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40901 Finance I:
Tutorial Two
SOLUTIO
NS
Q1. You have £10,000 in a savings account that pays interest annually of 8 per cent and you plan to reinvest your interest payments. You decide to add £2,000 per annum to this savings account at the end of each of the next five years. How much will you have in the account at the end of the fifth year, immediately after you pay in the £2,000 for that year?
YEAR NCF FVF FV(5)
0 10000 1.4693 14693.
1 2000 1.3605 2720.
2 2000 1.2597 2519.
3 2000 1.1664 2332.
4 2000 1.0800 2160.
5 2000 1.0000 2000.
Future Value 26426.
Alternatively: FV = 10000 * FVF(5,8%) + 2000 * FVAF (5,8%) FV = 10000 * 1.4693 + 2000 * 5.8666 = 26426
Q2. A credit card company specifies that it charges an annual rate of interest of 13 per cent but this is compounded monthly. A customer has an outstanding balance of £1,000 at the beginning of the year. Each month £80 of purchases are made on the card whilst payments of £150 are made to the credit card company. Determine the balance at the end of the year.
A net payment of £70 per month is made, and the year end or future value of
these payments can be determined. This sum can then be deducted from the future value of the opening balance. The monthly interest rate is 13/12% or 1.08333%
Balance at year end = 1,000 x FVF(12,1.083%) ‐ 70 x FVAF (12,1.083%)
= 1000 * 1.1380 ‐ 70 * 12.
= 1138.03 ‐ 891.
annual payments of £8,000. The leasing company will take back the machine after six years. The company’s production manager estimates that the machine’s value after six years is likely to be about £4,000. Is the leasing proposal acceptable if the company’s rate of interest is 10 per cent?
The real cost of purchase price of the machine is the initial outlay minus the present value of the expected resale proceeds
Net purchase cost = £40000 ‐ £ 4000 * PVF (6,10%)
= £40000 ‐ £4000 * 0.
= £37,742.
The leasing cost is the present value of the lease payments
= £5000 + £8000 * PVAF (6,10%)
= £5000 + £8000 * 4.
= £39842.09 Decision: purchase the machine
Q5. A senior manager has three years to go to retirement and is reluctant to accept additional responsibilities at this stage of his career. He has been asked to re‐organise the company’s training activities and has been offered a salary increase of £5,000 per annum as an inducement. It is pointed out to him that as his pension will be equal to 50 per cent of his salary over the last three years of employment the salary increase understates the benefits of accepting the additional responsibility. Assuming an interest rate of 6 per cent and an expected retirement period of 15 years determine the net present value of the inducement he is being offered and the effective annual increase in salary that this implies. Assume that all payments (cash flows) occur at the end of each year.
The present value of the expected increments in income and expected pension:
Time
1 ‐ 3
Incremental Earnings
5, 0
PVAF
PV
Time Incremental Earnings
PVAF (6%
PV
Equivalent annual increase in earnings for each of the next three years ie the equivalent annuity
for three years
= 33,751/PVAF 3/0.
Q6. Determine the minimum constant annual net cash flows for the next five years that will make an investment of £180,000 worthwhile if the required rate of return is 12 per cent.
NPV = 0 = ‐180,000 + X times PVAF 5/0.
= ‐180,000 + X 3.
Q8. Ms Shaw, the finance director of Petrie plc, is evaluating a proposed acquisition of Hogg plc.
Hogg plc is valued on the stock market at £160m and she believes that this is a fair value given the prospects of the company under its current management and its policies. To gain the approval of Hogg’s shareholders for the acquisition it will be necessary to make a cash offer of
£190 million. The £30 million premium needs to be covered by the expected costs savings that
Hogg’s more energetic and efficient management can secure in the running of Petrie’s operations in order to breakeven on the acquisition. Ms Shaw’s analysis suggests that annual savings of £3 million can be obtained in the running of one division and these savings can be assumed to be maintained indefinitely into the future. Another division offers scope for cost savings of £5 million per annum for the next ten years, but this requires expenditure on cost saving equipment that will cost £12 million. Ms Shaw’s analysis suggests that the acquisition and the various costs and benefits should be evaluated using a discount rate of 14 per cent. Does the acquisition appear to be capable of generating value on the terms outlined?
