Answer 1 PRIVATE V PUBLIC SECTOR OBJECTIVES (a) Financial objectives
(i) State owned enterprise
(1) The overall objective is commonly to fulfil a social need.
(2) Because of problems of measuring attainment of social needs the government usually sets specific targets in accounting terms.
(3) Examples include target returns on capital employed, requirement to be self financing, cash or budget limits.
(ii) Private sector
(1) The firm has more freedom to determine its own objectives.
(2) A capital market quotation will mean that return to shareholders becomes an important objective.
(3) Traditionally financial management sees firms as attempting to maximise shareholder wealth. Note that other objectives may exist, e.g. social responsibilities, and the concept of satisficing various parties are important.
(b) Strategic and operational decisions
The major change in emphasis will be that decisions will now have to be made on a largely commercial basis. Profit and share price considerations will become paramount. The following are examples of where significant changes might occur.
Financing decisions. The firm will have to compete for a wide range of sources of finance. Choices between various types of finance will now have to be made, e.g. debt versus equity.
Dividend decision. The firm will now have to consider its policy on dividend payout to shareholders.
Investment decision. Commercial rather than social considerations will become of major importance. Diversifications into other products and markets will now be possible. Expansion by merger and takeover can also be considered.
Threat of takeover. If the government completely relinquishes its ownership it is possible that the firm could be subject to takeover bids.
Answer 2 CAPITAL MARKET EFFICIENCY
The efficient market hypothesis is often considered in terms of three levels of market efficiency.
(a) Weak-form efficiency (b) Semi-strong form efficiency (c) Strong-form efficiency.
The accuracy of the statement in the question depends in part upon which form of market efficiency is being considered. The first sentence states that all shares prices are correct at all times. If “correct” means that prices reflect true values (the true value being an equilibrium price which incorporates all relevant information that exists at a particular point in time), then strong-form efficiency does suggest that prices are always correct. Weak and semi-strong prices are not likely to be correct as they do not fully consider all information (e.g. semi-strong efficiency does not include inside information). It might be argued that even strong-form efficiency does not lead to correct prices at all times as, although an efficient market will react quickly to new relevant information, the reaction is not instant and there will be a short period of time when prices are not correct.
The second sentence in the statement suggests that prices move randomly when new information is publicly announced. Share prices do not move randomly when new information is announced. Prices may follow a random walk in that successive price changes are independent of each other. However, prices will move to reflect accurately any new relevant information that is announced, moving up when favourable information is announced, and down with unfavourable information. If strong-form efficiency exists, prices might not move at all when new information is publicly announced, as the market will already be aware of the information prior to public announcement and will have already reacted to the information.
Information from published accounts is only one possible determinant of share price movement. Others include the announcement of investment plans, dividend announcements, government changes in monetary and fiscal policies, inflation levels, exchange rates, and many more.
Fundamental and technical analysts play an important role in producing market efficiency. An efficient market requires competition among a large numb of analysts to achieve “correct” share prices, and the information disseminated by analysts (through their companies) helps to fulfil one of the requirements of market efficiency, i.e. that information is widely and cheaply available.
An efficient market implies that there is no way for investors or analysts to achieve consistently superior rates of return. This does not say that analysts cannot accurately predict future share prices. By pure chance some analysts will accurately predict share prices. However, the implication is that analysts will not be able to do so consistently. The same argument may be used for corporate financial managers. If, however, the market is only semi-strong efficient, then it is possible that financial managers, having inside information, would be able to produce a superior estimate of the future share price of their own companies and that, if analysts have access to inside information, they could earn superior returns.
