Level 3 ABC 2021

U Win Bo Myint Advance Business Calculation LCCI-Level 3
Chapter – 1
Interest
Question – 1 (2-2000)
A bank customer deposits £4,310 at 5.5% per annum compound interest payable annually.
(a) Giving your answer to the nearest penny, state how much will be in the account:
(i) After 3 years
(ii) After 3 years and 3 months
(iii) After 3 years and 90 days
A bank successfully tenders £49,200 for a £50,000 Treasury Bill that runs for three months and is to be
redeemed at par.
(b) Calculate the rate of simple interest paid on the Treasury Bill.
Question – 2 (4-2002)
In 1996 a house was worth £88,000. Over the next 5 years it increased in value at a constant rate of 4% per
annum.
(a) Calculate the value of the house after 5 years.
(b) Giving your answer correct to the nearest pound, calculate the value of the house after 4 ½ years.
The value of a second house increased at the same constant rate over the same 5 years period. At the end
of the 5 years its value was £165,000.
(c) Giving your answer correct to the nearest thousand pounds, calculate the value of the house at the start
of the period.
Question – 3 (4-2003)
(a) A bank successfully tenders £487,000 for a Treasury bill that runs for six months and is to be redeemed
at par. Their investment gives a return of 5.3% per annum simple interest.
Calculate the value of the Treasury bill at redemption, giving your answer to the nearest £100.
(b) Jean deposits a sum of money for three years at a fixed rate of compound interest. After two years the
amount in the account is £171,396, and after three years the amount in the account is £177,394.86.
Calculate:
(i) The rate of compound interest
(ii) The original sum deposited
(iii) The interest on the account after the first year
Question – 4 (4-2008)
Rajesh deposits £15,000 in a bank account at 4% per annum simple interest.
(a) How much interest will Rajesh have earned after 3 years and 56 days?
Rajesh deposits a further £15,000 in another account at 4% per annum compound interest, for the same
period. Interest is added annually and at the end of the period, and is calculated as compound interest
throughout.
(b) How much more interest will Rajesh have earned from this account than from the simple interest
account?
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Question – 5 (3-2001)
(a) An investment account of $25,000 attracts 4.85% compound interest per annum, compounded six –
monthly.
(i) How much will be in the account after 5 years?
(ii) How much of this is interest?
A bank successfully tenders $96,500 for a $100,000 Treasury bill that has six months to run and is to be
redeemed at par.
(b) Calculate the rate of simple interest paid on the Treasury bill.
Question – 6 (2-2013)
Ellie uses the products method to check the interest on her savings account. She calculates that she is
receiving interest at the rate of approximately 0.015% per day.
Calculate:
(a) The annual rate of simple interest paid to Elli
(b) The interest earned on a balance of £12,000:
(i) For two days
(ii) For two years.
From 1 January 2003 to 31 December 2012, the value of Ellie’s house increased from £200,000 to
£320,000.
(c) Calculate the rate of increase per annum based on simple interest.
Ellie believes that the increase is approximately 4.8% per annum based on compound interest.
(d) Provide a calculation to show if Ellie is correct.
(e) State whether the true rate of compound interest is more than or less than 4.8% per annum.
Question – 7 (3-2013)
The rate of interest on an account is 3.5% per annum.
(a) Based on dividing the amount of interest equally between the first and second halves of the year, state
the rate of interest for a 6- month period (simple interest method).
(b) Based on the same proportional increase in the amount over the first and second halves of the year,
calculate the rate of interest for a 6- month period (compound interest method).
(c) Calculate the interest on £5,000 for a 6-month period using the rate calculated in (b).
Yoshi saves money as follows. At the start of the year, he deposits £10,000.
At the end of each year, the account earns 4% interest on the amount in the account at that time, and this is
added to the account.
(d) Calculate the amount of interest added at the end of the first year.
At the start of each year after the first, Yoshi deposits an additional amount equal to 5% of the amount in the
account during the previous year.
(e) Calculate:
(i) The amount in the account after Yoshi’s deposit at start of the second year
(ii) The amount in the account after Yoshi’s deposit at the start of the fourth year
(iii) The equivalent annual rate of compound interest that would increase £10,000 to the amount in (e)
(ii) by the start of the fourth year.
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Question – 8 (4-2013)
A bank successfully tenders £1,976,000 for a £2,000,000 Treasury bill that runs for three months and is to
be redeemed at par.
(a) Calculate the rate of simple interest per annum received on the investment in the Treasury bill.
The bank tenders £4,650,000 for a £5,000,000 Treasury bill that runs for two years and is due to be
redeemed at par.
(b) Calculate:
(i) The overall percentage interest received on the two-year investment in the Treasury bill
(ii) The rate of compound interest per annum that this represents.
The bank buys a €2,500,000 Treasury bill for €2,250,000. One year later, following a bail out agreement, the
bank redeems the bill for €1,800,000.
(c) Express the loss as a percentage of the investment.
Question – 9 (2-2014)
During a period of economic contraction, two investors are affected as follows.
(a) The value of the house belonging to investor A falls at a rate of 10% per annumfor 2 years. In each year
the percentage is calculated on the value at the start of the year.
If the value of the house is £240,000 at the start of the period, calculate the value of the house after 2
years.
(b) Investor A is interested to know the effect on a £240,000 house of a reduction in value of 10% each
year for 20 years.
Using the compound interest formula, calculate the value of the house after 20 years.
(c) The value of a unit trust purchased by investor B falls from £32 per unit to £26 per unit in 1½ years.
(i) Calculate the reduction in value as a percentage per annum based on simple interest
(ii) Calculate the reduction in value as a percentage per annum based on compound interest
Question – 10 (3-2014)
(a) A bank successfully tenders £240,000 for a £250,000 Treasury bill that runs for six months and is to be
redeemed at par.
Give your answers to two-figure accuracy, for example 4.7%.
(i) Basing your calculation on simple interest:
Calculate the annual rate of interest paid on the Treasury bill.
(ii) Basing your calculation on compound interest:
Calculate the annual rate of interest paid on the Treasury bill. Use the compound interest formula.
(iii) Compare your answers to (a)(i) and (a)(ii).
(b) Carl uses the products method to check his bank balance.
He calculates that he is receiving interest at the rate of approximately 0.00685% per day.
Take a year as being 365 days.
Basing your calculation on simple interest, calculate:
(i) the annual rate of interest
(ii) the interest due for a period of seven days when his balance was £999.99 in credit
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Question – 11 (4-2014)
Customer A deposited £12,000 in Bank B. Interest was added to the principal at the end of each year and
then also earned interest (i.e. compound interest). For the first three years only, the rate of compound
interest on the account was 2.5% per annum.
(a) Calculate the:
(i) interest added to the account at the end of year 1
(ii) amount in the account at the end of year 3 after adding interest
(iii) interest added to the account at the end of year 3
At the end of year 4, after adding interest, the amount in the account was £13,310.37
At the end of year 5, the interest added to the account was £399.31
(b) Calculate the rate of interest earned in year 5.
The rate of compound interest earned in years 6 and 7 was the same in each year.
At the end of year 7, after adding interest, the amount in the account was £14,263.55
(c) Calculate the rate of compound interest per annum earned in years 6 and 7.
Question – 12 (3-2000)
Miss Clarke has a bank account on which simple interest is earned at 3 ¼% per annum on credit balances.
Simple interest is charged by the bank at 11% per annum on debit balances.
Interest is calculated daily on all balances and paid/earned at the end of the month.
The account for August is shown below:
Date Details Debit Credit Balance
$ $ $
1 Aug Balance b/f 1,403.64 Cr
2 Aug Cheque 350.00 1,053.64 Cr
19 Aug Cheque 1,195.00 141.36 Dr
29 Aug Deposit 2,130.83 1,981.47 Cr
The balance at the end of August, before interest and charges, is $1,981.47 in credit.
(a) Giving your answer to the nearest cent, calculate the interest payable to, or by, Miss Clarke on 31
August.
The bank charges $20 for a letter to Miss Clarke telling her she is more than $100 overdrawn.
(b) Calculate the final balance figure.
Question – 13 (2-2009)
Simone has a bank account on which simple interest is earned at 2 ½% per annum on credit balances. The
bank charges simple interest of 6 ¾% per annum on debit balances.
Interest is calculated at the end of each day on all balances and paid/earned at the end of the month.
Simone’s bank statement for April 2008 is shown below. Two of the balance figures are omitted.
Date Details Debit (£) Credit (£) Balances (£)

