Ugbs 202 Pasco (Lawrence Edinam)
Ugbs 202 Pasco (Lawrence Edinam)
Ugbs 202 Pasco (Lawrence Edinam)
INSTRUCTIONS: Answer ALL questions in both sections (A and B). All questions must be
answered on this question paper. Carefully plan your answers to fit in the spaces provided.
SECTION A (25 marks): This section contains 10 mUltiple choice questions. Show your work
in the space provided under each question and select the correct answer. Each question carries
2.5 marks
Compute the current weighted quantity index of year 2. Taking year 1 to be the base period.
a. 135.10/0 b.130.10/0 c.115.40/0 d.lll.l% e. 117.10/0
8. Awuah has considered investing in the stock market. He has the following three stocks in mind:
stock A, B, and C. He understands that the economy could depress, recess, be normal or could
Boom. He also estimates a likelihood of each scenario been identical. The possible return on
each stock is given below.
State of the
Economy A B C
Recession 10% 20% 5%
Normal 30% -12% 5%
Boom 50% 9% 13%
Depression -20% 5% -5%
Calculate the variance of stocks A
Answer questions 9 & 10 with the infOlmation on three airline services shown in the table below.
Assume a rate of return of 10 percent for all instances.
Delux (In GHC) Regular (In GHC) EconOlny (In GHC)
Useful1ife 10 10 00
Question 1
A library prints past questions from a private printing press for GHC20 for the first 350 copies and
resells to students on campus. The library offers a marginal price reduction of 0.001 times the
number of additional copies above 350. For eXaInple, the cost of ordering 600 copies is 20*350 +
250* 19.75 = 11,937.5. Orders cannot be less than 350 nor more than 4000. The library takes orders
in batches per week and will want to make sure all copies are delivered to the clients before it
receives a new order. with the press. As a result, the selling price is a function of the number of
copies ordered and is set at p = 40 - 0.002x, where x is the nunlber of copies ordered p~r batch.
c. What is the profit if the library attempts taking an order of 450? (2 marks)
Question 2.
In line with the repercussion of the recent global pandemic, the formal sector is set to recover
'Impressively', with a chance of 0.350, 'Good' withprob.abilityofO.255 or 'Not good'. According
to data from the banking sector quarterly bulletin, each cedi invested in any Savings portfolio is
estimated to yield a return <of 25%, 180/0 or -30/0, whereas each cedi corn.rni,tted to any long-term
Investment portfolio will yield a return of 260/0, 18% or -50/0 according to the predicted
expectat ions of recovery respectively.
I-:J
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The infonnal sector is also expected to recover 'Impressively', with a chance of 0.45, 'Good' or
'Not good' with like chances. The report suggests that every cedi invested in any Savings portfolio
here will yield a return of220/0, 170/0 or 90/0 respectively, while each cedi invested in any long-telm
Investment will yield a return of 190/0, 15% or 80/0 respectively if the expected recovery plays out
as impressive, good, or not good.
An investor has $15,000 and $35,000 respectively to commit to Savings and Investments,
assuming the current rate is Ghc4= $1.
a. Which sector should be selected for long-telm Investments based on the expected return in
GHS? (10 marks)
b. Which sector should be selected (in GHS) for Savings based on the total expected return, if
administrative charges of $5 and $4 were included in the fOlmal and infOlmal sectors respectively?
(10 marks)
c. Which sector has the larger standard deviation from the expected return? Considering the
.respective administrative charges. (10 marks)
d. Which of the sectors carries more risk for long tenn Investments? Disregard the administrative
charges (10 marks)
e. Briefly explain the coefficient of variation and its relevance to investment decisions. (5
marks)
Question 3
The local government office of the AKWETEYMAN wishes to assess the viability of two
district recreational projects promised by the local assembly. The following cash flows frOlTI the
projects are shown below.
PROJECT A PROJECT B
Sunk cost GHC 150,000 GHC 140,000
Yearly return GHC 26,000 . GHC 23,000
Life span (years) 8 9
a. Calculate the payback period for both projects assuming at i = 0% (2 marks)
,~
b. Calculate the payback period for both projects at 10% interest rate. (Smarks)
c. What is the estimated Annual worth of recreational project A. Refer to (b) for rate of i (3
marks)
. L~
Chain Rule: dy = dy * du Laspeyres Prmce Index:
q.p.