Answer 3 BASIC DISCOUNTING
(a)
(i)
0.621) (70
0.683) (60
0.751) (50
0.826) (40
0.909) (30
× + ×
+
× + ×
+ ×
= $182
(ii)(30 × 1.736) + (50 × (3.791 – 1.736)) = $155
(iii)((50 + 60) × 0.909) + (70 × 0.826) + (80 × 0.751) = $222
(b) (i) $500 × 5.019 = $2,510
(ii)$500 × (5.019 × 0.870) = $2,183
(iii)$500 × (4.772 + 1) = $2,886
(c) (i) $15,000 ÷ 4.329 = $3,465
(ii)$15,000 ÷ (4.329 × 0.952) = $3,640
(iii)$15,000 ÷ (3.546 + 1) = $3,300
(d) (i) $1,500 ÷ 0.10 = $15,000
(ii)($1,500 ÷ 0.10) × 0.683 = $10,245
(e) $500 ÷ 0.482 = $1037
Answer 4 ELVIRA CO PLC (a) Payback period
A $100,000/$40,000 = 2.5 years (or 3 years, if cash flows arise at year end)
B After 4 years net position is $120,000-$40,000 = $80,000 negative. Payback = 4 years + $80,000/$200,000 = 4.4 years
C After one year cash $50,000 negative. Payback = 1 + $50,000/$80,000 = 1.6 years
(b) Accounting rate of return
A Total profit = total inflow – total depreciation = 160 - (100-10) = 70 Average profit = 70/4 = 17.5
Average investment = (cost + residual value)/2 = (100+10)/2 = 55 ARR = 17.5/55 = 31.8%
Answer 5 KHAN LTD
(a) NPV and IRR calculations
Promotion method NPV IRR
(ii) Internal rate of return
NPV = – 100 + 255 (1 + r)-1 – 157.5 (1 + r)-2 = 0
Solving this quadratic equation for “r” to find the internal rate of return (note – it is not likely that you will be required to solve quadratic equations under
Alternative 2
(i) Net present value
Cash 20% Present flow discount value $000 factor $000 Year 0 (50) 1.000 (50.00)
Year 1 0 0.833 0
Year 2 42 0.694 29.15 Year 3 42 0.579 24.32 ———
Net present value 3.47
——— (ii) Internal rate of return
The internal rate of return is estimated using linear interpolation.
Using a 20% discount rate (see above), the cash flow has an NPV of $3,470.
Using a 25% discount rate, the NPV of the cash flow is as follows.
Cash 25% Present
flow discount value
$000 factor $000
Year 0 (50) 1.000 (50.00)
Year 1 0 0.800 0
Year 2 42 0.640 26.88
Year 3 42 0.512 21.50
———
Net present value (1.62)
———
Therefore, the IRR (the discount rate that reduces net present value to zero) lies between 20% and 25%.
IRR ≈ 0.
(
)
620 ,1 470 , 3470 , 3 20
+
+ × (0.25 – 0.2) = 0.234
The internal rate of return is approximately 23%.
(b) Choice of project
However, it would be unwise to make the final decision solely on the basis of these calculations without investigating the risk attached to each alternative and the marketing and manpower factors that may be involved. For example, the heavy advertising characteristic of Alternative 1 may have a beneficial spin-off for the company’s other products, or the widespread use of agents with this alternative may again benefit the promotion of other products imported by Khan Ltd. In terms of the risk aspects, it may be judged that novelty products generally are high risk short-lived undertakings and that Alternative 1, which promotes the product for only a single year, may be a less risky approach than Alternative 2, which appears to extend the life by a further one or two years. In addition, there are innumerable other considerations which may be relevant to the decision, such as whether the promotion of this particular novelty product will adversely affect other products sold by the company.
The internal rates of return of the two alternatives have been ignored in formulating the decision advice for two main reasons. The first is that Alternative 1 has two internal rates of return, one above, the other below, the required rate. This conflicting investment advice clearly indicates that the use of internal rates of return is an unreliable (and unhelpful) investment decision guide.
The second reason for rejecting the IRR approach is more theoretical, but still valid for practical decision-making. It is that the decision rule selects between mutually-exclusive alternatives on the assumption that the opportunity cost of any investment’s cash flow is equal to the internal rate of return of that investment.
This can easily be demonstrated to be a fallacious assumption, as the opportunity cost of cash generated by a project is (or should be) reflected by the firm’s cost of capital at the time of generation, certainly not (except by chance) by the internal rate of return of the generating project.
In these terms the internal rate of return of a project can be seen as little more than an arithmetic artefact that has little economic rationale behind it, and is therefore an unreliable decision-making guide. Mr Court’s views are important and are commented upon in part (c) below, including reasons why the payback method was not used to help to reach a decision.
(c) Comments on Mr Court’s views
Mr Court makes two points of note – one concerns the payback method of investment appraisal, whilst the other concerns the relationship between reported profits and investment decision-making. These two points will be commented upon separately. (i) The payback method
The payback method of investment appraisal is relatively quick and simple to operate and understand. It calculates how quickly a project’s outlay is recovered from its generated earnings, usually cash flows, though alternatives are possible.
Notwithstanding these comments, payback can act as a useful guide to project desirability when liquidity is a problem for a company and the speed of a project’s return is of prime importance. This may be particularly true where, in addition, the investment opportunities are relatively small and where it may be felt that a full scale discounted cash flow evaluation is unnecessary.
However, in the situation given, there is no indication as to the relative size of the two promotion alternatives to the company as a whole but, on the basis that cash is not in short supply over the next three years, the firm does not appear to have any liquidity problem. Thus there would seem to be little evidence to support Mr Court’s preference for the payback method.