31 Mar/1 Apr Balance b/f ?
7 Apr Cheque 327.41 1,808.12 Cr
20 Apr Cheque 2,499.00 ?
25 Apr Deposit 3,654.50 2,963.62 Cr
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(a) Calculate
(i) The balance brought forward from 31 March
(ii) The balance at the end of the period 20 April to 24 April
(b) Giving your answer correct to four significant figures, calculate the percentage rate of interest per day
payable by the bank to Simone on credit balances.
Simone uses the products method to check the interest she receives from the bank.
(c) Calculate the interest received by Simone for the period from 7 April to 19 April inclusive.
Simone’s house increases in value from £105,000 to £185,000 over a period of 10 years.
(d) Calculate the steady rate of compound interest that this represents.
Question – 14 (2-2015)
Miss Marshall has a bank account on which simple interest is earned at 1.5% per annum on credit
balances (Cr). The bank charges simple interest at 8% per annum on debit balances (Dr).
Interest is calculated at the end of each day on the current balance at a daily rate of interest that is 1/365 of
the annual rate, and credited or debited to the account at the end of the month.
The account for September is shown below.
Date Details Debit Credit Balance
£ £ £
31 Aug Balance c/f ?
4 Sept Cheque 2,580.00 2,823.28 Cr
12 Sept Cheque 3,000.00 176.72 Dr
26 Sept Deposit ? 2,810.78 Cr
The balance at the end of September (length 30 days), before interest, is £2,810.78 in credit.
(a) Calculate the:
(i) opening balance carried forward from 31 August
(ii) amount of the deposit made on 26 September
(b) Show that the interest earned from the 26 September deposit to the end of September is £0.58, and
provide a more accurate figure.
(c) Calculate the interest charged for the period in September when the account was in debit.
The interest earned for the first 3 days of September is £0.666
(d) Calculate the balance at the end of September (length 30 days) after interest is paid and charged.
The bank charges £30 for writing a letter to Miss Marshall (on 1 October) telling her that she has been
overdrawn.
(e) Calculate this charge as a multiple of the interest charged for the period in September when the account
was in debit.
Question – 15 (3-2015)
Martin uses the products method to check the interest on his savings account. He calculates that he is
receiving interest at the rate of 0.0096% per day.
Calculate the:
(a) annual rate of simple interest paid to Martin
(b) interest earned on a balance of £25,000
(i) for 3 days
(ii) for 3 years
From 1 January 2000 to 1 January 2015, the value of Martin’s house increased from
£200,000 to £380,000.
(c) Calculate the rate of increase per annum based on simple interest.
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Martin believes that the increase is approximately 4.4% per annum based on compound interest.
(d) Provide a calculation to show if Martin is correct.
(e) State whether the true rate of compound interest per annum is exactly 4.4%, more than 4.4%, or less
than 4.4%.
Question – 16 (4-2015)
Investor A invests £170,000 in Investment Account B and receives interest, compounded six-monthly, at a
rate of 3% per six months.
(a) Calculate the:
(i) amount in the account after four years
(ii) portion of this amount that is interest, expressed as a percentage of the investment
(iii) annual rate of simple interest that would produce the same amount of interest over this period
A bank successfully tenders $484,000 for a $500,000 Treasury bill that runs for six months and is to be
redeemed at par.
(b) Calculate the rate of simple interest per annum received on this investment.
Question – 17 (3-2019)
Karnchana deposited 76,000 (Thai baht) in her bank account for 4 years.
(a) Calculate the total interest earned:
(i) at 2.9% simple interest per annum
(ii) at 2.9% compound interest per annum, with interest added at the end of each year.
Chanchai works out his bank interest using the products method, and he makes calculations based on
simple interest. His bank pays 8.25% interest per annum on credit balances, and charges 12.5% interest
per annum on debit balances. Interest is calculated daily on all balances and the net amount is added or
subtracted at the end of each month.
His bank statement for April 2019 shows the following entries in Thai baht.
Date Detail Debit Credit Balance
01/04/19 Balance b/f 14,500Cr
03/04/19 Rent for apartment 12,000 2,500Cr
09/04/19 Utilities for apartment 2,200 300Cr
15/04/19 Grocery store 2,300 2,000Dr
21/04/19 Transport pass 1,000 3,000Dr
27/04/19 Salary 19,800 16,800Cr
Chanchai’s balance at the end of April is 16,800 in credit, before application of interest and charges.
(b) Giving your answer to the nearest baht, calculate the net amount of interest that will be added to or
deducted from Chanchai’s account at the end of the month.
Chanchai’s bank charges 1,000 for a letter sent automatically to account holders whenever their account
exceeds a negative balance of 2,000
This charge appears on the account holder’s statement at the end of the month.
(c) Calculate the balance brought forward to May in Chanchai’s account, after interest and charges,
assuming no other transactions take place.
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Chapter – 2
Stock Exchange
Question – 1 (2-2000)
£100 of 5½% Government Stock can be bought for £83.75. A bank invested £60,970 in the stock.
(a) Calculate the normal value of stock bought by the bank.
The bank held the stock for 4¼ years.
(b) (i) Giving your answer to the nearest penny, calculate the total interest received.
(ii) Calculate the percentage yield over the 4¼ years.
Question – 2 (2-2001)
£100 of 9 ½% debenture stock can be bought for £84 ¾. Mrs Carter invested £91,530 in the stock and held
the stock for 3 years.
(a) Giving your answer to the nearest whole number per cent, calculate the interest only percentage yield.
Miss Lee invested £26,000 in a unit trust with an offer price of £4 per unit, and sold it after 2 ¼ years at
£5.09 per unit.
(b) Calculate the number of units purchased.
(c) Calculate how much profit Miss Lee made.
Question – 3 (2-2008)
£100 of 3¼% government stock can bought for £102. A bank invested £193,800 in the stock.
(a) Calculate the nominal value of the stock bought by the bank.
The bank held the stock for 4 years.
(b) Calculate the interest received over this period.
The bank could have purchased £204,000 of debenture stock for the £193,800.
(c) Calculate the cost of £100 of the debenture stock.
The bank could have invested the £193,800 instead in a unit trust with an offer price of £200 per unit, and
sold it after 4 years at £225 per unit.
(d) Calculate the number of units that could have been purchased.
Compare the increase in value of the units with the interest on the government stock and calculate how
much more or less the bank would have received if it had invested in the unit trust instead of government
stock.
Question – 4 (4-2000)
£100 of 4 ½% government stock can be bought for £85. A bank invested £348,500 in the stock.
The bank held the stock for 3 ¼ years.
(b) Calculate the interest received over this period.
The bank could have invested the same money instead in a unit trust with an offer price of £5 per unit, and
sold it after 3 ¼ years at £5.92 per unit. Assume that the unit trusts are accumulative in the price includes
the dividends.
(c) Calculate the number of units that could have been purchased.
(d) Calculate how much more the bank would have received, if it had invested in the unit trusts instead of
government stock.
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Question – 5 (3-2002)
An investor bought 5,000 8 ½% Preference Shares (nominal value $1) at 170 cents each, and 2,000
Ordinary Shares (nominal value $0.50) at 430 cents each.
(a) Calculate the total cost of the shares in dollars.
Broker’s commission was 0.25% of the total cost of the shares.
(b) Calculate the cost of the shares including commission.
After 2 years the Preference Shares were sold for a total of $10,500 and the Ordinary Shares were sold at
485 cents each. Broker’s rate of commission was the same as at the time of purchase.
(c) Calculate the total proceeds from the sale, after commission
The dividends declared on the nominal value of the Ordinary Shares were:
Year 1 15 cents per share
Year 2 12 cents per share
The dividends paid on the Preference Shares were calculated in the normal way.
(d) Calculate:
(i) The total dividends received by the investor on the Ordinary Share
(ii) The total dividends received by the investor on the Preference Shares
(iii) The total profit made by the investor, including purchase, sale, dividends and commissions, as a
percentage of the total original expenditure.
Question – 6 (2-2010)
An investor bought 2,500 4 ½% Preference Shares (nominal value £1) at 125 pence each, and 3,000
Ordinary Shares (nominal value £0.50) at 205 pence each.
(a) Calculate the total cost of the shares.
Broker’s commission is 0.6% of the nominal value of the shares.
(b) Calculate the commission paid on purchase of the shares.
After 2 years the Preference Shares are sold for a total of £3,400 and the Ordinary Shares are sold for
192 pence each.
The commission on the sales totaled £45 and dividends declared on the Ordinary Shares were:
Year 1 = 17 p per share Year 2 = 11 p per share
(c) Calculate:
(i) The total dividends received by the investor on the Ordinary Share
(ii) The total dividends received by the investor on the Preference Share
(iii) The total received from dividends and sales of the shares, net of commission
Question – 7 (3-2010)
Enrico buys 4,500 shares for £17.42 each and pays a commission of £36.
The nominal value of each share is £5.
(a) Calculate the cost of the shares, including commission.
In the first year, the company pays a dividend of 6.5% of the nominal value of the shares.
(b) Calculate the dividends paid to Enrico.
In the second year, the company pays no dividend. At the end of the second year, Enrico sells 2,500 of the
shares for £14.76 each. Enrico pays commission of 0.5% on the income from the sale.
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(c) Calculate the gain or loss to Enrico on the 2,500 shares. Include in your calculations:
The cost of the 2,500 shares at purchase;
 The proceeds and commission on their sale;
 The dividends received on these shares;
 An appropriate proportion of the commission paid on the initial purchase of 4,500 shares.
Enrico also buys 1,150 units in a unit trust for £31,303 and sells them after 3 years at £29 per unit.
(d) Calculate the percentage increase in value per annum.
Question – 8 (4-2012)
£100 of 3½ debenture stock can be bought for £91. Interest is paid half yearly. A bank invested £455,000 in
the stock.
The bank held the stock for 2½ years.
(b) Calculate the total interest received on the stock over this period.
The bank purchased 31,000 5½% Preference Shares (nominal value £5) at £1.88 per share.
(c) Calculate the cost of the shares.
(d) Calculate the dividend received each year.
The bank also purchased units in a unit trust with an offer price of £56 per unit, and sold the units after 3½
years at £63 per unit.
(e) Calculate:
(i) The increase in price per unit
(ii) The increase as a percentage increase per annum.
Question – 9 (2-2013)
Simon bought unit trust and invested for income. He invested £150,000 in a unit trust with an offer price of £
75 per unit, and sold the units after 3 years at the same price. During this period he received income from
the units of £38,400.This income was not reinvested in units.
Calculate;
(a) The number of units purchased
(b) The percentage yield per annum.
(c) The (3 year) income per unit.
Simon had to pay the following charges:
Fee on purchase: 0.1% of the sum invested
Fee on sale 0.25% of the sum received from the sale
Fund management fees of £1,350
Calculate:
(d) The total charges paid
(e) The total charges as a percentage of the original investment
(f) Simon’s income net of fees
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Question – 10 (3-2013)
Susan buys shares in the companies and later receives a dividend from each. She tabulates the figures as
follows:
Company A Company B Company C
Number of shares 4,000 2,500 ?
Normal value of one share £5.00 ? £0.50
Buying price per share £9.36 £13.02 144p
Broker’s commission £50 ? £60
Total cost of shares, including commission ? £32,625 £17,340
Dividend (percentage of nominal value) 4.5% 5.2% ?
Dividend (£) ? £260 £138
Supply the missing figures.
Question – 11 (4-2013)
Steve purchased units in a unit trust with an offer price of £400 per unit, and sold the units after three years
at £451 per unit.
(a) Express the increase in price of the units as a percentage increase per annum, based on simple
interest.
Steve bought 1,750 units in another unit trust and sold them later at £42.80 each, the total amount received
being £8,400 more than he bought them for.
(b) Calculate the original amount that Steve paid per unit.
Steve purchased 25,000 3½% preference shares (nominal value £5 per share) at £7.77 per share.
(c) Calculate:
(i) the total cost of the shares
(ii) the dividend received by Steve each year
(iii) his annual dividend as a percentage of the cost of investment
£100 of government stock can be bought for £88. Steve bought government stock and found that the
nominal value was £28,800 more than the amount he paid for it.
(d) Calculate how much Steve paid for the stock.
Question – 12 (2-2014)
Chou bought 35,000 units in a unit trust and sold them later for £17.50 each, the total amount received being
£9,100 more than she bought them for.
(a) Calculate the original amount Chou paid per unit.
Chou also purchased units in a unit trust with an offer price of £120 per unit, and sold the units after 5 years
for £135 per unit.
(b) Express the increase in price of the units as a percentage increase per annum based on simple interest.
Chou purchased 80,000 2¼% preference shares with a nominal value of £25 per share for £23.53 each.
(c) Calculate the:
(i) total cost of the shares
(ii) dividend received each year
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£100 of 2% Government Stock can be bought for £92. Interest is paid half yearly.
A bank invested £207,000 in the stock and held the stock for 3½ years.
(d) Calculate the:
(i) nominal value of the stock bought by the bank
(ii) total interest received over this period
Question – 13 (3-2014)
An investor bought 20,000 ordinary shares (nominal value £5 each) at £5.61 each. She paid a broker’s
commission of 0.25% on the nominal value.
(a) Calculate the cost of buying the shares, including commission.
After three years, the investor sold three-quarters of the shares for £6.40 each.
(b) Calculate the amount received from the sale, before commission.
The following day, the investor sold the remaining shares for £28,000. She paid a broker’s commission of
£180 in total for the two sales.
The dividends declared on the nominal value of the ordinary shares for the three years were:
Year 1 Year 2 Year 3
0.7% 0.6% 1.4%
(c) Calculate the excess of total amount received over total amount paid, including the purchase, sales,
dividends and commissions.
The investor also held stock of nominal value £88,000. Over a period of three years she received a total of
£5,544 interest.
(d) Calculate the annual rate of simple interest at which the stock was offered.
Question – 14 (4-2014)
(a) £100 of 4½% debenture stock can be bought for £95. Mrs Spring invested £80,750 in the stock and held
the stock for three years.
Calculate the:
(i) nominal value of the stock purchased by Mrs Spring
(ii) total interest received for the three-year period
(iii) percentage yield for the three-year period, based on interest only
(b) Ms Summers invested £123,750 in debenture stock with a nominal value of £150,000.
(i) Calculate the cost of £100 of debenture stock.
The percentage yield per annum, based on interest only, was approximately 4.85%.
(ii) Calculate the rate of interest on the nominal value of the stock.
Question – 15 (2-2015)
Gavin bought unit trusts and invested for income. He invested £130,000 in a unit trust with an offer price of
£65 per unit, and sold the units after 3 years at the same price.
During this period he received income from the units of £10,920. This income was not reinvested in units.
Calculate the:
(a) number of units purchased
(b) percentage yield per annum
(c) income per unit for the whole 3-year period
Gavin paid the following charges for the unit trusts:
Fee on purchase: 0.1% of the sum invested on purchase
Fee on sale: 0.2% of the sum received on sale
Fund management fees of £1,040
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Calculate:
(d) the total charges paid
(e) the total charges as a percentage of the original investment
(f) Gavin’s net income.
Question – 16 (3-2015)
Maisie bought two blocks of Government Stock, Stock A and Stock B, at different rates and values. She
tabulated her results as follows:
Stock A Stock B
Rate of interest (on nominal value of stock) pa 4% 4¾%
$100/£100 of stock bought at $87 ?
Amount invested $65,250 £102,600
Nominal value of stock purchased ? ?
Stock held for 3 years 4½ years
Total interest earned for the whole period ? ?
Total percentage yield on amount invested ? 25%
(a) Calculate the total percentage yield on the amount invested for Stock A.
(b) Calculate the cost of £100 worth of Stock B.
An investor bought 7,500 5½% Preference Shares (nominal value £5) at 820 pence each, and paid broker’s
commission of 1.1% of the nominal value of the shares.
(c) Calculate the total cost of the shares including the commission.
Question – 17 (4-2015)
Elena purchased units in Unit Trust C at £160 per unit and sold the units after 4½ years at £205 per unit.
(a) Calculate the increase in the price of the units as a percentage increase per annum, based on simple
interest.
Elena also bought 11,000 units in Unit Trust D and sold them later at £15.12 each, the total amount received
being £23,100 more than the original cost.
(b) Calculate the original amount Elena paid per unit.
Elena purchased debenture stock as follows:
Nominal value of stock purchased £60,000
Amount invested £53,700
Rate of interest on nominal value of stock 3.75% per annum
Elena later estimated that, over the period of time that she held the stock, she earned interest of just over
12½% of her investment.
(c) Calculate:
(i) the cost of £100 of debenture stock
(ii) the interest received per annum
(iii) 12½% of her investment
(iv) the number of years she held the stock
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Question – 18 (3-2019)
Avery purchased units in a unit trust with an offer price of £400 per unit, and sold the units after 4 years at
£360 per unit.
(a) Express the change in price of the units as a percentage change per annum, based on simple interest.
Avery then bought 4,630 units in a different unit trust and sold them 4 years later at £24.48 each. The total
amount received was £16,668 more than he paid for them.
(b) Calculate the original amount that Avery paid per unit.
The units continued to appreciate in value at the same rate of simple interest for a further 2 years.
(c) Calculate how much Avery could have sold the units for if he had held them for the extra 2 years.
Avery’s business partner, Breck, bought 12,000 ordinary shares in a company at 635 pence per share, and
sold them after 3 years at 755 pence per share.
Broker’s commission for the purchase was 0.5% of the purchase cost.
Broker’s commission for the sale was a flat fee of £350
No dividend was paid for the first two years.
In the final year a dividend of 9 pence per share was paid.
(d) Calculate the total profit made by Breck, taking account of the purchase, the sale, the dividend and
commissions.
(e) Express the average profit per annum as a percentage of the total cost of the shares, including
commissions.
13
Chapter – 3
Business Ownership
Question – 1 (2-2002)
An industrial product can be manufactured by two different methods of production. Using method X, fixed
costs are £3,400,000 and variable costs are £13 per product. Using method Y, fixed costs are £2,700,000
and variable costs are £20 per product.
(a) Calculate the level of output for which the total costs are the same.
(b) Calculate the total cost at this output
(c) Calculate the difference between the costs of Method X and Method Y for an output of 250,000 units.
Question – 2 (3-2010)
An industrial product may be manufactured by two methods of production.
Using Method X, fixed costs are £6,540,000 per period and variable costs are £57 per unit.
Using Method Y, fixed costs are £7,800,000 per period and variable costs are £45 per unit.
(a) Calculate the level of output per period for which the total costs are the same.
(b) Calculate the total cost per period for Method X at this output.
(c) State which method should be chosen for sales and production of 100,000 units per period.
(d) Explain how your answer to (a) supports your answer to (c).
Method X is chosen for production, and a selling price is set for break – even of 75,000 units per period.
