Limited is denoted as RB’ and σB respectively.
(c) Co-movements can be studied between securities by computing the Covariance and the association can
be studied using correlation coefficient between securities.
Probability (pi) {Rs’ - E (Ri)} {RB - E (Ri)} pi × {Rs’ - E (Ri)} × {RB - E (Ri)}
0.1 7% 12% 8.4%
0.5 2% 4% 4%
0.3 -3% -6% 5.4%
0.1 -8% -14% 11.2%
Value of correlation coefficient [r (S’, B)] = Cov. (S’, B) / σS’ × σB = 29% / 4% × 7.27% = 0.9972
As both the risk and return is high in case of Bhavana Limited we need to use the Coefficient of Variation to
determine where to invest funds.
It basically replicates the return from securities for each degree of risk taken. Lower the proportion higher
the eligibility of a security to qualify for investment.
It is clear from the above measure that investment in Bhavana Limited is better than to invest in
Sambhavana Limited. It is thereby recommended to invest in securities of Bhavana Limited.
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Construct portfolios with the following weights and determine the expected return on each of such asset-
mix along with the degree of risk association with the respective returns, when value of correlation
coefficient between securities are exactly 1, -1, 0, and 0.5.
Answer:
Required Formulas:
Expected Return from a Portfolio [E (RP)] = ∑ wi × Ri
Expected Risk from a Portfolio (σP) = √ (wI2 × σI2) + (wJ2 × σJ2) + 2 × wI × wJ × σI ×σJ × r(I,J)
Where, -1 < r(I,J)< 1, and ‘I’ and ‘J’ are two securities.
And when r(I,J) = ± 1, then we use the following equations which are derived form of the above one.
▪ Expected Risk from a Portfolio (σP) = {(wI × σI) + (wJ × σJ)}, when, r = +1,
▪ Expected Risk from a Portfolio (σP) = {(wI × σI) - (wJ × σJ)}, when, r = -1.
Using the formulas stated above we find the following table as result of the required questions regarding
Expected Return from a Portfolio and Expected Risk from the same Portfolio at different combinations of
investible funds and at different degrees of associations between securities.
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(b) If the Portfolio Manager seeks to reduce the Beta to 0.8, how much risk-free investment should he bring
in? Verify the result.
Answer:
If `13,00,000 is 70.86%
13,00,000 × 100
Total Portfolio should be = = `18,34,600
70.86%
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7. An investor estimates return on shares in two different companies under four different scenarios as under:
Scenario Probability of its happening Return on Security A (%) Return on Security B (%)
I 0.2 12 10
II 0.4 16 20
III 0.3 18 25
IV 0.1 25 30
(i) Calculate Expected rate of return if the investor invests all his funds in Security A alone or in Security B
alone.
(iv) If the investor invests 40% in Security A and 60% in Security B, what is the expected return and the
associated risk.
Answer:
(i) and (iii) Expected Returns and Risks Associated of Securities A and B
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Scenario Probability Return Expected Return Deviation (D) Deviation square Variance
(P) (%) (%) = from mean (D2)
(1) (2) (3) (4)= (2)*(3) 5=(3)- Σ (4)] (6)=[(3)- Σ (4)]2 6=(2)*(5)
16.7 12.01
Scenario Probability Return (%) Expected Return Deviation (D) Deviation square Variance
(P) (%) = from mean (D2)
(1) (2) (3) (4)= (2)*(3) 5=(3)- Σ (4)] (5)=[(3)- Σ (4)]2 6=(2)*(5)
I 0.2 10 2.0 -10.5 110.25 22.05
II 0.4 20 8.0 -0.5 0.25 0.1
III 0.3 25 7.5 4.5 20.25 6.075
IV 0.1 30 3.0 9.5 90.25 9.025
20.5 37.25
(ii) Expected return of Security B is higher than the Security A. So the investor will prefer Security B in terms of
Return.
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19.65
= 19.65/(3.465*6.103)=0.9292
Risk of portfolio i.e. standard deviation of Portfolio A and B [40% and 60% Ratio]
(σ) A and B = (3.4652 × 0.402 ) + (6.1032 × 0.602 ) + 2 × 0.9292(3.465 × 0.40 × 6.103 × 0.60)
8. Two securities X and Y have standard deviations of 4% and 10%. An investor is having a surplus of `10 Lakh
for investment in these two securities. How much should he invest in each of these securities to minimize
risk, if the correlation coefficient for X and Y is — (a) -1; (b) -0.40; (c) 0
Answer:
Weight of Security X WX a
σY 2 − Cov XY
Proportion of Investment in Security X, WX =
σX 2 + σY 2 − 2Cov XY
CovXY = ρXY × σX × σY
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Equity shares of
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Answer:
Equity shares of
A 70 140 70 5 75
B 80 150 70 5 75
CAPM Model
E[RP] = RM+β(RM-RF)
(b) Simple average return of portfolio = 935.78 + 33.31 + 28.37 + 39.49)/4 = 34.24%
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10. An investor has two portfolios known to be on minimum variance set for a population of three securities A, B
and C below mentioned weights —
WA WB WC
(a) What would be the weight for each stock for a portfolio constructed by investing ` 6,00,000 in Portfolio
X and ` 4,00,000 in Portfolio Y?