Compare present value of benefits with the costs of the premium
Time NCF PVF(14%) PV
1 → ∞ +3m 7.1429 21.429m
0 ‐12m 1.0000 ‐12.000m
1 → 10 +5m 5.2161 +26.
PV(benefits) = 35,
Q9. The Grampian Development Agency (GDA) is encouraging companies to set up new businesses by providing facilities at subsidised prices and allowing companies to acquire premises on deferred terms. Your company is interested in acquiring a building with a current market price of £100,000 and this would be made available for purchase at a price of £80,000 through the GDA. This can also be paid for by a series of six equal payments from the end of year four onwards. If your company decides to pay for the building on deferred terms an interest rate of
5 per cent per annum will be charged on the amount owing to the GDA. This interest rate is set below the prevailing commercial interest rate of 8 per cent that your company has to pay on its borrowing.
a) How much will the company owe the agency by the end of year three?
V 3 = 80,000 (1.05) 3 = 80,000 x 1.1576 = 92,
b) What will the constant annual payment have to be over years four to nine to pay off the loan?
V 0 = 92,610 = X PVAF6/.05 = X x 5.
X = 92,610/5.0757 = 18,
c) If the commercial rate of interest is 8 per cent determine the present value of the interest rate subsidy offered by the agency.
Calculate the present value of the series of payments at the commercial rule of interest of
8 per cent
V 3 = 18,246 x PVAF6/0.08^ = 18,246 x 4.
= 84,
V 0 = V 3 /(1 + 0.08) 3 = 84,349/ (1 + 0.08) 3 = 66959
The difference between the present value of these payments and the £80,000 is £13,
and constitutes the value of the interest subsidy.
d) If the commercial rate of interest is 10 per cent determine the present value of the interest rate subsidy offered by the agency.
- The Board of Directors of GMS Products plc have decided to sell one of its divisions, and the managers of this division have been negotiating terms for a management buyout. The company and the managers concerned have agreed a price of £4.0 million. The managers only have funds of £1.2 million available to invest, but have established that they can borrow £2.8 million from a bank at an interest rate of 14 per cent to cover the shortfall. The loan would be paid off in four equal annual instalments (covering interest on the outstanding balance as well as the repayment of the loan), at the end of each of the next four years. There is also the possibility of paying the company for the division on an instalment basis. The company has indicated that it is prepared to accept a down payment of £1.2 million and four annual payments of £840,000, but only if the buyout company continues to buy certain components from GMS Products for the next four years. The managers considering the buyout believe these components could be obtained more cheaply from another supplier, allowing them to save £100,000 per annum. Evaluate the financing possibilities and comment briefly on your analysis.
Cost of company’s instalment plan – assume opportunity cost of funds of 14 per cent
Year Cash Flow PVF (14%)
Present Value
Deposit 0 ‐1.20m 1.0000 ‐ 1.20m Loan Repayments
1 to 4 ‐0.84 2.
PV
3.65m
Add onto the present value of the payment to the company the added cost of the components.
Year Cash Flow PVF Present Value
Loan Savings 0 3.65 1.0000 3.65m
Added Costs 1 to 4 ‐0.1 2.9137 ‐0.
PV = ‐3.94m
The overall cost of the borrowing from the bank is £1.20m plus the value of the loan £2.80m, equal to £4.00m.
The arrangement with the company is preferable – it has a positive NPV £60,000 at the bank’s interest rate. Alternatively the annual payment to the bank can be derived, £2.80m/PVAF4/0.14^ =
£0.9610m and this compared with the payments to the company of loan repayment £0.84m
plus the added cost of components of £0.10m, giving £0.94m in aggregate. This is £0.0210m per annum less than the payments to the bank, taking the previous value (£0.021m times 2.4018) gives £0.016m. This is consistent with £60,000 calculated above when rounding errors are taken into account.
- Your company sells a machine for £22,000 and your marketing department would like to make this machine available for purchase on an instalment basis. Assume that there will be an initial payment of £4,000 followed by three equal instalments, to be paid at the end of years one to three. Determine the level at which the instalment should be set to allow the company to breakeven if the cost of funding the instalment programme will be 12 per cent.
Year Cash Flow PVF Present Value
Loan Offered 0 ‐ 18000 1.0000 ‐ 18000
Repayments 1 to 3 X 2.4018 18000
NPV 0
X is given by 18,000/2.4018 = 7494