(e) Calculate:
(i) The selling price
(ii) The profit for production and sales of 100,000 units per period
Question – 3 (2-2005)
An industrial product can be manufactured by two methods of production. Using Method X, fixed costs are
£2,500,000 per trading period and variable costs are £485 per unit of product. Using Method Y, fixed costs
are £4,780,000 per trading period and variable costs are £390 per unit of product.
Manufactured by Method X, the product has unit costs of production and distribution during a trading period
as shown in the table below. The figures include the unit variable costs and total fixed costs as above.
£
Components 255
Labour 175
Production overheads 50
Distribution expenses 130
(b) Calculate the number of units produced in the trading period.
The product is manufactured by Method X and is sold for £645 per unit of product.
(c) Calculate the break – even point for a trading period, and the total costs of production per trading period
at this output level.
14
Question – 4 (4-2003)
An industrial product may be manufactured by two methods of production. Using Method X, fixed costs are
£5,500,000 per period and variable costs are £535 per unit of product. Using Method Y, fixed costs are
£8,260,000 per period and variable costs are £420 per unit of product.
(a) Calculate the level of output per period for which the total costs are the same for the two methods of
production.
Produced by Method X the product has unit costs during a period as follows:
£
Components 275
Labour 180
The figures include variable costs and apportioned fixed costs.
(b) Calculate the number of units produced in the period.
(c) Compare the total costs of Methods X and Y at the level of output in (b) above.
Question – 5 (4-2004)
A factory manufactures two main products.
Product X has average unit costs of production during a trading year as follows:
£
Components 84
Labour 125
The production overheads do not vary irrespective of how many units are produced.
55% of the distribution expenses vary directly with the number of units produced.
80% of the labour costs vary directly with the number of units produced.
All the cost of the components varies directly with the number of units produced.
(a) Calculate
(i) The variable cost per unit
(ii) The fixed cost per unit for the trading year
Product Y has fixed costs of £3,250,000 and variable costs per unit of £210 during a trading year. It is sold to
wholesalers at £275 per unit.
(b) Calculate
(i) The number of units that must be sold in order to break even
(ii) The level of output required to provide a profit of £455,000.
Question – 6 (2-2012)
An industrial product may be manufactured by two methods of production.
Using Method X, fixed costs per period are £600,000 and variable costs are £295 per unit of product.
Using Method Y, fixed costs per period are £765,000 and variable costs are £240 per unit of product.
(b) The total cost for Method X at this output is £1,485,000. State the total cost for Method Y at this output.
(c) State, with a reason, when Method X should be used rather than Method Y.
15
Method Y is chosen for production, and the manufacturer sets a selling price of £300 per unit.
Calculate:
(d) The number of units for break- even
(e) The profit or loss at production, and sales of 10,000 units per period.
Question – 7 (2-2013)
Product A has variable costs of £ 160 per unit of product and fixed costs of £ 2,100,000 per period. Unit
costs of production during a trading period are as follows
£
Component 85
Labour 60
Distribution overheads 50
The cost of components varies directly with the number of units produced. 80% of the labor costs vary
directly with the number of units produced
The production overheads do not vary irrespective of how many units are produced.
(a) Calculate the percentage of distribution expenses that vary directly with the number of units production
(b) Calculate the fixed cost per units
(c) Calculate the number of units produced in the trading period
Product A breaks even on production and sales of 16,800 units per period.
(d) Calculate the selling price of Product A
(e) Calculate the total cost of production at break even
Question – 8 (3-2012)
An industrial product may be manufactured by two methods of production:
Using Method X, fixed costs are£1,500,000 per period and variable costs are £185 per unit of product. Using
Method Y, fixed costs are £1,700,000 per period and variable costs are £145 per unit of product.
(a) Calculate the level of output for which the total cost of production using Method X is equal to the total
cost of production using Method Y.
(b) Calculate the total cost of production per period for Method X at this output.
(c) State whether Method X or Method Y should be chosen for an expected production of 7,000 units per
period.
The business owner chooses Method X, and in the first production period produces and sells 7,000 units at
a selling price per unit of £399.
(d) Calculate the profit or loss.
Question – 9 (4-2012)
A manufacturer’s product is sold to customers at £ 60 each. Manufacturing costs are as follows
Fixed costs per period £ 1,625,000
Variable cost per unit £ 47
Calculate;
(a) The profit or loss at a level of production and sales of 110,000 units per period
(b) The level of production and sales to produce a profit of £ 325,000 per period
(c) The fixed costs per unit at a level of production of 130,000 units per period
(d) The break – even point in units per period
(e) The total cost of production at break even
16
Question – 10 (3-2013)
An industrial product may be manufactured by two methods of production:
Using Method X, fixed costs are£2,300,000 per period and variable costs are £215 per unit of product. Using
Method Y, fixed costs are £2,500,000 per period and variable costs are £190 per unit of product.
(a) Calculate the level of output for which the total cost of production using Method X is equal to the total
cost of production using Method Y.
(b) Calculate the total cost of production per period for Method X at this output.
The business owner chooses Method Y and in the first production period produces and sells 12,000 units at
selling price per unit of £ 399.
(c) Calculate the profit or loss in this period
In the second production period the fixed and variable costs remain the same.
The owner produces 15,000 units but only sells 13,500 units. Changes in technology mean that this product
has become obsolete and no more can be sold.
(d) Treating the unsold units as having zero value, calculate the profit or loss on production and sales
Question – 11 (4-2013)
Manufacturer A sells product P at £66 per unit of product.
Manufacturing costs are as follows:
Fixed cost per period £1,955,000
Variable cost per unit of product £49
(a) Calculate:
(i) the profit or loss at an output of 150,000 units of product per period
(ii) the break-even point in units of product per period
During a sales period, manufacturer A makes and sells 65,000 units of product Q.
During this period:
the fixed costs of distribution are £78,000 per period
the variable costs of distribution are £4.90 per unit of product
(b) Calculate the total cost of distribution per unit of product during this period.
In another period, manufacturer A makes and sells 125,000 units of product R at a selling price of £27.50,
and makes a profit of £126,150.
The variable costs are £18.80 per unit of product R.
(c) Calculate the break-even point in units of product per period.
Question – 12 (2-2014)
Using Method A, fixed costs are £5,970,000 per period and variable costs are £102 per unit. Using Method
B, fixed costs are £7,500,000 per period and variable costs are £85 per unit.
(a) Calculate the level of output per period for which the total costs are the same.
(b) Calculate the total cost per period for Method B at this level of output.
(c) State and explain which method should be chosen for production and sales of 120,000 units per period.
Method A is chosen for production, and a selling price is set for break-even of 75,000 units per period.
(d) Calculate the:
(i) selling price
(ii) profit for production and sales of 100,000 units per period
17
Question – 13 (3-2014)
Product P had unit costs of production and distribution during trading period A as follows. A percentage of
each figure (the percentage shown) varied directly with the number of units produced.
£ Percentage that is variable
Components 130 100%
Labour 220 85%
Production overheads 60 0%
Distribution expenses 70 60%
(a) Calculate, for trading period A,
(i) the variable cost per unit
(ii) the fixed cost per unit.
In trading period B, the variable cost per unit was £360, and the fixed cost per unit was £125. In this period,
the product was sold for £500 per unit and produced a profit of £480,000.
(b) Calculate the number of units produced and sold in trading period B.
In trading period B, unit costs of production were as shown below:
£ Percentage that is variable
Components 129 100%
Labour ? ?
Production overheads 61 0%
Distribution expenses 70 60%
(c) Calculate, for trading period B,
(i) the cost of labour per unit
(ii) the percentage of the labour cost that varied with the number of units produced
Question – 14 (4-2014)
Manufacturer A sells a particular product for £499. Production costs are as follows:
Fixed costs per period £433,500
Variable costs £329 per unit
(a) Calculate the break-even point in units produced and sold.
Manufacturer B sells a similar product. By investing in newer machinery, its fixed costs are higher at
£451,000 per period, while variable costs are lower at £295 per unit. This product is sold by Manufacturer B
for £490 per unit.
(b) Calculate the profit or loss per period for Manufacturer A and Manufacturer B for an output of 2,500
units each.
Manufacturer B then changes the selling price of its product for the following trading period, while the fixed
costs and variable costs remain at £451,000 per period and £295 per unit. The break-even point for
production and sales in this trading period is 2,200 units.
(c) For this trading period, calculate the:
(i) contribution per item
(ii) selling price
18
Question – 15 (2-2015)
Manufacturer A sells Product P for £275 per unit. Manufacturing costs are as follows:
(a) Calculate the:
(i) contribution per unit
(ii) break-even point in units produced and sold
Manufacturer A sells Product Q for £300 per unit. Manufacturing costs are as follows:
(b) Draw a break-even chart for Product Q, to an appropriate scale. Your chart should cover production
(output) from 0 units per period to 2,500 units per period.
(c) Show clearly on your chart the:
(i) output (units) for break even
(ii) total manufacturing cost for break even
(iii) profit for an output of 2,000 units
(iv) output for a loss of £55,000
Question – 16 (3-2015)
An industrial product may be manufactured using two alternative methods of production.
Using Method X, fixed costs per period are £840,000 and variable costs are £395 per unit of product.
Using Method Y, fixed costs per period are £1,020,000 and variable costs are £350 per unit of product.
(a) Calculate the level of output for which the total costs are the same for the two methods.
(b) State, with a reason, when Method X should be used rather than Method Y.
Method Y is chosen for production, and the manufacturer sets a selling price of £470 per unit.
(c) Calculate the:
(i) number of units to achieve break even
(ii) profit or loss on production and sales of 7,000 units per period
Question – 17 (4-2015)
Product A has unit costs of production during a trading period as follows:
Fixed (£) Variable (£)
Production overheads ? 0
Distribution expenses 12 36
Labour ? 68
Materials 0 62
(a) Calculate, for Product A, the:
(i) total distribution expenses per unit in this trading period
(ii) fixed distribution expenses as a fraction of the total distribution expenses
The total of all fixed and variable costs per unit in this trading period is £230.
The total cost of labour per unit in this trading period is £85.
(b) Calculate, for Product A in this trading period, the:
(i) fixed cost of labour per unit
(ii) production overheads per unit
(iii) total variable costs as a percentage of the total of all fixed and variable costs
19
In the same trading period, Product B has variable costs of labour per unit of £78.
This figure is 65% of the total cost of labour per unit for this product.
(c) Calculate the total cost of labour per unit for Product B in this trading period.
Question – 18 (3-2019)
Abitfit plc sells its most popular smart watch in the UK for £180 (British pounds) per unit. Production costs
are as follows:
Fixed costs £567,000 per month
Variable costs £153 per unit.
(a) Calculate the break-even point in units per month.
Wuahei sells a similar smart watch with fixed costs of £717,000 per month and variable costs of £132 per
unit. This smart watch is sold at a price of £169 each.
Last month Abitfit plc and Wuahei both had an output and sales of 25,000 units.
(b) (i) Calculate and compare the profits of the two manufacturers for last month.
(ii) Calculate Wuahei’s profit per smart watch as a percentage of the sales price.
20
Chapter – 4
Profitability & Liquidity
Question – 1 (2-2000)
The following information relates to a retailer’s business at the end of the first year of trading:
£
Annual sales 33,200
Annual purchase 17,250
Sales returns 2,500
Purchase returns 680
Initial stock value 1,800
Final stock value 1,650
General expenses 900
Postage 110
Telephone 215
Advertising 95
Van expenses 1,420
(a) Calculate: (i) Gross profit
(ii) Net profit
(iii) Gross profit as a percentage of the net turnover
(iv) Overhead expenses as a percentage of the net turnover
(b) Give a brief explanation of :
(i) The difference between gross and net profit
(ii) The gross profit percentage.
The retailer’s capital invested in the business was £ 110,000. This money could have been invested at 7%
per annum.
(c) State, with reasons, whether this would have been a better option.
Question – 2 (4-2011)
The following information relates to a retailers business at the end of the first year of trading.
£
Annual sales 183,700
Annual purchases 84,590
Sales returns 3,980
Purchase returns 2,305
General expenses 9,360
Postage 540
Telephone & Internet 1,030
Advertising 8,650
Vehicle expenses 8,600
Calculate:
(a) The cost goods sold
(b) Gross profit as a percentage of net sales
(c) Overhead expenses as a percentage of net sales
(d) The average length of time that items remained in stock, given your answer in days
21
Question – 3 (3-2010)
Mary is a retailer. In a given trading period her sales were £1,010,000 less sales returns of £24,500. During
the trading period the average amount owed to Mary by her debtors was £51,300.
(a) Calculate the average credit given by Mary to her debtors, in days.
(b) Give a brief explanation of the average credit given by Mary.
Mary’s ratio for overhead expenses to net sales during the period was 14%.
(c) Calculate the amount of overhead expenses during this period.
During the trading period: the average credit taken by Mary from her creditors was 21 days; the average
money owed by Mary to her creditors was £39,900; her purchases, before purchase returns, were £700,000.
(d) Calculate:
(i) Mary’s net purchases for the period
(ii) Mary’s purchase returns for the period
Question – 4 (3-2011)
The balance sheet of Rhodes Retail at the end of a trading year showed current assets of £41,764 and
current liabilities of £19,700.
The current assets included stock of £15,450, a bank account, cash of £485 and an amount of £20,330
owed by debtors.
(a) Calculate the:
(i) Current ratio
(ii) Balance in the bank account.
(b) State whether or not you judge the liquidity of the business to be healthy
(c) Give a reason for your answer to (b).
The average stock held during the trading year was £14,800 and the net purchases during the year were
£186,300.
(d) Calculate the:
(i) Stock held at the beginning of the trading year
(ii) Cost of goods sold
(iii) Rate of stock turn
Question – 5 (2-2013)
(a) At the end of the year 2012 the following information applied to Company X:
Current liabilities £7,400,000
Current ratio 2.4 : 1
Acid test ratio 1.15 : 1
Calculate:
(i) the current assets
(ii) the stock held by Company X at that time
(iii) Give one reason why you think the liquidity of Company X is healthy.
(b) During 2012 the following information relates to Trader Y:
£
Net sales 1,930,000
Cost of goods sold 1,460,000
Overhead expenses 180,000
22
Calculate:
(i) gross profit
(ii) net profit
(iii) net purchases
(iv) the average period of time (in days) that items remain in stock
Question – 6 (3-2013)
The following figures relate to a trading year for trader Amelia.
£
Annual sales 65,000
Annual purchases 42,400
Sales returns 2,950
Purchases returns 2,250
Money owed by debtors at year end 2,890
Money owed to creditors at year end 2,310
Stock at start of year 2,990
Stock at end of year 2,100
Postage and telephone 1,700
Heating and lighting 5,310
Rent 11,605
Bank at year end 1,070
Cash at year end 177
(a) Calculate the ratios for:
(i) overhead expenses to turnover
(ii) end of year working capital
(b) Calculate the ratios for:
(i) Average credit taken from creditors in days
(ii) Average credit given to debtors in days
State which of these, if either;
(iii) Gives the average time it takes Amelia to pay her creditors
(iv) Gives the maximum time it takes Amelia to receive payment from her debtors
Question – 7 (4-2013)
The following information relates to business B in the most recent financial year:
£
Overheads 42,357
Turnover (Net sales) 299,250
Capital 420,900
Gross profit 71,820
Stock at start of year 17,000
Stock at end of year 14,500
Calculate:
(a) the gross profit percentage on turnover
(b) the percentage return on capital employed
(c) the average stock held
(d) the annual rate of stockturn
(e) the average number of weeks that items remain in stock
23
Question – 8 (2-2014)
The following information relates to a retailer’s business at the end of the first year of trading.
£
Annual sales 2,370,000
Annual purchases 1,096,000
Sales returns 155,000
Purchases returns 62,000
Opening stock value 120,000
Closing stock value 132,000
Calculate the:
(a) net sales
(b) net purchases
(c) net profit
(d) average number of days that items remain in stock
(e) rate of stockturn per annum
Question – 9 (3-2014)
For Company C during Year A (not a leap year), the rate of stock turn was 12.5 per annum
(a) Calculate the average number of days that items were held in stock.
At the end of Year A, the current liabilities of Company C were £596,000, the current assets (including stock)
were £1,341,000, and the stock held was £417,200.
(b) Calculate:
(i) the current ratio
(ii) the acid test ratio
(c) Based on your figure for the acid test ratio, advise the owner of Company C whether the company is
healthy or not. Explain your answer with reference to the standard guideline figure and what that tells
us, importantly, about the liquidity of Company C.
The average stock held during Year A was £430,000.
(d) Calculate:
(i) the stock held at the beginning of Year A
(ii) the cost of goods sold during Year A
Question – 10 (4-2014)
In a given trading period, purchases for Retailer R were £741,500 and purchases returns were £11,500.
During the trading period the average amount owed by
Retailer R to her creditors was £58,000.
(a) Calculate the average credit taken by Retailer R from her creditors, in days. Take a year to be 365 days.
The acid test ratio of Retailer R is 1.65: 1
(b) Explain why this figure is considered healthy.
The current liabilities of Retailer R are £396,000 and the current assets are £970,200.
(c) Calculate the:
(i) stock held by Retailer R
(ii) current ratio
(d) Advise Retailer R, giving a reason, whether her current ratio is considered healthy.
24
Question – 11 (2-2015)
(a) The Balance Sheet of Retailer A at the end of the first year of trading is shown below.
Balance Sheet as at 31 December Year 1
£ £ £
Fixed Assets Figure omitted
Current Assets
Stock 9,500
Debtors 14,490
Bank 2,035
Cash 495 26,520
Amounts due within 12 months
trade creditors (11,050)
Net Current Assets 15,470
261,300
Amount due after 12 months
mortgage on premises (93,800)
167,500
Using the above figures from the Balance Sheet, calculate for Retailer A the
(i) current ratio
(ii) borrowing ratio (capital gearing ratio)
(iii) fixed assets
(b) During 2014 the following information relates to Retailer B.
£
Net sales 490,000
Cost of goods sold 341,000
Opening stock 24,500
Closing stock 19,500
Calculate the:
(i) gross profit
(ii) net purchases
(iii) rate of stock turnover (stockturn) per annum
25
Question – 12 (3-2015)
The following balance sheet refers to the first year of trading.
Balance Sheet at 31 December Year 1
£ £ £
Fixed Assets
Premises Figure missing
Equipment 19,000
Furniture 12,100
Transport 33,350
189,450
Current Assets
Stock 30,100
Debtors 6,160
Bank 1,740
Cash 270 38,270
Amounts due within 12months
trade creditors ( 8,600)
Net Current Assets 29,670
219,120
Amount due after 12 months
mortgage on premises (86,320)
132,800
Financed by
Capital 130,000
Add net profit Figure missing
Less drawings (9,400) 132,800