(b) Suppose the investor invests ` 5,00,000 out of ` 10,00,000 in Security A. How he will allocate the balance
between security B and C to ensure that his portfolio is on minimum variance set?
Answer:
A 6,00,000 x 0.30 = 1,80,000 4,00,000 x 0.20 = 80,000 2,60,000 2,60,000 ÷ 10,00,000 = 0.26
B 6,00,000 x 0.40 = 2,40,000 4,00,000 x 0.50 = 2,00,000 4,40,000 4,40,000 ÷ 10,00,000 = 0.44
C 6,00,000 x 0.30 = 1,80,000 4,00,000 x 0.30 = 1,20,000 3,00,000 3,00,000 ÷ 10,00,000 = 0.30
WA + WB + WC =1
WB + WC = 0.50 ...(1)
A simple linear equation establishing an equation between two variables WA and WB or the Variables WB
and WC in the given manner—
WC = a + b WB
Substituting the values of WA&WB from the data given (Portfolio X and Y), we get -
0.30 = a + b x 0.40
0.30 = a + b x 0.50
b=0
a = 0.30
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WC = 0.30 - WB
or
WC + 0 WB = 0.30 ...(2)
A = ` 5,00000 (Given)
Alternatively,
Since the Proportion of Investment in C is 0.30 and is constant across both the Portfolio, any linear equation
drawnfrom the Data given would result in the Weight of C being a constant 0.30.
Therefore WA= 0.50 (Given), WC = 0.30 (Constant), therefore WB = 0.20 (WB= 1- 0.50 - 0.30 = 0.20).
11. The following information is available regarding three Mutual Fund schemes.
If the risk free return is 6%, return on market portfolio is 15% with a standard deviation of 4%, ascertain:
(a) Total gain and net gain under Fama’s Net Selectivity.
Answer:
Particulars X Y Z
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A. Actual Risk Premium (RP - RF) (24-6)= 18% (16-6)=10% (12-6)=6%
B. Desired Risk Premium [(RP - RF) × σP÷ σM] (9%×8÷4)=18% (9%×4÷4)=9% (9%×3÷4)=6.75%
C. Desired Risk Premium [(RP - RF × σP÷ σM] )×ρPM 5.4% 6.3% 3.375%
or Risk Premium in B × ρPM (18%×0.30) (9%×0.70) (6.75×0.50)
Notes:
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Study Note – 9
FINANCIAL RISKS
Learning Objective: After studying this chapter, the students will be able to:
• Understand risk, identify operational risk, liquidity risk,
Operational risk and Foreign Exchange Risk.
Answer:
Operational risk is the risk that is not inherent in financial, systematic or market-wide risk. It is the risk remaining
after determining financing and systematic risk, and includes risks resulting from breakdowns in internal
procedures, people and systems.
Operational risk losses include internal frauds (insider trading, misappropriation of assets)or external frauds like
theft, natural disasters like terrorism or system related failures like M&A related disruption and other
technological breakdowns. However, operational risk is harder to quantify and model than market and credit
risks.
Answer:
The potential loss amount due to market risk may be measured in a number of ways or conventions.
Traditionally, one convention is to use Value at Risk (VaR). The conventions of using VaR are well established
and accepted in the short-term risk management practice. However, it contains a number of limiting
assumptions that constrain its accuracy. The first assumption is that the composition of the portfolio measured
remains unchanged over the specified period. Over short time horizons, this limiting assumption is often
regarded as reasonable. However, over longer time horizons, many of the positions in the portfolio may have
been changed. The Value at Risk of the unchanged portfolio is no longer relevant.
• Market risk cannot be eliminated through diversification, though it can be hedged against.
• Financial risk, market risk, and even inflation risk, can at least partially be moderated by diversification.
• The returns from different assets are highly unlikely to be perfectly correlated and the correlation may
sometimes be negative. However, share prices are driven by many factors, such as the general health of
the economy which will increase the correlation and reduce the benefit of diversification.
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• If one constructs a portfolio by including a wide variety of equities, it will tend to exhibit the same risk and
return characteristics as the market as a whole, which many investors see as an attractive prospect.
• However, history shows that even over substantial periods of time there is a wide range of returns that an
index fund may experience; so an index fund by itself is not “fully diversified”. Greater diversification can be
obtained by diversifying across asset classes; for instance a portfolio of many bonds and many equities can
be constructed in order to further narrow the dispersion of possible portfolio outcomes.
Answer:
(i) Credit default risk: The risk of loss arising from a debtor being unlikely to pay its loan obligations in full or the
debtor is more than 90 days past due on any material credit obligation; default risk may impact all credit
sensitive transactions, including loans, securities and derivatives.