~1 Ot m Quantity Index: L~-l Poi qni
dx du dx Li=1 qoiPni Li=1 Poiqni
.
Paasche: Pnce Index:
L~
~;]
q .p .
m m Future value: pel + on
Li=1 qniPoi
.
AnnuIty: p= iA [(1+i)n- 1 ]
Ci+On F= ~ [(1
I
+ on - 1] Perpetuity: P = ~I
n
EeX) = L
i=l
PiX i = P1X 1 + P2 X 2 + P3 X 3 + ... + PnXn
Coefficient of Variation: SD
M
Variance:2:f=l Pi ex - xa 2
n
O·=-y-
Index Number: ............ .... .. .. ........ .
'·,' Signature ..... . ....... .. ... .... . .
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UNIVERSITY OF GHANA
INSTRUCTIONS: Answer ALL questions in both section A and section B. All questions must be
answered on the question sheet. Carefully plan your answers to fit the spaces provided No
credit will be given for an answer with no work shown.
Section A (25 marks): this section contains 10 questions. Show your workings in the space
provided and circle the correct answer. Each question carries 2.5 marks.
1. Suppose a demand function is given by the relation P(q) = 500 - 3q, where q is the quantity
and p is the price. Which of the following is true about the function?
i. Price is inversely related to quantity
ii. As demand increases price decreases
iii. Price and quantity are equal for any integer
iv. The function that relates quantity and price is a linear function
v. The domain of the function is restricted to positive real numbers
3. \Vhich of the following are true about Net Present Value (NPV) and Internal Rate of Return (
(IRR) techniques?
i. Both the NPV and the IRR are investment appraisal tools
ii. NPV can be used to appraise two mutually exclusive projects regardless of any differences in
their lifespan.
iii. One should be careful when using IRR since it can lead to incoLTect investment decision
especially when the cash f10w is non-conventional (i.e. cash f10w consi st of both positive and
non-positive values)
iv. When IRR is greater than NPV, it means the investment is profitable.
v. NPV and IRR both rely on time value of money.
A. i, and v only B. i, ii, and iii only C . i, iii, iv, and v D. i, iii, v E. i, ii, and v only
5. Alexander has found the house of his dream. He has GHC 50,000 to use as a down payment
and has considered bOLTowing GHC 250,000 from his banle The current mortgage interest rate is
6 percel t per year compounded annually. If he is to make equal monthly payments for fifteen
years, how much will his monthly mortgage payment be?
) 6. A wuah is thinking about investing in the stock market. He has the following three stocks in
mind: stock A, B, and C. He understands that the economy could be in a state of Recession,
Normal, Boom, or in Depression. He also estimates a likelihood of each scenario been identical.
The possible return on each stock is given below;
State of the
Economy A B C
Recession 10% 20% 5%
Normal 30% -12% 5%
Boom 50% 9% 13%
Depression -20% 5% -5%
7. Use the Simpson rule to evaluate the following integral: IZ3 x ;2+1 dx, assume n = 4
I Index Number: .. .... .... ..... .......... ... . /-- Signature ............ .... ....... .
I The table below has information on the cash flow of a proj ect under financial appraisal. Use this (
I to answer question 8 and 9.
9. What is the net present value of the project at an interest rate of 10 percent per year?
10. The table below has data on wages paid to four groups of workers and the number of workers
in each group . Compute the current weighted wage index of year 3 using year 1 as the base year.
i. Calculate the maximum rate of return for the project (IRR). (4 marks)
ii. If the Minimum Acceptable Rate of return for Guinness Ghana is 5%, based on the calculated
IRR in (i) above, would you recommend Guinness Ghana to invest in the project? Provide
reason for your answer. (2 marks)
b. A Company is interested in buying a new genenl-purpose machine to aid its production levels (
and in the end result in higher profits. In the market for general-purpose machines, there are
two alternatives available - Machine A and Machine B \vith cash flows given as fo1 ows:
The cost of machine A is GH¢8S,000 and that for machine B GH¢ 103,000. Both machines
have a salvage value of zero at the end of their respective economic life (S years for machine A
and 4 years for machine B). Cash inflow from machine A is as follo ws; GH¢19000,
GH¢22S00, GH¢31000, GH¢40S00 and GH¢46000 for year 1,2,3,4 and S, respectively. Cash
inflow from machine B is GH¢31 000 in year 1, GH¢50,SOO in year 2, GH¢50,5 00 in year 3
and GH¢35,OOO in year 4. Machine A will require servicing in year 2 and 3, which will cost the
company GH¢ 6500 per each of the service years. Machine B will require servicing in year 2
and 3, which will cost the company GH¢ 7000 per year for each ofthe servicing years.