(a) Using the balance sheet, calculate the:
(i) current ratio
(ii) acid test ratio
(iii) borrowing (gearing) ratio
(iv) value of premises
(v) net profit
For the second year of trading, the average stock was £26,250.
(b) Calculate the stock held at the end of the second year of trading.
Question – 13 (4-2015)
At the end of the year 2014, the following information applied to Company X:
Current liabilities £19,200,000
Current ratio 2.3 : 1
Acid test ratio 1.1 : 1
(a) Calculate, for Company X, the:
(i) current assets
(ii) stock held at that time
(b) Give one reason why you think the liquidity of Company X is healthy, based on the current ratio.
(c) Explain why an acid test ratio of 1: 1 or better is considered healthy.
26
During 2014, the following information related to Trader Y:

£
Net sales 1,540,000
Cost of goods sold 1,095,000
Opening stock 65,000
Closing stock 61,000
(d) Calculate, for Trader Y, the:
(i) net profit
(ii) net purchases
(iii) average number of days that items remained in stock
(assume 1 year = 365 days)
Question – 14 (3-2019)
Pulau Pillows Pte Ltd manufactures bedroom accessories in Singapore. Its trading for 2018 had the
following details (given in Singapore dollars, S$).
S$
Overheads 76,930
Turnover (net sales) 542,000
Capital employed 528,875
Gross profit 119,240
Stock at the start of the year 48,140
Stock at the end of the year 52,340
Calculate the:
(a) gross profit percentage on turnover
(b) percentage return on capital employed
(c) annual rate of stockturn
(d) average number of days that items remain in stock.
27
Chapter – 5
Investment Appraisal
ARR = Average revenue return per annum net of repair and maintenance
Initial cost of Project
Question – 1 (3-2000)
A business owner has a choice of two investment projects. The initial cost of Project A is £ 130,000 and that
for Project B is £ 100,000. Repair and maintenance costs are expected to average £ 8,000 per annum for
Project A and £ 5,000 for Project B.
Estimated revenue returns for the first three years are as follows;
Year Project A Project B
1 50,000 40,000
2 60,000 50,000
3 70,000 60,000
(a) Use the average rate of return method of investment appraisal to advise which Project is the better
invest.
The net present value for Project A is calculated for three possible discounting factors, with the following
results;
Discount Factor NPV
£
16% 2,550
17% 290
18% (1,940)
(b) Estimate as a % to one decimal place, the internal rate of return.
Question – 2 (2- 2010)
A business owner calculate the payback period for 2 investment projects.
The estimated costs and returns are as follows:
Project One (£) Project Two (£)
Year 1 cash inflow 25,000 -10,000 (outflow)
Year 2 cash inflow 50,000 75,000
Payback period 2 years 9months 3 years 7months
(a) Calculate the cost of Project One.