(ii) Counterparty risk: The risk of loss arising from non performance of counterparty in trading activities such as
buying and selling of commodities, securities, derivatives and foreign exchange transactions. If inability to
perform contractual obligations in such trading activities is communicated before the settlement date of
the transaction, then counterparty risk is in the form of pre-settlement risk, while if one of the counterparty
defaults on its obligations on the settlement date, the counterparty risk is in the form of settlement risk.
(iii) Concentration risk: The risk associated with any single exposure or group of exposures with the potential to
produce large enough losses to threaten a lender’s core operations. It may arise in the form of single
name concentration or industry concentration.
(iv) Country risk: The risk of loss arising from sovereign state freezing foreign currency payments
(transfer/conversion risk) or when it defaults on its obligations (sovereign risk).
Answer:
Market liquidity risk arises from situations in which a party interested in trading an asset cannot do it because
nobody in the market wants to trade for that asset. Liquidity risk becomes particularly important to parties who
are about to hold or currently hold an asset, since it affects their ability to trade. Manifestation of liquidity risk is
very different from a drop of price to zero. The important causes of liquidity risk are:
(i) In case of a drop of an asset’s price to zero, the market is saying that the asset is worthless. However, if one
party cannot find another party interested in trading the asset, this can potentially be only a problem of
the market participants with finding each other. This is why liquidity risk is usually found to be higher in
emerging markets or low-volume, less-structured markets.
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(ii) On the other hand, funding liquidity risk is a financial risk due to uncertain liquidity. An institution might lose
liquidity if its credit rating falls, it experiences sudden unexpected cash outflows, or some other event
causes counterparties to avoid trading with or lending to the institution. A firm is also exposed to liquidity risk
if markets on which it depends are subject to loss of liquidity.
Answer:
It is the risk that the changes in values of one or more assets that support an asset-backed security will
significantly impact the value of the supported security. This kind of risk especially arises in securitization
transactions where by cash flows due on assets/receivables are pooled together to issue securities, the
servicing of which is backed by the cash flows on such underlying assets. The factors that may cause changes
in values of assets backing the securities include interest rate, term modification, and prepayment risk.
Prepayment Risk: Prepayment is the event that a borrower prepays the loan prior to the scheduled repayment
date. Prepayment takes place when the borrowers can benefit from it, for example, when the borrowers can
refinance the loan at a lower interest rate from another lender. Prepayments result in loss of future interest
collections because the loan is paid back pre-maturely and can be harmful to the loan-backed securities,
especially for long term securities. A second, and maybe more important consequence of prepayments, is the
impudence of un-scheduled prepayment of principal that will be distributed among the securities according to
the priority of payments, reducing the outstanding principal amount, and thereby affecting their weighted
average life.
If an investor is concerned about a shortening of the term about contraction risk and the opposite would be the
extension risk, the risk that the weighted average life of the security is extended. In some circumstances, it will
be borrowers with good credit quality that prepay and the credit quality pool backing securities will deteriorate
as a result. Other circumstances will lead to the opposite situation.
Answer:
Foreign Investment Risk is associated with investment in foreign securities and assessing foreign investment risk
means looking closely at what is happening in the country of origin of security. The general economy of that
country will have some impact on the future business operations of the issuer. Foreign investment risk involves
considering the degree of political risk associated with the holding. The important causes are: Changes in
currency exchange rates, Dramatic changes in market value, Political, economic and social events, Lack of
liquidity and Less information.
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Study Note – 10
Learning Objective: After studying this chapter, the students will be able to:
• determine forward and future price, calculate margin, calculate
time value and intrinsic value of option and valuation of option
contracts.
(i) An investor bought 2,000 shares of X Ltd. for `90 per share. The initial margin is 50%. The maintenance
margin is 40%. If the stock price decreases to `70 per share. The additional funds put by the investors
to his margin account is –
(a) `20,000
(b) `20,500
(c) `21,000
(d) `22,000
(ii) What should be the price of call, if value of a put `5, strike price `100, rate of interest 6% p.a. , time
period -2 months?
(a) `4
(b) `5
(c) `6
(d) `7
(iii) An investor purchases a July Call Option of X Ltd. with a strike price of `100 for a premium of `7. Till
what level the investor will not realize his profit.
(a) ` 105
(b) `107
(c) `110
(d) `115
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(iv) In a put-call parity, the pay-offs of buying stock can be replicated by:
(a) Buying a call and buying a put option
(b) Buying a call and writing a put option
(c) Writing a call and buying a put option
(d) Writing a call and writing a put option
(v) A stock is currently sells at `350. The put option to sell the stock sells at `380 with a premium of `20. The
time value of option will be
(a) `10
(b) `10
(c) `20
(d) 0
(vi) The spot value of NIFTY is 6430. An investor bought a two month NIFTY for 6410 call option for a
premium of ` 24. The option is
(a) In-the Money
(b) At-the Money
(c) Out-of the Money
(d) Insufficient Data
(vii) Shares of C Ltd. is traded at `1,150. An investor is bullish about the market. He buys two one month call
option contracts (one contract is 100 shares) on C Ltd. with a strike price of `1,195 at a premium of `35
per share. Three months later, if the share is selling at `1240 what will be net profit/loss of the investor
on the position?