One final point is that the supporters of payback claim that the method does attempt to allow for uncertainty in that it prefers fast payback projects. Such a claim is really unjustified as it is based on the belief that uncertainty is concerned with the timing of a project’s return. This is somewhat naive.
(ii) Investment appraisal and reported profits
Mr Court’s second comment highlights a real problem in that a different approach is used for investment decision-making (discounted cash flows) from that used for reporting the success or otherwise of the decisions made (reported profits). Most investment opportunities undertaken by firms have returns whose generation covers a relatively long time period (several years). It is one of the tasks of published accounts (and particularly the profit and loss account) to cut up this continuous stream of wealth generation into a series of time periods: the accounting year.
It is certainly a powerful argument that, as well as undertaking NPV calculations, management should also consider the implications for the published accounts of any investment opportunity – especially if the projects are of a substantial size. For instance, if a particular project had a healthy positive NPV but its acceptance would have an adverse effect on the published financial accounts, although it would be unwise for the project to be rejected on these grounds alone, management should make strenuous efforts to ensure that its investment plans are fully communicated to and understood by the shareholders and the bonds market in general.
Answer 6 FIORDILIGI PLC
t0 t1 t2 t3 t4 t5
$000 $000 $000 $000 $000 $000 Labour
Skilled 10,000 × 0.5 × Nil –
10,000 × 0.5 × $4.00 20.0 20.0
8,000 × 0.5 × $4.00 16.0 16.0 Unskilled 10,000 × 2 × $2.50 50.0 50.0 50.0
8,000 × 2 × $2.50 40.0 40.0
Materials
Ping 10,000 × 2 × $1.40 28.0 28.0 28.0
8,000 × 2 × $1.40 22.4 22.4 Pang 46,000 × 0.5 × $1.80 41.4
Pong 10,000 × 1.5 × $0.80 12.0 12.0 12.0
8,000 × 1.5 × $0.80 9.6 9.6
Overheads
Variable 10,000 × 0.5 × $1.40 7.0 7.0 7.0
8,000 × 0.5 × $1.40 5.6 5.6 Fixed Rent 2.0 2.0 2.0 2.0 2.0
Rates 1.0 1.0 1.0 1.0 1.0 ——— ——– ——– ——– ——– ——– 83.4 100.0 120.0 112.0 96.6 62.6 ——— ——– ——– ——– ——– ——–
Revenue 10,000 × $18 180.0 180.0 180.0
8,000 × $14 112.0 112.0
Costs (as above) (83.4) (100.0) (120.0) (112.0) (96.6) (62.6) Purchase of plant (60.0)
Resale 6.0
——— ——– ——– ——– ——– ——– Net cash flow (143.4) 80.0 60.0 68.0 15.4 55.4 ——— ——– ——– ——– ——– ——–
Discount factors at 15% 1.000 0.870 0.756 0.658 0.572 0.497
Present values ($000) (143.0) 70.0 45.0 45.0 9.0 28.0
NPV = + $54,000 ————
Answer 7 HULME LTD
(a) Cash flows resulting from manufacture and sale of Champs
Ref to Time 1 Time 2 Time 3 Time 4 workings $000 $000 $000 $000
Machine (150) – – –
Labour (1) – (75) (210) (252) Materials
Alpha (2) (100) (110) (121) –
Beta (3) (90) (121) (133) – Overheads (4) – (50) (55) (61)
——– ——– ——– ——– Total outflows (340) (356) (519) (313)
Sales (5) – 600 660 726
——– ——– ——– ——– Net inflow/(outflow) (340) 244 141 413
——– ——– ——– ——–
20% discount factor 1.000 0.833 0.694 0.579
Present value (340) 203 98 239
Net present value = $200,000 ————
On the basis of the estimates given, production of Champs is worthwhile.
Note Time 0 is taken to be the date on which manufacture would commence, i.e. 1 January 19.00; time 1 is 31 December 19.00, etc.
WORKINGS
For explanations of the figures used, see part (b).
(1) Labour cost
$ Year 1 Skilled 25,000 hours @ $3 75,000
Unskilled No cost incurred – ———– 75,000 ———–
Year 2 Skilled 25,000 × ($3 × 1.2) 90,000 Unskilled 50,000 × ($2 × 1.2) 120,000 ———– 210,000 ———–
(2) Material Alpha
Current buying price is 50c per kg, rising at 10% per annum.
Time 0 cost 50c × 200,000 = $100,000 Time 1 cost $100,000 × 1.1 = $110,000 Time 2 cost $110,000 × 1.1 = $121,000
(3) Material Beta
Quantity held is enough for one year.