The cost of project Two is £175,000.
(b) Calculate the estimates cash inflow for Project Two in year 4.
28
The owner estimates the following figures for Investment Project Three.
£
Cost (year 0) 1,750,000
Year 1 Net cash inflow 300,000
The owner calculate the net present value, using a discount rate of 8% and the following table
Discount rate 8%
Year 1 0.926
Year 2 0.857
Year 3 0.794
Year 4 0.735
(c) Calculate the net present value of Project Three on the basis of the figures given.
The owner recognizes that this is a negative figure, and therefore does not accept the project.
(d) Explain why a project with a negative figure for net present value is rejected by the owner.
Later, the owner believes that the Project will receive a net cash inflow in year 5 of £200,000.
(e) Calculate the new net present value at the discount rate of 8%.
Question – 3 (3-2010)
(a) Advisor A uses the following formula to calculate the average rate of return (ARR) of investment
projects:
ARR = Average annual income net of depreciation and repair and maintenance costs
She estimates the following figures for Investment Project Q:
Initial cost of Project Q £3,200,000
Total income net of depreciation and repair and maintenance costs £5,280,000
Average rate of return 27.5%
Calculate the expected length of Project Q in years.

(b) Investment Project R has an initial cost of £1,900,000 and is anticipated to have a life of five years, no
scrap value, and to give the following returns:
£
29
(i) Calculate the payback period of Project R.

Advisor A calculates the net present value of Project using a discounting factor of 7%.
(ii) Copy and complete the following table, based on a discounting factor of 7%.
£ Factor Present Value
Year 0 cash outflow 1,900,000 1 (1,900,000)
Year 1 cash inflow 300,000 0.935 280,500
Year 2 cash inflow 500,000 ? 436,500
Year 3 cash inflow ? 0.816 652,800
Year 4 cash inflow 600,000 0.763 457,800
Year 5 cash inflow 300,000 0.713 213,900
Net present value ?
Question – 4 (3-2011)
A business owner has a choice of two investment projects. The estimated life of each project is 5 years. The
cost of Project one is expected to be £ 1,350,000 to be paid in year 0.The estimated net cash inflow for
Project one is £400,000 in each of the five years
(a) Calculate the payback period for Project one in years and months
The cost Project two is expected to be £ 1,700,000 with half of this to be paid at the start of the project (year
0) and half a year later (during year 1)
The net cash outflow in year 1 ( including allowing for the expenditure of half the cost) is £350,000.The net
cash inflow for the remaining four years is £ 500,000 in each year.
(b) Calculate the payback period for Project Two.
(c) On the basis of payback period, advise the business owner.
(d) Calculate the net present value of Project One using the following table of discount factors.
Year 1 2 3 4 5
Discount factor 0.926 0.857 0.794 0.735 0.681
Question – 5 (2-2013)
Advisor Alice uses the following formula to calculate the average rate of return (ARR) of investment projects:
ARR = Average annual revenue returns net of depreciation and repair and maintenance costs
She estimates the following figures for Investment Project P:
Initial cost of Project P £6,500,000
Total revenue returns of Project P over its lifetime £10,300,000
(before deducting depreciation and repair and maintenance costs)
Average depreciation and repair and maintenance costs per annum £150,000
Average rate of return 17.5%
Calculate:
(a) the average annual revenue returns net of depreciation and repair and maintenance costs
(b) the expected lifetime of Project P in years
30
Question – 6 (3-2013)
Business owner A has a choice of 2 investment projects.
Business adviser B estimates the costs and returns as follows:
Project One Project Two
£ £
Cost (year 0) 700,000 750,000
Year 1 cash inflow 150,000 -200,000 (outflow)
(a) For Project Two calculate the payback period. Give your answer in years and months.
The payback period for Project One is 2 years 10 months.
(b) Advise the business owner which project is the better investment.
Business adviser B uses a required rate of return of 10% and the following table of discount factors:
Year Discount factor
Year 1 0.909
Year 2 0.826
Year 3 0.751
Year 4 0.683
(c) Using the above figures, calculate:
(i) the present value of the expected cash inflow for Project One in year 4
(ii) the present value of the expected cash inflow and outflow for Project Two in years 1 and 2
combined
Business adviser C estimates that the cash inflow for Project One in year 1 will be £200,000 and that the
other figures will remain the same.
(d) Calculate the payback period for Project One on the basis of the figures of business adviser C.
Question – 7 (4-2013)
A business owner has a choice of two investment projects.
The estimated life of each project is five years.
Further information is as follows:
Project One Project Two
£ £
Initial cost 1,000,000 1,700,000
Repair and maintenance costs per annum 120,000 200,000
Revenue returns Year 1 200,000 250,000
Year 2 350,000 750,000
Year 3 500,000 750,000
Year 4 500,000 750,000
Year 5 250,000 500,000
(a) Calculate the average rate of return for each project.
The owner estimates the following figures for Investment Project P:
£
Cost (year 0) 2,000,000
31
(b) Using the following table of discounting factors, calculate the net present value for Project P.
Discounting factor
Year 1 0.901
Year 2 0.812
Year 3 0.731
Year 4 0.659
(c) Calculate the percentage rate of return per annum represented by this table.
Question – 8 (2-2014)
Almander calculates the expected average rate of return (ARR) of investment project X as 28%, using the
formula:
ARR = Average revenue return per annum net of repair and maintenance costs
Initial cost of the project
He uses estimated figures as follows:
Initial cost of the project £950,000
Average cost of repairs and maintenance per annum £70,000
Life of the project 5 years
He further estimates that the gross revenue return before deducting the cost of repairs and maintenance will
be £375,000 for each of the first 4 years.
(a) Using Almander’s formula, calculate the estimated figures for the:
(i) average revenue return per annum net of repair and maintenance costs
(ii) gross revenue return for year 5 (before deducting the cost of repairs and maintenance)
Birgit estimates the net present value of investment project Y at two discount rates, with the following results:
Discount rate 8% Net present value = £66,000
Discount rate 11% Net present value = £12,000
(b) Use Birgit’s figures to calculate the internal rate of return for investment project Y.
(c) Given that the investor requires investment project Y to earn at least 11.5% per annum, advise the
investor, with reasons, whether to proceed with the investment.
Question – 9 (3-2014)
(a) The net present value of investment Project A at two discount rates is estimated as follows:
Discount rate 6% 10%
Net present value £79,800 (£79,800)
Estimate the internal rate of return of Project A.
(b) A business owner has a choice of two investment projects. The estimated costs and returns are as
follows (all figures are in £).
Project B Project C
Cost (outflow) (6,500,000) (4,000,000)
Year 1 cash inflow 1,500,000 600,000
Year 2 cash inflow 2,500,000 2,400,000
Year 3 cash inflow 2,500,000 2,400,000
Year 4 cash inflow 2,000,000 2,400,000
Calculate:
(i) the payback period for each project in years and months, and advise the owner which is the better
investment
(ii) the revised payback period for Project C on the basis that the actual cash inflow for the first three
years is as shown, but the actual cost is 10% more than the figure shown
32
Question – 10 (4-2014)
A business owner has a choice of two investment projects. The estimated costs and returns are as follows:
Project P Project Q
£ £
Cost (outflow) 5,000,000 3,200,000
Year 1 cash inflow (250,000) outflow 250,000
Year 2 cash inflow 3,000,000 1,900,000
Year 3 cash inflow 3,000,000 2,100,000
(a) For Project P calculate the payback period, giving your answer in years and months.
(b) The payback period for Project Q is 2 years 6 months. Advise the business owner which project is the
better investment. To gain marks, you must explain your choice.
(c) Using the following table, based on a discount rate of 7%, calculate the net present value for Project P.
Discount factor
Year 1 0.935
Year 2 0.873
Year 3 0.816
At a discount rate of 5% the net present value of Project P is £75,000.
(d) Using this information and your answer to (c), estimate the internal rate of return for Project P.
(e) At a discount rate of 7.5%, the net present value of Project Q is £366,500.
Based on this new information, advise the business owner which is the better investment, giving a clear
reason.
Question – 11 (2-2015)
The estimated costs and returns for investment Project P are as follows.
£
Cost 6,000,000
Year 1 net cash inflow 2,000,000
(a) Calculate the payback period of Project P in years and months.
The potential investor for Project P requires a payback period of three years or better.
(b) Advise the potential investor for Project P. You must give a reason for your advice.
The investor estimates the following figures for an investment in Project Q:
Initial cost of project £15,000,000
Expected life of project 6 years
Total return before allowing for repairs and maintenance £25,800,000
Average cost per annum of repairs and maintenance £850,000
(c) Calculate the expected average rate of return of Project Q.