(a) `1000
(b) `1200
(c) `1500
(d) `2000
(viii) A stock index currently stands at 7000. The risk free interest rate is 8% p.a. continuously compounded
and the dividend yield on the index is 4% p.a. What should be the futures price for a four month
contract? [Given e(.08-.04)4/12 = 1.013423]
(a) 7093.96
(b) 7097.34
(c) 7098.68
(d) 7099.25
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(ix) A 6-month forward contract on a non-dividend paying stock when the stock price is ` 60 and the risk-
free interest rate (with continuous compounding) is 12% p.a. What is the forward price? [Given e0.06 =
1.0618]
(a) `61.86
(b) `62.23
(c) `64.23
(d) `65.27
(x) If you sell a call option on a share with a strike price of ` 375, market price of `360, and a premium of `
21.What is the maximum loss on expiry of this position?
(a) ` 354
(b) Unlimited
(c) ` 396
Answer:
Question (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x)
Answer: (a) (c) (b) (b) (d) (a) (d) (a) (a) (b)
2. On 31.8.2018, the value of stock index was ` 8,800. The risk free interest rate has been 8% p.a.. The dividend
yield on this stock index is as under:
The duration of the contract is four months and the interest is calculated continuously compounded daily.
You are required to calculate the future price of contract deliverable on 31.12.2018. (e0.01583 = 1.01593)
Answer:
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= `8,800 x e(0.08-0.0325)4/12
3. An investor has bought a futures contract on the stock of Maruti Udyog Ltd. at `410. Each contract consists
of 400 shares. The initial margin is set by the exchange at 5%, while the maintenance margin is 90% of the
initial margin. Clearing prices of the stock for next 10 days are given below:
Day 1 2 3 4 5 6 7 8 9 10
Price (`) 410 420 400 390 440 441 450 460 455 465
Assume that on the 10th day, the investor squares off his position at `465. Find out the gain and losses of
long and short positions of the investor. You are requested to show all necessary calculations.
Answer:
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4. A portfolio manager owns three stocks and its details are under:
The BSE-SENSEX is at 28000 and futures price is 28560. Use stock index futures to (i) decrease the portfolio
beta to 0.8 and (ii) increase the portfolio beta to 1.5. Assume the index factor is 100. Find out the number of
contacts to be bought or sold of stock index futures.
Answer:
Stock Market value of stock Proportion Beta of the stock Weighted beta
(` in Lakh)
X 1600 4/13 1.1 0.34
Y 2400 6/13 1.2 0.55
Z 1200 3/13 1.3 0.30
5200 1.19
Value per futures contract = Index price per contract × Lot size per futures contract
= `28000×100 = `28,00,000
(i) To reduce portfolio beta to 0.8, the manager should sell index futures contract.
• Value per futures contract = Index price per contract*Lot size per futures contract
= `28000*100 = `28,00,000
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(1.19 − 0.8)
No of Contracts = 5,200 Lakh × 28 Lakh = 72 contracts
(ii) To increase the portfolio beta to 1.5 the manager should buy index futures contract.
• Value per futures contract = Index price per contract × Lot size per futures contract
5. XYZ Ltd. shares are presently quoted at `100. The 3 Month Call Option carries a premium of `15 for an
Exercise Price of `120 and a 3 Month’s put option carries a premium of `20 for a strike price `120.
If the spot price on the expiry date is in the range of `90 to `160 with an interval of `5, calculate Net Pay-Off
for both call option and put option from the option buyer’s perspective and option writer’s perspective.
Answer:
Call Option
Spot Exercise Gross Premium Action Net Payoff Net Payoff
Price Price (`) Payoff (Long/Buyer) (Short/Seller)
90 120 0 15 Lapse (15) 15
95 120 0 15 Lapse (15) 15
100 120 0 15 Lapse (15) 15
105 120 0 15 Lapse (15) 15
110 120 0 15 Lapse (15) 15
115 120 0 15 Lapse (15) 15
120 120 0 15 Lapse (15) 15
125 120 5 15 Exercise (10) 10
130 120 10 15 Exercise (5) 5
135 120 15 15 Exercise 0 0
140 120 20 15 Exercise 5 (5)
145 120 25 15 Exercise 10 (10)
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150 120 30 15 Exercise 15 (15)
155 120 35 15 Exercise 20 (20)
160 120 40 15 Exercise 25 (25)
Put Option
Spot Exercise Gross Premium Action Net Payoff Net Payoff
Price Price (`) Payoff (Long/Buyer) (Short/Seller)
90 120 30 20 Exercise 10 (10)
95 120 25 20 Exercise 5 (5)
100 120 20 20 Exercise 0 0
105 120 15 20 Exercise (5) 5
110 120 10 20 Exercise (10) 10
115 120 5 20 Exercise (15) 15
120 120 0 20 Lapse (20) 20
125 120 (5) 20 Lapse (20) 20
130 120 (10) 20 Lapse (20) 20
135 120 (15) 20 Lapse (20) 20
140 120 (20) 20 Lapse (20) 20
145 120 (25) 20 Lapse (20) 20
150 120 (30) 20 Lapse (20) 20
155 120 (35) 20 Lapse (20) 20
160 120 (40) 20 Lapse (20) 20
Assuming it is possible to borrow money in the market for transactions in securities at 12% perannum,
you are required:
(i) to calculate the theoretical minimum price of a 6-months forward purchase; and
Answer:
The arbitrageur can borrow money @ 12 % for 6 months and buy the shares at `1,800.