Time 0 realisable value 100,000 × 90c = $90,000 Time 1 buying price 100,000 × $1.10 × 1.1 = $121,000 Time 2 buying price 121,000 × 1.1 = $133,100
(4) Overheads
The only relevant costs are variable overheads, which rise at 10% per annum.
Year 1 cost 100,000 × 50c = $50,000 Year 2 cost $50,000 × 1.1 = $55,000 Year 3 cost $55,000 × 1.1 = $60,500
(5) Sales
The selling price rises at 10% per annum.
Year 1 100,000 × $6 = $600,000 Year 2 $600,000 × 1.1 = $660,000 Year 3 $660,000 × 1.1 = $726,000
(b) Brief explanations of the figures used (1) Machine
Although the machine is owned already, it has an opportunity cost if used on this project, which is the revenue forgone if it is not sold now for $150,000.
(2) Labour
In the first year of the project the company will have to pay for extra skilled labour only, as there is enough surplus unskilled labour to cover the necessary 50,000 hours on the project. As this unskilled labour is paid whether or not the Champs are produced, there is no relevant unskilled labour cost in year 1 of the project.
(3) Material Alpha
Alpha is used regularly by the company on many projects. If existing inventory are used to manufacture Champs, the company will have to buy in more inventory of Alpha for its other projects. The relevant cost of Alpha is thus always its buying price, which is expected to rise by 10% per annum.
(4) Material Beta
Present inventory of Beta are sufficient for the first year’s production of Champs. Since there is no alternative use for Beta within the company, the opportunity cost of existing inventory is the realisable value of 90c per kg.
After one year present inventory will be exhausted, and the relevant cost of further supplies of Beta will be the buying price.
(5) Overheads
Fixed costs allocated from head office will be irrelevant to this decision as they will be incurred whether or not Champs are produced.
Depreciation is irrelevant to a project appraisal based on cash flows.
The only relevant cost is, therefore, the variable overhead.
(c) Factors not included in the calculations which may affect the decision (i) Availability of more profitable projects
The project has been appraised in its own right, but it should be compared with alternative uses for the funds employed, particularly if there are constraints on capital or other resources.
(ii) Scarcity of resources
The calculations assume that there is no scarcity in supply of the resources used on the project, e.g. that sufficient supplies of Alpha or skilled labour are available at the prices stated and that the use of them will not affect the quantities available for the company’s normal operations. If there is a scarcity in supply, the opportunity cost of these resources will include the lost contribution through not using the resources on alternative projects.
(iii) Risk and uncertainty of estimates
Most of the figures used in the project appraisal are subject to uncertainty. The decisions might be affected by revised estimates of the following.
(1) The sales price/sales volume relationship. Marketing of the Champ may encourage others to compete with the new product, leading to reduced sales, or to reduced selling price, or to a combination of the two.
(4) Whether head office fixed costs would be unaltered by the new project. In practice, the addition of a new line is likely to increase fixed costs. Additional staff may be employed in accounts, despatch or stores, for example, not directly connected with the new product line, but ultimately resulting from the increased turnover. The need for additional storage area may require the utilisation of space which could otherwise have been sub-let. If so, the rental income forgone would be treated as a relevant cash outflow.
Other more general possibilities, such as a change of government or a change in fiscal policy, may affect the profitability of the project.
(iv) Management and labour skills
The calculation assumes that the necessary skills exist for this new project or that they can be quickly acquired without any teething problems. In practice, this would be a major factor in the decision.
(v) Technological change
Changing technology may render the Champ obsolete before the end of three years.
Answer 8 BAILEY PLC
(a) Investment appraisal of production of Oakmans
Year 1 2 3 4 5 6 7
$ $ $ $ $ $ $
Contribution before labour costs 139,150 153,065 168,371 92,604 101,865 Labour cost (39,675) (45,626) (52,470) (30,171) (34,696) Redundancy payments (15,741)
Redundancy payments avoided 20,700
Machine overhaul (79,860)
———– ———– ———– ———– ——— ——— ——— 20,700 99,475 27,579 100,160 62,433 67,169
Tax at 35% (7,245) (34,816) (9,653) (35,056) (21,852) (23,509) Cost of machine (209,000)
WDAs 18,288 13,716 10,287 7,715 5,786 17,359 ———– ———– ———– ———– ——— ——— ——— Net cash flows (188,300) 110,518 6,479 100,794 35,092 51,103 (6,150)
———– ———– ———– ———– ——— ——— ——— 20% factors 0.833 0.694 0.579 0.482 0.402 0.335 0.279 Present value (156,854) 76,699 3,751 48,583 14,107 17,120 (1,716)
Net present value = $1,690 ———
Conclusion
Explanatory notes
(1) Contribution from sales before labour cost
These cash flows have been grouped as they all inflate at 10% per annum. At current values the cash flow per unit is as follows.