Investment Project R is estimated to have a net present value of £50,000 at a discount factor of 7% and a
net present value of negative £150,000 at a discount factor of 8%.
(d) Calculate the internal rate of return of Project R.
33
Question – 12 (3-2015)
A business owner has a choice of two investment projects, Project A and Project B.
The estimated costs and returns are as follows:
ProjectA Project B
£ £
Initial cost (investment) 230,000 150,000
Year 4 cash inflow 60,000 Figure missing
Year 5 cash inflow 60,000 Figure missing
(a) Calculate the payback period for Project A. Give your answer in years and months.
The payback period for Project B is 3 years 3 months.
(b) Advise the business owner which project is the better investment. You must give a reason.
(c) Calculate the net present value of Project A, using a discount rate of 8% and the following table.
Discount factor
Year 1 0.926
Year 2 0.857
Year 3 0.794
Year 4 0.735
Year 5 0.681
The net present value of Project B, using the same discount rate, is £7,740 (positive).
(d) Calculate the revised net present value of Project B if the year 1 cash inflow is increased from £25,000
to £35,000.
Question – 13 (4-2015)
The estimated revenue returns for Investment Project P are as follows:
£1,300,000 in year 1
£2,000,000 in each of the years 2 to 7
£0 in year 8 and subsequent years
The repair and maintenance costs are expected to be £250,000 in each of the first seven years.
(a) Calculate, for Investment Project P, the:
(i) estimated revenue return net of repair and maintenance costs in year 1
(ii) total estimated revenue returns net of repair and maintenance costs for the first seven years
(iii) average estimated revenue returns net of repair and maintenance costs overthe first seven years
Investor A calculates the average rate of return of Investment Project P to be 22%, based on an estimated
life of seven years. The calculation he used is average estimated revenue returns net of repair and
maintenance costs, divided by the initial cost of the project.
(b) Calculate the initial cost of Investment Project P.
Investor A calculates the net present value of Investment Project Q to be £280,000 at a discount factor of
10%, and £80,000 at a discount factor of 12%.
(c) Calculate the internal rate of return of Investment Project Q, using the figures from Investor A.
Investor B calculates the net present value of Investment Project Q to be £80,000 at a discount factor of
12%, and (£30,000) at a discount factor of 13%.
(d) Calculate the internal rate of return of Investment Project Q, using the figures from Investor B.
Investor A calculates the payback period of Investment Project R to be six years and eight months, based on
an initial cost of £2,500,000 and a net cash inflow of £400,000 in each of the first six years.
(e) Calculate the expected net cash inflow in year 7.
34
Question – 14 (3-2019)
Bundaberg Mill Ltd is an Australian company that mills sugar cane for export.
The owners are considering a new processing factory to increase output. The capital cost of the factory is
AU$6,700,000 (Australian dollars), and the company hopes to recover its investment within a four-year
period. The estimated costs and returns for the first three years are as follows:
Year AU$
0 Cash outflow (6,700,000)
1 Cash inflow 750,000
2 Cash inflow 2,700,000
3 Cash inflow 2,700,000
The owners make allowance for price changes, inflation, and for opportunity loss of not investing in
alternatives, by calculating the net present value of the project using a discount rate of 7.5%, and the
following table.
Year 7.5% Discount rate factors
1 0.930
2 0.865
3 0.805
4 0.749
5 0.697
(a) Calculate the net present value of the project after three years.
(b) How much cash inflow would be required in Year 4 in order to achieve a net present value of AU$0 (i.e.
complete recoup of funds with interest), using the 7.5% discount rate factors?
Give your answer to the nearest hundred Australian dollars.
Assuming that the NPV after four years is AU$0, Bundaberg Mill Ltd plans for a cash inflow of AU$1,000,000
in Year 5 so that the NPV over the five-year period is AU$697,000
Using the same cash inflows, the NPV of the project after five years at a discount rate of 12% is –$121,477
(negative). These values are shown on the graph above.
(c) Using only the graph above, estimate the internal rate of return of the project, explaining briefly how you
arrived at your answer.
35
Chapter – 6
Bankruptcy
Question – 1 (4-2008)
The following information relates to the business of a bankrupt trader:
£
Cash in hand 105
Creditors ?
Machinery 11,500
Bank overdraft 25,300
Trade debtors 6,090
Stock 16,420
Office equipment ?
Vehicles 17,000
Total assets 59,140
Total liabilities 97,500
(a) Calculate the value of her office equipment and the amount owed to creditors.
The assets were realized in full at their book values, listed above.
Creditors’ include £3,700, which, together with the bank overdraft, are secured. Hence, £29,000 of the
liabilities, made up of the bank overdraft and other secured creditors, must be paid first and in full.
Calculate:
(b) the rate in the £ that an unsecured creditor will receive
(c) the amount owed to an unsecured creditor who receives £13,420
Question – 2 (3-2008)
(a) The following information relates to the bankruptcy of Company P:
Total assets available for creditors £52,184
Total owed to secured creditors £11,110
Total liabilities £85,790
Calculate:
(i) How much is owed to unsecured creditors
(ii) The assets available for unsecured creditors
(iii) The rate in the pound paid to unsecured creditors
(b) The following information relates to the bankruptcy of Company Q:
Total liabilities £64,950
Assets available for unsecured creditors £23,310
Rate in the pound paid to unsecured creditors 60 p
Calculate:
(i) How much is owed to unsecured creditors
(ii) How much is owed to secured creditors
(iii) The total assets available for creditors
36
Question – 3 (4-2000)
Jo is owed £5,000 by a company called Dodgy, Inc. When the company is declared bankrupt, Jo finds she is
an unsecured creditor and eventually receives only £3,000 in payment.
(a) Calculate the rate in the £ which is payable to unsecured creditors.
The total owed to unsecured creditors by Dodgy, Inc is £98,000.
The company also owed £20,500 to secured creditors.
The expenses of winding up the business were £7,800.
(b) Calculate the value of the assets of the business.
(c) Express the assets as a fraction of the liabilities.
(d) Express the assets as a percentage of the liabilities.
Give your answer as a whole number per cent.
Question – 4 (3-2002)
Joe is owed $25,000 by a failed company. When the company is declared bankrupt, Joe finds he is an
unsecured creditor and eventually receives only $7,000 in payment.
(a) Calculated the rate in the $ which is payable to unsecured creditors.
The total owed to unsecured creditors by the failed company is $55,000.
The company owes $20,000 to secured creditors.
The expenses of winding up the business are $13, 500.
(b) Calculated the total amount paid to unsecured creditors.
(c) Calculated the value of the assets of the business prior to incurring winding up expenses.
(d) Express the assets as fractions of the total amount owed to creditors. Give the fraction in its
simplest terms.
Question – 5 (3-2011)
A bankruptcy trader owed £77,200 to her creditors, of which £28,850 was secured against assets. The
assets of the business raised £57,900, out of which £1,974 was paid in fees during the process of
bankruptcy.
(a) Calculate the assets, before fees, as a percentage of the liabilities.
(b) Express this as a ratio of liabilities, in its simplest terms.
Calculate:
(i) how much in the £ was paid to the unsecured creditors
(ii) how much was paid to an unsecured creditor who was owed £22,500
The assets of the business at the time of bankruptcy were as follows:

Asset Value realized
Cash in hand 211
Machinery 9,500
Trade debtors 25,200
Office equipment 2,650
Vehicles 13,400
Plus stock
(c) Calculate the value realized for the stock.
37
Question – 6 (2-2012)
(a) In bankruptcy A unsecured creditors receive £ 0.45. A lender is owed £ 120,000 of which 20% is
secured against assets. Calculate the amount received by the lender
(b) In bankruptcy B; the total liabilities are £ 560,000
The amount owed to unsecured creditors is £ 375,500 and an unsecured creditor who is owed £50,000
receives £18,000.
The expenses of winding up the business are £ 4,500.
Calculate;
(i) The rate payable to unsecured creditors
(ii) The total assets realized
(c) Sebastian is owned money in two bankruptcies C and D. He is owed £ 28,500 as unsecured creditors
in bankruptcy C that pays £ 0.29 in the pound to unsecured creditors. He is also owed £ 40,000 in
bankruptcy D as the sole secured creditor. The total assets of D, after winding up expenses realized £
36,000.
Calculate how much Sebastian receives in total.
Question – 7 (3-2012)
In bankruptcy A, liabilities total £1,700,000 and assets total £612,000.
(a) Write the relationship of assets to liabilities as a ratio in its simplest form.
(b) Calculate the assets as a percentage of liabilities.
Secured creditors were owed £68,000. The remaining creditors were unsecured.
(c) Calculate the dividend payable to unsecured creditors as a rate in the pound.
(d) Using the exact figure for dividend, calculate:
(i) How much is paid to an unsecured creditors who is owed £9,600
(ii) How much is owed to an unsecured creditors who is paid £3,700.
Question – 8 (4-2012)
(a) In each of the following two bankruptcies calculate the rate in the pound paid to unsecured creditors,
and the amount received by an unsecured creditor who is owed £ 15,000.
(i) Bankruptcy X: An unsecured creditor who is owed £34,500 is paid £14,145
(ii) Bankruptcy Y: The total liabilities are £141,800, of which £95,300 is owed to secured creditors. The
total assets available for creditors are £110,180.
(b) In another bankruptcy, Bankruptcy Z, an unsecured creditor who was owed £39,000 received £2,535.
The company owed a total of £257,000 to unsecured creditors and £145,000 to secured creditors. The
expenses of winding up the business were £9,395.
Calculate the value realized for the assets of the business.
Question – 9 (2-2013)
Chung is owed £8,500 by Trader T, who is declared bankrupt.
Chung finds he is an unsecured creditor and eventually receives only £1,870 in payment.
Calculate:
(a) The rate in the £ which is payable to unsecured creditors
(b) The amount received by an unsecured creditor who is owed £5,450
(c) The amount owed to an unsecured creditor who is paid £6,160.
38
The total owed to unsecured creditors by Trader T is £120,000.

She also owes £50,000 to secured creditors
The expenses of winding up the business are £6,900.
(d) Calculate the value of the trader’s assets achieved at liquidation
(e) Express this value of the assets as a percentage of the liabilities before liquidation
Question – 10 (3-2013)
A bankrupt trader owed £87,500 to her creditors, of which £28,100 was secured against assets. The assets
of the business raised £52,500, out of which £4,204 was paid in fees during the process of bankruptcy.
(a) Calculate the ratio of assets, before fees, to liabilities, in its simplest terms.
(b) Calculate:
(i) The amount available for unsecured creditors after payment of fees
(ii) How much in the £ was paid to the unsecured creditors
(iii) How much was paid to an unsecured creditors who was owed £5,500
The assets of the business at the time of bankruptcy were as follows:
Asset Value realized
(£)
Cash in hand 72
Machinery 8,500
Office equipment 3,060
Vehicles 11,950
Plus stock
(c) Calculate the value realized for the stock.
Question – 11 (4-2013)
In bankruptcy A, unsecured creditors receive £0.40 in the pound.
A lender is owed £250,000, of which 30% is secured against assets.
(a) Calculate:
(i) the amount received by the lender as a secured creditor
(ii) the amount received by the lender as an unsecured creditor
In bankruptcy B:
the total liabilities are £820,000
the amount owed to secured creditors is £395,000
an unsecured creditor who is owed £60,000 receives £21,000
the expenses of winding up the business are £11,250.
(b) Calculate:
(i) the rate in the pound payable to unsecured creditors
(ii) how much is owed to unsecured creditors
(iii) the total assets realised
Lucy is owed £44,000 as an unsecured creditor in bankruptcy C, which pays £0.17 in the pound to
unsecured creditors.
She is also owed £76,700 in bankruptcy D, as the sole secured creditor.
The total assets of D, after winding up expenses, realized £28,500
(c) Calculate how much Lucy receives in total.
39
Question – 12 (2-2014)
(a) In each of the following two bankruptcies, A and B, calculate the rate in the pound paid to unsecured
creditors and the amount owed to an unsecured creditor who is paid £7,500.
(i) Bankruptcy A: An unsecured creditor who is owed £22,500 is paid £6,750.
(ii) Bankruptcy B: The total liabilities are £184,000 of which £125,000 is owed to secured creditors. The
total assets available for creditors after winding up expenses total £148,600.
(b) In Bankruptcy C, an unsecured creditor who was owed £22,000 received £3,520.
The company owed a total of £87,000 to unsecured creditors and £45,000 to secured creditors.
Calculate the total assets available for creditors after winding up expenses.
Question – 13 (3-2014)
The following information relates to the business of a bankrupt trader.
£
Cash in hand 280
Trade creditors 212,000
Value of machinery 32,400
Bank overdraft ?
Value of stock 15,900
Value of office equipment 8,300
Value of vehicles ?
The trader’s total assets are 120,180.
(a) Calculate the value of vehicles.
The trader’s total liabilities are £237,000, including winding up expenses of £7,000.
(b) Calculate the amount owed to the bank in the form of a bank overdraft.
£32,000 of the liabilities is owed to secured creditors and must be paid first and in full.
The winding up expenses must also be paid in full.
(c) Calculate:
(i) the rate in the £ that an unsecured creditor will receive
(ii) the amount owed to an unsecured creditor who receives £4,305
(iii) the total amount paid to a creditor who is owed £9,000, of which half is secured
Question – 14 (4-2014)
A bankrupt trader owes £29,500 to fully secured creditors and £118,000 to unsecured creditors.
The assets of the business realised £88,500.
(a) Express the business assets as a percentage of the liabilities.
(b) State how much will be paid to the unsecured creditors.
(c) Calculate how much in the £ will be paid to the unsecured creditors.
In another bankruptcy, £0.395 in the £ was paid to unsecured creditors.
(d) Calculate:
(i) how much was paid to an unsecured creditor who was owed £34,600
(ii) how much was owed to an unsecured creditor who was paid £15,800
40
Question – 15 (2-2015)
The following table summarises the bankruptcy of two companies.
Company A Z
£ £
Assets
Total assets available for creditors 520,000 ?
Liabilities
Total owed to secured creditors 403,000 ?
Total owed to unsecured creditors 450,000 350,000
Total liabilities ? 690,000
Distribution of Assets
Assets available for unsecured creditors ? ?
Rate in the pound paid to unsecured creditors ? 0.41
(a) Calculate, for Company A, the:
(i) total liabilities
(ii) assets available for unsecured creditors
(iii) rate in the pound paid to unsecured creditors
(iv) amount owed to an unsecured creditor who is paid £22,100
(v) total assets as a percentage of the total liabilities
(b) Calculate, for Company Z, the total assets available for creditors.
Question – 16 (3-2015)
(a) In the bankruptcy of Trader T, the total assets available for creditors were £104,368. The total liabilities
were £171,580 of which £22,220 was owed to secured creditors.
Calculate:
(i) how much is owed to unsecured creditors
(ii) the assets available for unsecured creditors
(iii) the rate in the pound paid to unsecured creditors
(b) In the bankruptcy of Trader U, the total liabilities were £194,850. After paying secured creditors, the
assets available for unsecured creditors were £69,930 which provided a rate of 60p in the pound for
payment to unsecured creditors
Calculate:
(i) how much is owed to unsecured creditors
(ii) how much is owed to secured creditors
(iii) the total assets available for creditors
Question – 17 (4-2015)
Bankrupt Trader T owed £15,200 to secured creditors and £279,800 to unsecured creditors.
The assets of the business realised £94,400.
(a) Calculate the business assets as a percentage of the liabilities.
The cost of winding up the business was £9,250 and this is an additional secured expense.
(b) Calculate the:
(i) total now owed to secured creditors
(ii) total paid to secured creditors
(iii) total paid to unsecured creditors
(iv) dividend paid to unsecured creditors, expressed as a rate in the pound
(v) amount paid to an unsecured creditor who is owed £17,820
41
Question – 18 (3-2019)
Fallito Farms is a bankrupt company in Italy that owes 94,250€ (euro) to fully secured creditors and 89,000€
to unsecured creditors.
(a) The assets of the business realised 125,400€.
(i) Express the business assets as a percentage of the liabilities.
(ii) Calculate how much will be paid in total to the unsecured creditors.
(iii) Calculate the dividend rate to be paid to unsecured creditors.
A Spanish services firm, Arruinado Architects, became bankrupt owing money to several creditors including
Juan and Maria. Only one of them is, in part, a secured creditor.
Juan is owed 12,000€ and is paid 6,645€.
Maria is owed 26,000€ and is paid 9,620€.
(b) State which of them is, in part, a secured creditor. Explain how you know this.
(c) Calculate:
(i) the rate in the euro paid to an unsecured creditor
(ii) how much is owed to one of them as a secured creditor.
42
Chapter – 7
Fixed Assets and Depreciation
Question – 1 (3-2008)
A factory owner buys two machines. Machine A costs £1,060,000 and is estimated to have a life of 4 years
and a scrap value of £20,000.
Using the equal installment method:
(a) Calculate the percentage of the cost to be written off each year. Give your answer correct to 3
significant figures.
(b) Prepare a depreciation schedule that shows:
(i) The annual depreciation for each year
(ii) The accumulated depreciation for each year
(iii) The book value at the end of each year.
Machine B is depreciated by the equal installment method over 6 years. It has the same scrap value as
machine A. It also has the same book value at the end of year one as machine A.
(c) Calculate the original cost of machine B.
Question – 2 (4-2010)
A trader buys machinery costing £19,900. He expects it will last for 7 years and have a scrap value of
£1,000. He uses the straight line (equal installment) method of depreciation and depreciates by a full year in
the year of purchase and nothing in the year of disposal.
(a) Prepare the depreciation schedule for the first 3 years to show annual depreciation, accumulated
depreciation, and the book value at the end of each year.
After 3 years, the trader reconsiders the lifetime of the machine. He now believes that new development in
technology mean that it must be replaced in a further two years, at which time it will have a scrap value of
£1,500. He recalculates the depreciation for the fourth and fifth years, again using the straight line method.
(b) Calculate:
(i) The revised amount of depreciation for year 4
(ii) The increase in annual depreciation from year 3 to year 4
Question – 3 (2-2002)
A communications system is purchased for £595,000. It is expected to have a working life of 3 years, after
which the scrap value is expected to be £50,000.
(a) Using the diminishing balance method, calculate the rate of deprecation.
(b) Prepare a deprecation schedule that shows:
(i) The amount of depreciation each year
(ii) The accumulated depreciation each year
(iii) The book value at the end of each year.
(c) In part (b), the book value at the end year 3 may not be exactly £50,000. Explain why this would not be
a problem.
43
Question – 4 (3-2007)
A machine that costs £195,000 is estimated to have a life of 4 years and a scrap value of £5,000.
(a) Using the reducing balance method, calculate the rate of depreciation and show your workings.
(b) Using the reducing balance method and a rate of depreciation of 60%:
(i) Copy and complete the following depreciation schedule:
Year Yearly Cumulative Book Value