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At the same time he can sell the shares in the futures market at `1,950. On the expiry date 6 months later, he
could deliver the share and collect `1,950 pay off `1,908 and record a profit of `42 (`1,950 – `1,908)
7. Consider a two year American call option with a strike price of `100 on a stock the currentprice of which is
also `100. Assume that there are two time periods of one year and in eachyear the stock price can move
up or down by equal percentage of 20%. The risk free interestrate is 6%. Using binominal option model,
calculate the probability of price moving up anddown. Also draw a two step binomial tree showing prices
and payoffs at each node.
Answer:
D (144)
B (120)
A (100) E(96)
C (80)
F(64)
P = Probability
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The two step Binominal tree showing price and pay off
B (120)
C (80)
The value of an American call option at nodes D, E and F will be equal to the value of European option at these
nodes and accordingly the call values at nodes D, E and F will be 44, 0 and 0 using the single period binomial
model the value of call option at node B is
C = e–rt [fup + fd (1–p) where fu payoff at D and fd payoff at E, with continuous compounding
At node B the payoff from early exercise will pay ` 20, which is less than the value calculated using the single
period binomial model. Hence at node B, early exercise is not preferable and the value of American option at
this node will be ` 13.49. If the value of an early exercise had been higher it would have been taken as the
value of option. The value of option at node ‘A’ is
8. From the following data for certain stock, find the value of a call option using Black-Scholes Model :
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Answer:
In (S / K) + (r + σ 2 / 2)t
d1 =
σ t
d2 = d1 − σ t
Where,
e = exponential term
In = natural logarithm
0.0646 + (0.2)0.5
=
0.40 × 0.7071
0.1646
=
0.2828
= 0.5820
N(d1) = N (0.5820)
N(d2) = N (0.2992)
Value of option
75
= 80 N(d1) − × N(d2)
1.062
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75
Price = 80 ×0.7197 − × 0.6176
1.062
= `(57.57 – 43.61)
= `13.96
9. Mr. B decides to purchase Two Infosys call options which have a delta of 0.75 each. He also plans to
simultaneously hedge by buying Four Infosys Put Options which has a positive delta of 0.375. What is the
net delta of each position? What is the net delta of overall position? Is he fully hedged?
Answer:
Delta of long calls and short puts are positive and that of short calls and long puts are negative. Deltas for call
options are always positive, which means that a long call should be hedged with a short call position in the
underlying asset and vice-versa. Deltas for put options are always negative which means that a long put should
be hedged with a long position in the underlying asset and vice-versa. Delta is between 0 and +1 for calls and
between 0 and -1 for puts.
Since net delta of the entire position is zero, Mr. B is perfectly hedged. This means that whatever losses he might
incur the call position/put position would be compensated exactly in the put/call position.
Explain how the two firms would enter into a swap transaction to reduce their interest costs, if Firm A does
not want to pay more than LIBOR+0.35%.
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Answer:
Swap Design:
Step 1: Find the interest differential in fixed market. Here it is 100 bps.
Step 4: Firm’s A objective is to go for floating payment but wants to pay LIBOR+0.35%. In other words, as against
the market cost of LIBOR+0.75%, it wants to pay LIBOR+0.35% implying a savings of 0.40%. Out of possible 0.75%
(quality spread), B would save 0.35% i.e. B’s cost would be 10.65%.
11. Company P Ltd. and Q Ltd. have been offered the following rate per annum on a `200 crore five year loan:
Company P Ltd. requires a floating rate loan and Q Ltd. requires a fixed rate loan.
You are required to design a swap arrangement that will net a bank acting as intermediary at 0.5% p.a.
and be equally attractive to both the companies. Also find out the effective interest rates.
Answer:
Particulars `
P Ltd. Is the stronger Company (due to comparative interest advantage). P has an advantage of 1.40% in
Fixed Rate and 0.50% in Floating Rate. Therefore, P Ltd. Enjoys a higher advantage in Fixed Rate loans.
Therefore, P Ltd. Will opt for Fixed Rate Loans with its Bankers. Correspondingly Q Ltd. Will opt for Floating
Rate Loans with its bankers.
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P Ltd. Q Ltd.