$ Sales price 35
Material and other consumables (8) It is assumed that there is no Variable overheads (4) change in head office fixed
—— costs if Oakman is produced Net contribution before labour cost 23
——
(2) Labour cost
At current prices the labour cost per unit of 2 hours × $3 is included, as the six employees would not be paid if the Oakman were not produced.
(3) Redundancy payment
This is the payment to the three redundant employees in four years’ time.
(4) Redundancy payments avoided
If the Oakman were not produced, there would be a payment of 6,000 hours ×
$3 × 1.15 to the six employees who would be made redundant. This is avoided and hence is an incremental cash flow.
(5) Purchase and maintenance of machine
These are the cash flows that will be incurred.
(6) Overhead costs
It is assumed that the overhead costs will be allowed for tax in the year in which they are incurred.
(7) Taxation
(8) Writing down allowances
WDA Tax saved Timing
$ $ $
Cost – paid at end of first year (t1) 209,000
WDA year 1 (52,250) 52,250 18,288 t2 ———–
156,750
WDA year 2 (39,188) 39,188 13,716 t3 ———–
117,563
WDA year 3 (29,391) 29,391 10,287 t4 ———–
88,172
WDA year 4 (22,043) 22,043 7,715 t5 ———–
66,129
WDA year 5 (16,532) 16,532 5,786 t6 ———–
49,597 Proceeds – end of year 6 – ———–
Balancing allowance 49,597 49,597 17,359 t7 ———–
(9) General comments
The production of Oakman has been evaluated by considering the incremental change in the company’s cash flows caused by a decision to produce. These have been valued at the actual cash flow in each year, after allowing for the differing effects of inflation on each item. These money cash flows have then been discounted at the money cost of capital (net of corporation tax).
An alternative would have been to calculate a “real” discount rate for each cash stream and discount the un-inflated cash flows at that rate.
(b) Discussion of investment appraisal problems caused by high inflation rates
The existence of high rates of inflation creates problems in investment appraisal by contributing to the uncertainty attached both to the cash flows themselves and the appropriate discount rate. It is unlikely that in any investment appraisal situation each cash flow stream will be affected in the same way by inflation. The budget must predict as accurately as possible the anticipated level of inflation.
The conventional treatment of inflation is to discount the anticipated money cash flows at a money discount rate. This money rate would normally be derived from the so-called “dividend valuation model”, to give the shareholders’ required rate of return and the required rate of return for other suppliers of capital such as debenture holders. Such a required rate of return will consist of both a real rate reflecting the “time value of money” to the providers of funds, plus an additional return to compensate for the decrease in purchasing power caused by inflation.
Clearly, with higher anticipated inflation rates, such a money rate will be higher than with lower rates. However, the company must anticipate such a required rate of return when evaluating capital projects. With high inflation rates this anticipation becomes more difficult, as again the expectations of the shareholders as to the effect of inflation on them will become more diverse. Moreover, with the increased probability of changes in inflation in the future, the required rate of return is unlikely to be constant over the life of the project. The company will be faced with increasing uncertainty as to whether it is acting in the best interests of shareholders by accepting or rejecting a particular project.
Finally, it should be noted that the above comments refer to the problems presented to investment appraisal by expected or anticipated inflation. The correct treatment in capital budgeting of unanticipated inflation has so far defied a workable solution, and this represents a serious gap in the theory of financial decision-making.
Answer 9 STAN BELDARK
(a) Optimal replacement period
The effects of increasing running costs and decreasing resale value have to be weighed up against capital cost. Road fund licence etc can be ignored, since Stan will always pay $300 per year per car.
The following table is one of the quickest ways to reach an answer.
Running PV Cum PV Resale PV of NPV of Cum EAC cost of RC of RC value RV car discount
$ $ $ $ $ $ factor $
Life 1 3,000 2,727 2,727 3,500 3,182 5,045 0.909 5,550 Life 2 3,500 2,891 5,618 2,100 1,735 9,383 1.736 5,405 Life 3 4,300 3,229 8,847 900 676 13,671 2.487 5,497
From the above table it can be seen that the optimal replacement period is every two years.
(b) Discussion of investment appraisal and high inflation rates
The existence of high inflation creates problems in investment appraisal by contributing to the uncertainty attached both to the cash flows and to the appropriate discount rate. It is unlikely that in any investment appraisal each cash flow stream will be affected in the same way by inflation. Higher rates of inflation will tend to be more volatile than lower rates, especially as government action will be directed to reducing them.