i. Draw a cash flow diagram for each of the machine (note the cash flows are the cost and
revenue of the COmpfu'1Y). (4 marks)
ii. Based on the NPV criteria and interest rate of 15%, recommend which machine should the
company invest in. (6 marl{s)
)", iii. What is the annual worth of each machine based on the annual worth criteria and an interest
rate of l5%? Which machine will you recommend based on this criterion? (4 marks)
iv. Which of the two (NPV or Annual worth) approaches is appropriate for evaluating the two
machine presented above? (1 mark)
c.
i. What is the difference between a sinking fund and amortization? (3 marks)
- ii:-A debt of GH¢600 is to be repaid by two equal yearly payments with interest at the rate of 5%
per year compounded annually. Complete the following amortization schedule for this debt.
(6 marks)
Period Principal at beginning of period Interest paid Annual payment Principal Repaid
1
Total
Question 2. (
a. The value of a house at the time of its completion was GH¢ 500,000. If the rate of change of
the value of the house can be modeled by ~~ = lOe o.oSt , where t is the time in years since the
house was built, and V is the value of the house (in thousands of Ghana cedis) :
Page 8 of 13 Examiners : Dr. A. Afful-D adzie, Dr. A. Karimu, and Mr. D. Agozie
Index Number: ................ ............ . Signature ....................... .
) b. Ghana Bakery Company has observed that, due to how it is charged for electricity
consumption by ECG, the profit for the first 10,000 units of lkg brown bread that it bakes in a
day is GH¢ 2 per unit. The profit on each of the units beyond 10,000 is decreased by GH¢ 0.0001
times the number of additional units of bread baked in a day. For example, the total profit when
15,000 units of the lkg brown bread are baked is 15,000(2)+5000(1.5).
i. What level of output will maximize the company's daily profit? (10 marks)
iii ..Suppose the profit maximizing output for the day has already been ordered in advance. If a
large grocery store which happens to be an important customer ask for extra 5000 loafs of the
1kg bread in addition to its daily order, how much would the company loose it agrees to honour
the extra demand? (2 marks)
Q3. Avroah Limited, is a small scale supplier of medical items. A recent call for tender
I
: 2dvertised by the Ministry of Health (MOH) in the Ghanaian daily graphic, call for the supply of
Medical supplies 1 (MS 1) and Medical supplies 2 (MS2). Awuah is determined to tender for the
I
: contract but is considering whether to tender for only MS 1, only MS2, or both.
I To submit a tender, Awuah would have to carry out a comprehensive analysis at a cost. These
I costs are estimated to be GH¢50,000 if he tenders for only MSl, GH¢24,000 if he tenders for
I only MS2, and GH¢55,000 ifhe tenders for both MSI and MS2.
I Since there will be competitors, Awuah is torn between submitting a higher, medium, or lower
: tender. Information on these possible levels oftender, their tender sum (i.e payoff) together with
I their chances of winning are summarized in the table below.
Tend er Option Leve l of tender Tender sum (GH¢) Chances of winning (%)
MS 1 Only High 130,000 40
Low 115,000 85
MS 2 Only High 80,000 70
Medium 75,000 80
Low 70,000 95
MSI and MS2 High 190,000 55
Low 140,000 70
In addition, if a tender is successful, there will be a component supply cost of GH¢ 18,000 if the
tender was for only MS 1, GH¢ 16,000 for only MS2, and GH¢24,OOO for both MS 1 and MS2.
a. Draw a decision tree diagram to represent the following problem.
I Index Number: ......... .... ... ...... ... ... . Signature .......... .. ....... .... .
I d. An insider has contacted Awuah with an offer, that, in return fo r GH¢20,OOO in cash she will
ensure that if he tenders GH¢80,OOO for contract ~v1 S2 only, his tender is guaranteed to be
successful. Should A wuah accept her offer or not and VI"hy?
Geometric gradient
PT =A [1 - ~i-=H) n] ;
l- 9
when 9 "* i
PT = A [1 : J; when 9 =i
Where; 9 = growth rate (rate of increase)
i = interest rate
Perpetuity/Capitalized cost
A
P=-
i
Expectation