1. P Ltd. will borrow at fixed rate. 1. Q Ltd. will borrow at Floating rate.
2. Pay interest to bankers at fixed rate (i.e. 12%) 2. Pay interest to bankers at Floating rate
(MIBOR+0.6%)
3. Will collect from Company Q Ltd. interest amount 3. Will pay Company P Ltd. interest amount
differential i.e. Interest computed at fixed rate differential i.e. Interest computed at fixed rate
(12%) Less Interest Computed at Floating Rate of (12%) Less Interest Computed at Floating Rate of
(MIBOR+0.1%)=11.9%-MIBOR (MIBOR+0.1%)=11.9%-MIBOR
4. Receive share of gain from Company Q Ltd. 4. Pay to Company P Ltd. its share of gain (0.2%).
(0.2%).
5. Effective Interest Rate = 2-3 = 12%-(11.9%- MIBOR) 5. Pay Commission Charges to the bank for
-0.2% = MIBOR-0.1% arranging interest rate swap i.e. 0.5%.
6. Effective Interest Rate = (2+3+4+5)=MIBOR + 0.60
% + 11.9% - LIBOR + 0.5% + 0.2%=13.20%
12. X Ltd. and Y Ltd. both wish to raise USD 20 million loan for 5 years. X Ltd. has the choice of issuing fixed rate
debt at 7.50% of floating rate debt at LIBOR + 25 bps. On the other, Y Ltd. which has a lower credit rating,
can issue fixed rate debt of the same maturity at 8.45% or floating rate at LIBOR + 37 bps. X Ltd. prefers to
issue floating rate debt and Y Ltd. prefers fixed rate debt with a lower coupon. City bank is in the process of
arranging an interest rate swap between these two companies.
X Ltd. negotiates to pay the bank a floating rate of LIBOR while the bank agrees to pay X Ltd. a fixed rate of
7.60%.
Y Ltd. agrees to pay the bank a fixed rate of 7.75% while the bank pays Y Ltd. a floating rate of LIBOR flat.
Answer:
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This needs to shared between X Ltd. and Y Ltd. and City Bank
(ii) Savings
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Study Note – 11
(i) The price of a bond just before a year of maturity is $10,000. Its redemption value is $10500 at the end
of the that period. Interest is $700 p.a. The Dollar appreciates by 2% during the that period. The rate of
return would be----
(a) 12%
(b) 12.5%
(c) 13.25%
(d) 14%
(iii) In July, the one year interest rate is 4% on Swiss Francs and 13% on US dollars. If the current exchange
rate SFr 1=$0.63, what is the expected future exchange rate in one year?
(a) $ 0.5561
(b) $ 0.6845
(c) $ 0.8542
(d) $ 0.8283
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(iv) Between 2000 and 2015, the ¥/$ exchange rate moved from ¥226.63 to ¥93.96. During this same 15
year period, the consumer price index (CPI) in Japan rose from 91.0 to 119.2 and the US CPI rose from
82.4 to 152.4. If PPP held over this period, what would the ¥/$ exchange rate have been in 2015?
(a) ¥ 140.13
(b) ¥ 152.15
(c) ¥160.51
(d) ¥ 180.18
(v) The 90-day interest rate is 1.85% in USA and 1.35% in the UK and the current spot exchange rate is
$1.6/£. The 90-day forward rate is-
(a) $1.607893
(b) $ 1.901221
(c) $ 1.342132
(d) $ 1.652312
(vi) The current spot rate for the U.S. dollar is `66. The expected inflation rate is 6.5% in India and 3% in USA.
The expected rate of dollar a year hence is --
(a) `72.33
(b) `72.12
(c) `69.33
(d) `66.89
(vii) The following rates are prevailing: Euro/$:1.1916/1.1925 and $/£:1.42/1.47 what will be the cross rate?
(a) 1.6921/1.7530
(b) 1.7530/1.6921
(c) 1.6921/1.1925
(d) 1.7530/1.1916
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How many dollars should a firm sell to get ` 5 crore after 2 months?
(a) $105500
(b) $106500
(c) $107500
(d) $108500
Answer:
Answer:
The Foreign Exchange Market (Forex, FX, or currency market) is a form of exchange for the global
decentralized trading of international currencies. Financial centers around the world function as anchors of
trading between a wide range of buyers and sellers around the clock, with the exception of weekends. The
foreign exchange market determines the relative values of different currencies. The foreign exchange market
assists international trade and investment by enabling currency conversion. For example, it permits a business in
the United States to import goods from the European Union member states, especially Euro zone members, and
pay Euros, even though its income is in United States dollars. It also supports direct speculation in the value of
currencies, and the carry trade, speculation based on the interest rate differential between two currencies.
(iii) to furnish facilities for hedging foreign exchange risks - hedging function.
Answer:
(i) Interest Rate Differentials: Higher rate of interest for a investment in a particular currency can push up the
demand for that currency, which will increase the exchange rate in favour of that currency.
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(ii) Inflation Rate Differentials: Different countries’ have differing inflation rates, and as a result, purchasing
power of one currency will depreciate faster than currency of some other country. This contributes to
movement in exchange rate.