The existence of high rates of inflation will also affect the discount rate used. The conventional treatment is to discount the anticipated money cash flows at a money discount rate. This money rate would normally be the yield for shareholders and the required rate of return for other suppliers of capital such as debenture holders. Such a required rate of return will be a rate reflecting the time value of money to the provider of funds, plus an additional return to compensate for the decrease in purchasing power caused by inflation.
Clearly, with higher anticipated inflation rates such a money rate will be higher than with lower rates. However, the company must anticipate such a required rate of return when evaluating capital projects. With high inflation rates this anticipation becomes more difficult, as again the expectations of the shareholders as to the effect of inflation on them will become more diverse. Moreover, with the increased probability of changes in inflation in the future the required rate of return is unlikely to be constant over the life of the project. The company will be faced with increasing uncertainty as to whether it is acting in the best interests of shareholders by accepting/rejecting a particular project.
Answer 10 TALEB LTD
Summary showing the optimal replacement policy for Taleb’s Dot machines Replacement cycle Annual equivalent net revenue
$000 1 year
2 years 3 years 4 years
8.0 11.1 *
9.8 10.3
* optimal policy
Replacement of the Dot machine every two years results in the greatest annual equivalent net revenue for the company (i.e. $11,100) and therefore is the recommended replacement policy.
WORKINGS
Annual production/sales (units) 500,000 400,000
$ $
Annual revenue ($0.12 per unit) 60,000 48,000 Less Annual variable costs ($0.04 per unit) (20,000) (16,000)
——— ———
40,000 32,000
(i) One year replacement
Year 0 Year 1 $000 $000 Machine outlay (60)
Scrap value 40
Running costs (6)
Contribution 40
—— ——
Net cash flow (60) 74
—— ——
Net present values = – 60 + (74 × 0.909)
= 7.266
Annual equivalent = 7.266 ÷ 0.909
≡ $7,993 ——— (ii) Two year replacement
Year 0 Year 1 Year 2 $000 $000 $000 Machine outlay (60.0)
Scrap value 25.0
Running costs (6.0) (6.5)
Contribution 40.0 40.0
——— ——— ——— Net cash flow (60.0) 34.0 58.5
——— ——— ———
Net present values = – 60 + (34 × 0.909) + (58.5 × 0.826)
= 19.227
Annual equivalent = 19.227 ÷ 1.736
≡ $11,075 ———–
(iii) Three year replacement
Year 0 Year 1 Year 2 Year 3 $000 $000 $000 $000 Machine outlay (60.0)
Scrap value 10.0
Running costs (6.0) (6.5) (7.5) Contribution 40.0 40.0 32.0
——— ——— ——— ——— Net cash flow (60.0) 34.0 33.5 34.5
——— ——— ——— ———
Net present values = – 60 + (34 × 0.909) + (33.5 × 0.826) + (34.5 × 0.751) = 24.4865
(iv) Four year replacement
Year 0 Year 1 Year 2 Year 3 Year 4 $000 $000 $000 $000 $000 Machine outlay (60.0)
Scrap value 0
Running costs (6.0) (6.5) (7.5) (9.0) Contribution 40.0 40.0 32.0 32.0
——— ——— ——— ——— ——— Net cash flow (60.0) 34.0 33.5 24.5 23.0
——— ——— ——— ——— ———
Net present values = – 60 + (34 × 0.909) + (33.5 × 0.826) + (24.5 × 0.751) + (23 ×
0.683)
= 32.6855
Annual equivalent = 32.6855 ÷ 3.170
≡ $10,311 ———–
Answer 11 STICKY FINGERS PLC (a) No rationing
Present values
Year 0 1 2 3 4
Time t0 t1 t2 t3 t4
Discount factor 1 0.870 0.756 0.658 0.572
$000 $000 $000 $000 $000 Project A (1,500) (435) 907 395 172 Project B (2,000) (870) 1,890 1,645 1,430 Project C (1,750) 435 832 921 572 Project D (2,500) 609 680 855 172 Project E (1,600) (435) 151 1,842 1,316
NPV $000
Project A (461)
Project B 2,095 Therefore, accept all projects with a Project C 1,010 positive NPV - projects B, C and E
Project D (184)
(b) Single-period capital rationing
Project A B C D E
NPV ($000) (461) 2,095 1,010 (184) 1,274 Investment, t0 ($000) 1,500 2,000 1,750 2,500 1,600
NPV/$ – $1.05 $0.58 – $0.80
Rank – 1st 3rd – 2nd
Therefore, accept B and 1610E.