Depreciation Depreciation At Year End
0 195,000
1 ? 117,000 78,000
2 46,800 163,800 ?
3 18,720 ? ?
(ii) Calculate the book value at the end of year 4.
Question – 5 (2-2012)
A factory machine cost £9,500,000. It is depreciated by the equal installment method. After 3 years, its book
value is £5,600,000.
Calculate:
(a) The amount of depreciation each of the first 3 years
(b) The percentage of the original cost depreciated in each of the first 3 years
(c) The depreciation in the third years as a percentage of the book value after 2 years
(d) The expected life of the machine at this rate of depreciation
(e) The rate of depreciation by the diminishing balance method over the first 3 years that would achieve the
same book value at the end of 3 years
Question – 6 (4-2012)
Factory F buys two machines, Machine A costs £95,500 and is estimate to have a life of 4 years and a scrap
value of £7,500. It is depreciated by the equal installment method.
(a) Using the equal installment method, calculate:
(i) The percentage of the cost to be written off during the first year
(ii) The book value after one year
(iii) The accumulated depreciation after three years.
Machine B is depreciated by the equal installment method over five years. It has the same scrap value as
machine A. It also has the same book value at the end of one year as machine A.
(b) Calculate the cost of machine B.
Factory G buys Machine C for £120,000, and depreciates it by the reducing balance (diminishing balance)
method with an annual rate of depreciation of 44%.
(c) Calculate the book value of Machine C after 2 years
44
Question – 7 (3-2013)
Machine A has an initial cost of £290,000 and is depreciated by the equal installment method, at the rate of
£35,000 per year until the book value is less than £35,000.
Calculate, for machine A:
(a) The book value at the end of one year
(b) The anticipated life as a whole number of years
(c) The residual value at the end of that period
Machine B is depreciated by the diminishing balance method.
It has an initial cost of £450,000 and a book value after one year of £270,000
Calculate, for machine B:
(a) The rate of depreciation
(b) The book value after 2 years
(c) The amount of depreciation expected during year 3.
Question – 8 (2-2013)
A factory machine that costs £4,600,000 is expected to have a life of 5 years and a scrap value of
approximately £300,000.
Depreciation is first calculated on the basis of the equal installment method.
Using this method it is expected to depreciate each year by 18.7% of its original value.
Calculate:
(a) the amount of depreciation each year
(b) the book value after 3 years
(c) the total depreciation over the period of the first 3 years
As an alternative, depreciation is calculated on the basis of the diminishing balance method.
Using this method it is expected to depreciate each year by 42.5% of its value at the start of that year.
(d) Calculate:
(i) the amount of depreciation in the first year
(ii) the book value after 3 years
(e) State, with workings, the method for which the scrap value is closest to £300,000.
Question – 9 (4-2013)
Machine A costs £195,000 and is estimated to have a life of four years and a scrap value of £15,000. It is
depreciated by the equal installment method.
(a) (i) Calculate the annual depreciation.
(ii) Prepare a depreciation schedule for years 0 to 4 that shows:
the annual depreciation
the accumulated depreciation
the book value at the end of each year.
Machine B is depreciated by the reducing balance (diminishing balance) method.
The depreciation schedule for the first three years is as follows:
Annual Accumulated Book value
depreciation depreciation at end of year
£ £ £
Year 0 (Initial cost) ?
Year 1 72,000 ? ?
Year 2 39,600 111,600 48,400
Year 3 21,780 133,380 26,620
45
(b) Calculate:
(i) the accumulated depreciation in year 1
(ii) the book value at the end of year 1
(iii) the initial cost of machine B
(iv) the annual rate of depreciation
Question – 10 (2-2014)
A factory machine costs £500,000 and is expected to have a life of 5 years.
A calculation is made of depreciation using the diminishing balance method.
On this basis it is expected to be worth 65% of its original value after one year.
(a) State the rate of depreciation.
(b) Prepare a depreciation schedule, based on the diminishing balance method for the 5 years, that
shows for each year:
(i) the annual depreciation
(ii) the accumulated depreciation at the end of the year
(iii) the book value at the end of the year
A calculation of depreciation is then made based on the equal installment method, with a residual value of
£50,000 at the end of the 5-year period.
(c) Calculate the annual depreciation.
(d) Prepare a depreciation schedule, based on the equal installment method for the 5 years, that shows
for each year:
(i) the accumulated depreciation at the end of the year
(ii) the book value at the end of the year
(e) State which method shows the highest book value at the end of year 1, and by how much
Question – 11 (3-2014)
A factory machine that costs £185,000 is estimated to have a life of four years and a scrap value of £10,000.
(a) Using the equal installment method, calculate:
(i) the percentage of the cost that must be written off in total over four years
(ii) the percentage of the cost to be written off in the first year
(iii) the book value after two years
(b) Using the reducing balance method, calculate:
(i) the annual rate of depreciation
(ii) the book value after two years
Question – 12 (4-2014)
Machine A costs €150,000 and is estimated to have a life of four years and a scrap value of €5,000.
(a) Using the diminishing balance method, show that the rate of depreciation is approximately 57%. Show
all your working, and provide a more accurate percentage value.
(b) Using a rate of depreciation of 57%, copy and complete the following depreciation schedule for Machine
A, inserting the missing figures.
Year Yearly Depreciation Cumulative Book value at year end
(€) depreciation (€) (€)
0 150,000
1 ? 85,500 64,500
2 36,765 122,265 ?
3 15,809 ? ?
4 ? ? 5,128
46
Machine B is depreciated by the diminishing balance method, and has the following book values:
At the end of year 2 £220,000
At the end of year 3 £110,000
It has a scrap value of approximately £7,000.
(c) Calculate the:
(i) book value of Machine B at the end of year 4
(ii) original cost of Machine B
(iii) expected life of Machine B
Question – 13 (2-2015)
Manufacturer M buys two machines, A and B. Machine A costs £135,000 and is estimated to have a life of
five years and a scrap value of £15,000. It is depreciated by the equal installment (straight line) method.
(a) Using the equal installment method, calculate the:
(i) total amount to be written off over the lifetime of the machine
(ii) amount to be written off in the first year
(iii) book value after one year
(iv) accumulated depreciation after three years
Machine B is depreciated by the equal installment method over four years. It has the same scrap value of
£15,000 as Machine A. It also has the same book value at the end of one year as Machine A.
(b) Calculate the original cost of Machine B.
Manufacturer N buys Machine C for £150,000 and depreciates it by the reducing balance (diminishing
balance) method with an annual rate of depreciation of 44%.
(c) Calculate the book value of Machine C after two years.
Question – 14 (3-2015)
Derek and Clive find the following depreciation table for an item with a life of 4 years, with most figures
missing.
Year Depreciation Cumulative Book value
for each year depreciation at year end
0 - - Initial cost
1 37,500
2
3 13,500
4 Scrap value
Derek completes the table based on the equal installment method.