(iii) Government Policies: Government may impose restriction on currency transactions. Through RBI, the
Government, may also buy or sell currencies in huge quantity to adjust the prevailing exchange rates.
(iv) Market Expectations: Expectations on changes in Government, changes in taxation policies, foreign trade,
inflation, etc. contributes to demand for foreign currencies, thereby affecting the exchange rates.
(v) Investment Opportunities: Increase in investment opportunities in one country leads to influx of foreign
currency funds to that country. Such huge inflow will amount to huge supply of that currency, thereby
bringing down the exchange rate.
(vi) Speculations: Speculators and Treasury Managers influence movement in exchange rates by buying and
selling foreign currencies with expectations of gains by exploiting market inefficiencies. The quantum of
their operations affects the exchange rates.
Answer:
(a) Issue Intermediaries: ADRs are issued by Overseas Depository Bank (ODB), who has a Domestic Custodian
Bank (DCB) in India.
(b) Deposit of Securities: Company willing to raise equity through ADRs should deposit the securities with the
DCB in India.
(c) Authorization for Issue of ADRs: The Indian Company authorizes the ODB to issue ADR against the security of
Company’s Equity Shares.
(d) Issue of ADR: ODB issues ADRs to investors at a predetermined ratio to the Company’s securities.
(e) Redemption of ADR: When an investor redeems his ADRs, the appropriate number of underlying equity
shares or bonds is released.
(f) Dividend / Interest: The Indian Company pays interest to the ODB, which in turn distributes dividends to the
ADR holders based on the prevailing exchange rate.
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Answer:
(a) Any entity incorporated in a jurisdiction that requires filing of constitutional and/or other documents with a
registrar of companies or comparable regulatory agency or body under the applicable companies
legislation in that jurisdiction;
(b) Any entity that is regulated, authorized or supervised by a central bank, such as the Bank of England, the
Federal Reserve, the Hong Kong Monetary Authority, the Monetary Authority of Singapore or any other
similar body provided that the entity must not only be authorized but also be regulated by the aforesaid
regulatory bodies;
(c) Any entity that is regulated, authorized or supervised by securities or futures commission, such as the
Financial Services Authority (UK), the Securities and Exchange Commission, the Commodities Futures
Trading Commission, the Securities and Futures Commission (Hong Kong or Taiwan), Australia Securities and
Investments Commission (Australia) or other securities or futures authority or commission in any country,
state or territory;
(d) Any entity that is a member of securities or futures exchanges such as the New York Stock Exchange
(Subaccount),London Stock Exchange (UK), Tokyo Stock Exchange (Japan), NASD (Sub-account) or other
similar self-regulatory securities or futures authority or commission within any country, state or territory
provided that the aforesaid organizations which are in the nature of self-regulatory organizations are
ultimately accountable to the respective securities / financial market regulators.
(e) Any individual or entity (such as fund, trust, collective investment scheme, Investment Company or limited
partnership) whose investment advisory function is managed by an entity satisfying the criteria of (a), (b),
(c)or (d) above.
Answer:
The decision to invest abroad takes a concrete shape when a future project is evaluated in order to ascertain
whether the implementation of the project is going to add to the value of the investing company. The
evaluation of the long term investment project is known as capital budgeting. The technique of capital
budgeting is almost similar between a domestic company and an international company. However, the one
has to address the following issues related to International Capital Budgeting:
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Answer:
(i) Commercial companies: An important part of this market comes from the financial activities of companies
seeking foreign exchange to pay for goods or services.
(ii) Central banks: National central banks play an important role in the foreign exchange markets. They try to
control the money supply, inflation, and/or interest rates and often have official or unofficial target rates
for their currencies.
(iii) Hedge funds as speculators: About 70% to 90%of the foreign exchange transactions are speculative. In
other words, the person or institution that buys or sells the currency has no plan to actually take delivery of
the currency in the end; rather, they are solely speculating on the movement of that particular currency.
They control billions of dollars of equity and may borrow billions more, and thus may overwhelm
intervention by central banks to support almost any currency, if the economic fundamentals are in the
hedge funds’ favor.
(iv) Investment management firms: Investment management firms (who typically manage large accounts on
behalf of customers such as pension funds and endowments) use the foreign exchange market to
facilitate transactions in foreign securities.
(v) Retail foreign exchange traders: Individual Retail speculative traders constitute a growing segment of this
market with the advent of retail foreign exchange platforms, both in size and importance. Currently, they
participate indirectly through brokers or banks. There are two main types of retail FX brokers offering the
opportunity for speculative currency trading: brokers and dealers or market makers.
(vi) Non-bank Foreign Exchange Companies: Non-bank foreign exchange companies offer currency
exchange and international payments to private individuals and companies. These are also known as
foreign exchange brokers but are distinct in that they do not offer speculative trading but rather currency
exchange with payments (i.e., there is usually a physical delivery of currency to a bank account).