(c) Single-period capital rationing – inflows and outflows, negative NPVs
Using benefit cost ratios
investment Rationed
NPV
Benefit/cost NPV per Ranking $1 invested
Project A *
Project B $2,095/$1,000 $2.10 2
Project C *
Project D $184/$700 $0.26 **
Project E $1,274/$500 $2.55 1
Notes
* Project A would never be accepted because it has a negative NPV and uses up funds in the restricted year.
Project C would always be accepted since it has a positive NPV and releases funds in the restricted year. A total of $700,000 is then available.
** Project D has a negative NPV but releases funds at t1.
If project D is accepted, this makes an extra $700,000 available at t1. However, in doing so a negative NPV (– $184,000) is incurred. Thus, it is necessary to examine whether the extra positive NPV generated by the additional investment finance outweighs this cost.
(1) Available capital = $200,000. Accept projects C, E and 20% B. Total NPV = $2,703,000.
(2) If D is accepted the available capital becomes $1,400,000 [$200,000 + $500,000 (from project C) + $700,000 (from project D)]. Accept projects C, D, E and 90% B. Total NPV = $3,985,500. This is the optimal solution.
(d) Indivisible projects
Possible investment “portfolios” are B or C or E or (C and E)
(e) Multi-period capital rationing
Note – it is not likely that you will be required to solve a multi period capital rationing situation in exam conditions. It is enough to be aware of the technique that would be used i.e. linear programming
Let a = the proportion of project A undertaken etc. Let z = NPV
Sticky Fingers should aim to maximise an objective function
z = – 461a + 2,095b + 1,010c – 184d + 1,274e
subject to constraints
1,500a + 2,000b + 1,750c + 2,500d + 1,600e ≤ 3,000
500a + 1,000b + 500e ≤ 200 + 500c + 700d
a, b, c, d, e ≤ 1
Non-negativity conditions
a, b, c, d, e ≥ 0
Answer 12 ARMSTRONG PLC (a) Investment decision
t0 t1 t2 t3 t4 t5 t6
$ $ $ $ $ $ $
Contribution from
new product 30,000 50,000 60,000 122,500 122,500 Contribution forgone
from old product (30,000) (22,500) (4,500) (1,500) –
Advertising (14,200)
———– ——— ——— ——— ——— —–—— ——— – 27,500 41,300 121,000 122,500 Tax at 35% (9,625) (14,455) (42,350) (42,875)
Land (120,000) 160,000
New building (30,000) 25,000
CAs (W1) 420 420 420 420 420 (350) ———– ——— ——— ——— ———– ———– ——— (150,000) 420 27,920 32,095 106,965 265,570 (43,225) ———– ——— ——— ——— ———– ———– ——— Discount factor
at 15% 1 0.870 0.756 0.658 0.572 0.497 0.432 Present value
$(150,000) 365 21,108 21,119 61,184 131,988 (18,673)
This NPV does not include cash flows relating to the acquisition of the burnishing machine. Of the two options for the acquisition, leasing has the lower present value of costs, at $61,981 (see part (b)). Since this is lower than the present value of the benefits from the project ($67,091 above), the project is worthwhile, and should be undertaken.
(b) Financing options (burnishing machine) (i) Purchase
Present value $
Purchase price 100,000
Tax saved (W2) (25,996)
———– 74,004 ———– (ii) Leasing
Present value $ Lease rentals $21,800 × (1 + 3.170) 90,206 Tax relief $21,800 × 0.35 × 3.791 (28,925)
——— 61,981 ———
The above calculations demonstrate that, at a discount rate of 10%, leasing is the preferred method of financing the machine. This does not mean, however, that the project is worth undertaking. As shown in (a) above, the decision must be taken after comparison of the present value of the cheaper option with the present value of the benefits to be obtained from acquiring the machine and undertaking the project.
The calculations above have been made at a discount rate of 10%, the after-tax cost of borrowing from the bank to finance the purchase. This rate is taken to be risk-free and is the appropriate rate to use for risk-less flows such as those in the two financing options.