(a) Complete Derek’s table for years 0 to 4.
Derek and Clive then calculate the depreciation rate based on the reducing balance method.
Derek gives a figure of 36%, and Clive gives a figure of 40%.
(b) Provide a calculation to show which of them is correct using the figures provided in the table above.
(c) Using the reducing balance method and the correct figure for the rate of depreciation, calculate the:
(i) scrap value
(ii) initial cost
(iii) depreciation in year 1
47
Question – 15 (4-2015)
Factory Machine F is depreciated by the equal installment method.
The book value of Factory Machine F is £580,000 at the end of year 1, and is £160,000 at the end of year 4.
(a) Calculate, for Factory Machine F, the:
(i) annual depreciation
(ii) initial cost
(iii) estimated scrap value at the end of year 5
Factory Machine M is depreciated by the diminishing balance method.
The book value of Factory Machine M is £580,000 at the end of year 1, and is £160,000 at the end of year 4.
(b) Calculate, for Factory Machine M, the:
(i) annual rate of depreciation
(ii) book value at the end of year 2
(iii) estimated scrap value at the end of year 9
Question – 16 (3-2019)
Hobart Wholefoods Ltd manufactures health foods in Australia. The company buys a new machine for
crushing wheat grains. The machine costs AU$9,400,000.
It is depreciated by 23% of its value each year, using the reducing balance method of depreciation.
(a) Prepare a depreciation schedule for the first 4 years showing annual depreciation, accumulated
depreciation and book value at the end of each year.
(b) Calculate the:
(i) amount of depreciation that occurs in the 6th year
(ii) book value at the end of 7 years
(iii) amount of depreciation that occurs in the 9th year.
A second machine for sterilising foods is depreciated for 6 years by the equal instalment method. The
annual depreciation is AU$52,575 and the machine will finally be sold for a scrap value of AU$26,000
(c) Calculate the original cost of this machine.
48
Chapter – 8
Index Number
Question – 1 (2-2000)
An index of retail prices in a particular country is show below:
Index 1995 1996 1997 1998
1980= 100 258 270 277 285
(a) Give a brief interpretation of the 1998 index number, as if explaining it to a client.
(b) Calculate a revised index with a new base year of 1995=100.
An index of industrial production is shown below:
1997 (1995=100) 1999 (1997=100)
109 103
(c) (i) Calculate the index of industrial production for 1999 with 1995 as the base year.
(ii) Give a brief interpretation of your answer.
Question – 2 (2-2002)
An index has had the following values over the period 1998 to 2001, with 1998 as the base year:
1998 1999 2000 2001
100.0 103.9 107.5 111.0
(a) Calculate these indices as a chain base index. Give each answer correct to one decimal place.
(b) Give a brief interpretation of the index figure of 107.5 in section (a)
The following is a section of a chain base index:
1998 1999 2000 2001
104.2 103.8 103.7 99.1
(c) Calculate index values for these years based on 1998=100.
Question – 3
Company A sells Product P with the following prices:
Year 2003 2004 2005 2006
Price ($) 40.96 46.08 57.60 50.40
(a) Calculate the prices of Product P for years 2004 to 2006 as a chain base index.
(b) Giving your answers correct to four significant figures, calculate the index of prices for Product P for the
years 2003 to 2006 with year 2003 as the base year.
The price relative for Product P for year 2003 with 2002 as the base year is 1.28.
(c) Calculate the selling price of Product Pin year 2002.
49
Question – 4
Company A sells Product P with the following prices
Year 2002 2003 2004 2005
Price (£) 10.24 12.80 15.20 17.10
(a) Calculate the prices of Product P for years 2003 to 2005 as a chain base index.
(b) Giving your answers correct to four significant figures, calculate the index of prices for Product P for the
years 2002 to 2005 with year 2002 as the base year.
(c) The price relative for year 2002 with 2001 as the base year is 1.28.
Calculate the selling price of Product P in year 2001.
Question – 5 (2-2001)
An index of retail prices at January 2000 is shown below:
Group Weight Index (Jan 1995 =100)
Food 170 162.0
Housing 212 189.7
Fuel and light 56 150.8
Durable household goods 102 133.2
Clothing and footwear 49 157.7
Transport 115 141.4
(a) Giving your answers to the nearest whole number, calculate the overall index of retail prices with
January 1995 = 100.
(b) Give an explanation of your answer to part (a) in terms of a percentage increase or decrease.
The index has had the following values over the period 1995 to 1999, with 1995 as the base year.
1995 1996 1997 1998 1999
100 110.0 118.8 134.5 147.2
(c) Calculate these indices as a chain base index. Give each answer correct to one decimal place.
Question – 6 (4- 2001)

An index of retail prices at January 2001 is shown below:
Group Weight Index (Jan 2000=100)
Food 180 98.3
Housing 221 101.7
Fuel and light 48 104.4
Durable household goods 99 97.9
Clothing and footwear 37 100.8
Transport 131 102.6
(a) A statistician calculates the weighted index for the above table to be 100.6. She wishes to know the
effect of the reduction in food costs on the index.
Calculate the weighted index for the above items that are not Food.
(b) Comment on your answer to part (a) in terms of a percentage increase or decrease.
An index of industrial production is shown below:
1997 2000
(1995=100) (1997=100)
111 107
50
(c) (i) Calculate the index of industrial production for 2000 with 1995=100.
(iii) Give a brief interpretation of your answer.
Question – 7 (2-2012)
An index of production has the following values, based on year 2008=100.
Year 2008 2009 2010 2011
Index 100 115.0 92.0 96.6
(a) Explain the percentage change that occurred between 2008 and 2011
(b) Calculate the indices for 2010 and 2011 as a chain base index
(c) Calculate the percentage change in production from 2009 to 2011
The production in 2007 was 15% lower than in 2008.
(d) State the index for 2007, with 2008 as the base year
(e) Calculate the index for 2008, with 2007 as the base year.
Question – 8 (2-2013)
(a) Company M sold 68,000 monitors in year 2011 and 78,880 monitors in year 2012.
Calculate the quantity relative for year 2012 with 2011 as the base year.
(b) The number of monitors sold by Company M fell by 15% from year 2010 to year 2011.
(i) Express the quantity sold in 2011 as a quantity relative based on year 2010.
(ii) Calculate the number of monitors sold in 2010.
(c) In year 2012 Company M cut the price of its monitors by 5% of the year 2011 price.
Express the income from sales of monitors in 2012 as an index, based on the income from sales of
monitors in year 2011 = 100.
(d) The cost of components for the monitors sold by Company M was as follows:
2011 £70 per monitor
2012 £75 per monitor
Calculate the average cost of components per monitor sold in the period 2011 to 2012 inclusive.
Question – 9 (3-2013)
An index of retail prices at January 2013, based on January 2000 =100, is shown below:
Group Weight Index Weight x Index
Food ? ? ?
Housing 299 221.0 66,079.0
Fuel and light 121 230.7 27,914.7
Durable household goods 152 166.0 25,232.0
Clothing and footwear 61 148.6 9,064.6
Transport 187 205.1 38,353.7
1,000 201,798.0
The totals include the missing figures for Food.
A statistician calculates the weighted index for the above completed table to be 201.8.
Calculate:
(a) the missing figure for Weight for Food
(b) the missing figure for Weight x Index for Food
(c) the missing figure for Index for Food
(d) the weighted index for the above items that are not Food
51
(e) the percentage increase in the weighted index when Food is not included compared to when it is
included.
Question – 10 (2-2014)
Company X sold 85,000 units of item A in 2010 and 95,200 units in 2011.
(a) Calculate the quantity relative for item A for 2011 with 2010 as the base year.
Company X sold item B at £2.40 in 2010, and at an increased price in 2011. The price relative for item B for
year 2011 with a base year of 2010 was 1.025
(b) Calculate the selling price for item B in 2011.
The following table shows the prices and sales for both items in 2010 and 2011. Some figures have been
omitted.
Item A 2010 2011
Price(£) Sales(units ) Price (£) Sales(units)
2.80 85,000 2.66 95,200
Item B 2010 2011
Price(£) Sales(units) Price (£) Sales(units)
2.40 ? ? ?
The quantity relative for sales (units) of item B for 2011 with 2010 as the base year was 1.2
(c) Explain the quantity relative for item B as a percentage change from 2010 to 2011.
State the percentage increase or decrease and what has changed.
(d) Calculate the:
(i) price relative for item A for 2011 with 2010 as the base year
(ii) index for total value of sales for item A for 2011 with 2010 as the base year
(iii) index for total value of sales for item B for 2011 with 2010 as the base year
Question – 11 (3-2014)
A company sells Product P with the following prices and numbers of units sold:
Year 2010 2011 2012
Sales (units) 250,000 225,000 252,000
Price £20.00 £21.40 £19.90
Calculate:
(a) the index of sales (units) for Product P for each of the years 2011 and 2012, with year 2010 as the base
year
(b) the chain base index for the price of Product P for the years and figures shown
(c) the sales (units) in year 2013 if the chain base index for sales (units) in 2013 is 105
(d) the index of sales (pounds sterling) for Product P for each of the years 2011 and 2012, with year 2010
as the base year
Question – 12 (4-2014)
An index of production had the following values over the period 2010 to 2013, with 2010 as the base year.
2010 2011 2012 2013
100 120.0 126.0 138.6
(a) Give a full interpretation of the index figure of 126.0 above.
(b) Calculate these indices as a chain base index.
52
The following is a section of a chain base index.

2010 2011 2012
105.2 103.9 98.9
(c) Calculate index values for these three years, with 2010 as the base year.
Give each answer to an appropriate degree of accuracy.
(d) Calculate the weighted average cost per item on a purchase of 350 items, if 200 of the items cost €6.23
each and the remaining 150 items cost €5.95 each.
Question – 13 (2-2015)
An index of production had the following values over the period 2011 to 2014, with 2011 as the base year
2011 2012 2013 2014
100.0 115.0 110.4 115.0
(a) Calculate these indices as a chain base index. Give your answers to an appropriate degree of accuracy.
(b) Calculate the weighted average cost per item on a purchase of 300 items, where:
100 of the items cost $5.13 each
the remaining items cost $4.95 each.
(c) Kelly purchased 50 units of Product A at £3.60 each, and a further 40 units of Product A at a different
price per unit. The average cost per unit was £3.56
Calculate the:
(i) total cost to Kelly
(ii) cost per unit of the further 40 units
Question – 14 (3-2015)
A company sells Product P with the following prices and numbers of units sold:
Year 2010 2011 2012 2013 2014
Sales (units) 225,000 250,000 215,000 240,000 300,000
Price per unit £50 £45 £48 £49.50 £42
Calculate the:
(a) index of sales (units) for Product P for each of the years 2012, 2013 and 2014, with year 2011 as the
base year
(b) index of sales (units) for Product P for year 2010, with year 2011 as the base year
(c) price relative for year 2013, with year 2011 as the base year
(d) index of sales value (pounds sterling) for Product P for year 2014, with year 2011 as the base year
(e) percentage increase in sales value (pounds sterling) for Product P from year 2010 to year 2013
Question – 15 (4-2015)
Company A sells 30,000 units of Item B at £4.80 per unit in 2012, and 36,000 units of Item B at £6.00 per
unit in 2013.
(a) Calculate the following values for Item B for 2013 with 2012 as the base year:
(i) quantity relative for unit sales
(ii) price relative for unit prices
(iii) index of total sales value
53
The index for unit sales of Item B for 2014 with 2013 as the base year is 115.
(b) (i) Calculate the unit sales of Item B for 2014.
(ii) Write out the chain base index for unit sales of Item B for the years 2013 and 2014.
The price relative for unit prices of Item B for Company A for 2012 with 2000 as the base year is 1.6.
(c) Calculate the unit price of Item B in the year 2000.
Question – 16 (3-2019)
The largest exports from Malaysia in January 2019 are shown below.
Product group Weight Index
(Jan 2018 = 100)
Palm oil products 101 82.7
Electrical/electronic products 645 108.2
Timber products 39 104.7
Energy products
Liquid natural gas 98 137.5
Refined petroleum 70 70.1
Crude petroleum 47 98.9
(a) Calculate the overall weighted index of exports in January 2019, with January 2018 = 100, for all
products together.
Give your answer correct to one decimal place.
(b) Calculate the weighted index for Energy products only in January 2019, with January 2018 = 100
Give your answer correct to one decimal place.
The international price of liquid natural gas per MMBtu has varied over the past five years. The commodity
price in US dollars (US$) in January of each year has the following values.
Year 2015 2016 2017 2018 2019
Price (US$) per MMBtu 3.10 2.42 3.11 3.39 2.82
(c) (i) Calculate a price index for each of the five years, using 2015 as the base year.
The figures are recalculated as a chain base index.
(ii) Calculate the new chain base index figure for 2019 only.
54

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U Win Bo Myint Advance Business Calculation LCCI-Level 3

Date Details Debit (£) Credit (£) Balances (£)

Supply the missing figures.

Less drawings (9,400) 132,800

During 2014, the following information related to Trader Y:

(a) Calculate the cost of Project One.

Calculate the expected length of Project Q in years.

(i) Calculate the payback period of Project R.

(c) Calculate the expected average rate of return of Project Q.

The assets of the business at the time of bankruptcy were as follows:

The total owed to unsecured creditors by Trader T is £120,000.

Year Yearly Cumulative Book Value

Derek completes the table based on the equal installment method.

Question – 6 (4- 2001)

The following is a section of a chain base index.

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