(vii) Money transfer/remittance companies and bureau de change: Money transfer companies/remittance
companies perform high-volume low-value transfers generally by economic migrants back to their home
country. The four largest markets receiving foreign remittances are India, China, Mexico and the
Philippines. The largest and best known provider is Western Union with 345,000 agents globally followed by
UAE Exchange.
$/£ 1.3690/1.3728
S.Fr/DEM 1.0050/1.0098
$/S.Fr 0.8810 / 0.8823
And if DEM / £ in the market are 1.5580 /1.5596
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If so, show how $20,000 available with you can be used to generate risk - less profit.
Answer:
= 1.55902
= 1.55048
Since both the rates are apart there exist an arbitrage opportunity.
Gain of US $ 97.04
US $ (20097.04- 20,000)
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US $ (20097.04- 20,000)
9. S Ltd. an Indian based company has subsidiaries in US and UK whose forecast surplus fund for the next 30
days (June 2018) are given below:
$/` £/`
$ 1.6%/1.5%
£ 4.0%/3.8%
The Indian operation is forecasting a cash deficit of `400 million. It is assumed that interest rates based on
over a year of 360 days.
Required:
(i) Calculate the cash balance in Rupees at the end of 30 days period (at the end of June 2018) for each
company under each of the following scenarios ignoring transaction costs and taxes:
(a) Each company invests/finance its own cash balance/deficits in local currency independently.
(b) Cash balances are pooled immediately in India and the net balances are invested/borrowed for
the 30 days period.
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(ii) Which method do you think preferable from the parent company’s (S Ltd.) point of view?
Answer:
(a) Computation of Cash Balances at the end of 30 days of S Ltd. (At the end of June 2018)
(Figures in million)
= ` (402.80)+490.408+491.267
= ` 488.875 million
(Figure in million)
Particulars `
India (400.00)
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From S Ltd.’s point of view ‘immediate cash pooling to India’ is preferable as it maximizes the total cash
balance of the company after 30 days comparing to acting independently.
10. On 19th April 2018 the following are the spot rates:
(i) A trader sells an at-the-money spot straddle expiring at three months (July 19). Calculate gain or loss if
three months later the spot rate is EURO/USD 1.2900.
(ii) Which strategy gives a profit to the dealer if five months later (Sep. 19) expected spot rate is USD/INR 45.00.
Also calculate profit for a transaction USD 1.5 million.
Answer:
(i) Straddle is a portfolio of a Call and a Put option with identical Strike price. A trader sells Straddle of at the
Money Straddle by selling a call option and put option with strike price of USD per EURO.
At the expiry of three months spot rate is 1.2900 i.e. higher than Strike Price. Hence, buyers of the call option
will exercise the option, but buyer of Put option will allow the option to lapse.
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11. X Ltd. an Indian company has a payable of US$ 1,00,000 due in 3 months. The company is considering to
cover the payable through the following alternatives:
(iii) Option
Exchange rate:
Spot `/$45.50/45.55
US 4.5/5.0 (Deposit/Borrow)
Call option on $ with a strike price of `46is available at a premium of ` 0.10/$. Put option on $ with a strike
price of `46.00 is available with a premium of `0.05/$.
Treasury department of the company forecasted the future spot rate after 3 months to be:
` 45.60/$ 0.10
`46.00/$ 0.60
`46.40/$ 0.30
Answer:
Spot: 45.50/45.55
US 4.5/5.0
India 10.0/11.0
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The firm should borrow `and convert it into $ at the spot rate. Then the $ proceeds for 3 –m to be invested
and the payable will be settled at maturity out of the $ investment.
1,00,000
$ to be invested to get $ 1,00,000 3-m hence is: 0.045 = $98,887.52
1+
4
To get $ 98,887.52 the amount of ` required is = (98,887.52×45.55) = `45,04,326.54. So, the firm has to borrow
a sum of `45,04,326.54.
0.11
Hence, rupee repayment after 3-m is = ` 45,04,326.54 × 1 + = ` 46,28,195.52
4
Since the firm has a $ liability, it should go long on call $ option. That means the firm will buy $ call option
with a strike price of`46.00 at a premium of`0.10/$.
The firm can also go short on the put option, that is sell $ put option with a strike price of `46.00 at a
premium of ` 0.05/$.
Suggestion: ‘Forward Hedge’ is suggested for X Ltd. to cover the payable since the rupee outflow is less than
the outflow under money market hedge and also less than the expected outflow under option covers.
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12. X Ltd., an Indian Exporter has an ongoing order from USA for 2000 pieces per month at a price of $100 per
piece. To execute the order, the exporter has to import Yen 6000 worth of material per piece. Labour costs
are `350 per piece while other variable overheads add upto ` 700 per piece. The exchange rates are
currently `35/$ and Yen 120/$. Assuming that the order will be executed after 3 months and payment is
obtained immediately on shipment of goods, calculate the loss/gain due to transaction exposure if the
exchange rates change to `36/$ and Yen 110/$.
Answer:
Less: Costs
Profit = `14,00,000
Less: Costs
Profit = `1281,818
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