WORKINGS
Capital allowances
(1) Building
$ Years 0 to 4 WDA 4% × $30,000 1,200
——— Tax saved 35% × $1,200 420 ——— Timing t1 to t5
Year 5 Sale proceeds 25,000
Written down value $30,000 – 5 × $1,200 (24,000) ———
Balancing charge 1,000
———
(2) Burnishing plant
Tax CAs Tax saved Time Discount PV
WDV at 35% factor
at 10%
$ $ $ $
Cost (t0) 100,000
WDA (year 0) (25,000) 25,000 8,750 t1 0.909 7,954 ———
75,000
WDA (year 1) (18,750) 18,750 6,563 t2 0.826 5,421 ———
56,250
WDA (year 2) (14,062) 14,062 4,922 t3 0.751 3,696 ———
42,188
WDA (year 3) (10,547) 10,547 3,691 t4 0.683 2,521 ———
31,641
WDA (year 4) (7,911) 7,911 2,769 t5 0.621 1,720 ———
23,730
SV (year 5) –
——— Balancing allowance
(year 5) 23,730 23,730 8,305 t6 0.564 4,684
——— ———– ——— ———
100,000 35,000 25,996
———– ——— ———
Answer 13 COMPOUNDING AND DISCOUNTING (a) T = p (1 + r)n
p = present value r = interest rate
n = number of times compounded T = terminal value
(i) T = 1 (1 + 0.1)1 = $1.10 (ii) T = 1 (1 + 0.1)2 = $1.21 (iii) T = 1 (1 + 0.1)3 = $1.33 (iv) T = 1 (1 + 0.1)10 = $2.59
(b) The present value of $T in n years time at r% per annum ⇒
p = n r) (1
T
+ or T (1 +r)-n
(i) r = 10%, n = 1, discount factor = 0.909
(ii) r = 10% n = 2 discount factor = 0.826
(c) Year end Cash flow Discount factor Discounted
(r = 10%) cash flow
(d) Year end Cash flow Discount factor Discounted
(r = 10%) cash flow
(e) Year end Investment Compound interest Compounded
(f) Year beginning Investment Compound interest Compounded
(g) Year beginning Investment Compound interest Compounded
factor cash flow
Imagine investing $1.00 for 1 year
(i) 8% per annum nominal ≡ 4% per 6 months
Date Deposit Compound interest Compounded
Alternatively: Using equal triangles $1,860 more than the sum of $10,000 in one year’s time, $20,000 in two years’ time and $30,000 in three years’ time.
(n) Year end Cash flows Discount factors PV
(note – it is not likely that you will be required to solve quadratic equations under exam conditions)
The value x = 1.07 gives a realistic (i.e. positive) answer
x = 1 + r = 1.07
r = 0.07 i.e. IRR = 7%
(o) Calculate the expected cash flows for each year
Year end Expected Discount factors PV
cash flow 14%
$000 $000
0 (30.00) 1.000 (30.00)
1 11.50 0.877 10.09
2 12.25 0.769 9.42
3 12.00 0.675 8.10
4 12.50 + 2 = 14.50 0.592 8.58
—— NPV = 6.19 —— NPV @ 14% = $6,190,000
Answer 14 DESPATCH CO
Time Cash 14% factor PV
$ $
0 (12,000) 1 (12,000)
1 – 10 2,000 5.216 10,432
10 500 0.27 135
——— (1,433) ———
As the NPV is negative at 14% the company should not undertake this project.
Answer 15 DISCOUNTED CASH FLOW (a) (i) Alternative machines
Year 8% Factor Machine 1 PV Machine 2 PV
$ $ $ $ 0 1 (10,000) (10,000) (9,000) (9,000) 1 0.926 1,000 926 1,200 1,111 2 0.857 1,600 1,371 1,500 1,286 3 0.794 2,500 1,985 3,500 2,779 4 0.735 2,500 1,838 2,000 1,470 5 0.681 2,500 1,702 2,000 1,362 6 0.630 1,500 945 2,000 1,260 7 0.583 2,500 1,458
——— ———
225 268
——— ———
(ii) Comment
Since the difference between the two figures is marginal it may be prudent to carry out a “sensitivity analysis” on the result.
The cash flow figures are estimates for several years ahead. A small change in any of these figures could affect the result to such an extent that machine 1 might be the better investment.
Changes could even lead to the projects having negative NPVs since the values are only small positive figures. Investments with negative NPVs should be rejected.
(b) Device
Time Cash 7% factor PV
$ $
1 (40,000) 0.935 (37,400)
2 – 29 2,000 12.278 (W) – 0.935 22,686 ———
Negative NPV (14,714)
———
∴ Firm should not produce the device.
WORKING
1
0.07
1– 1.07129
= 12.278(c) Crusher
Time Cash 12% factor PV
$ $
0 (6,000) 1 (6,000)
3 – ∞ 1,200 1/0.12 – 1.690 = 6.643 7,972 ———
Positive NPV 1,972
———
∴ The crusher should be purchased.
Alternatively
Time Cash Time Cash
$ $
3 – ∞ 1,200 is the same as 1 – ∞ 1,200 × 2
12 . 1 1
Therefore PV of perpetuity = $1,200 × 2 12 .
1 1 × 0.1 = $7,972 12
(d) IRR
Since the internal rate of return is greater than the return which J can obtain elsewhere, he would be advised to invest in the scheme.
(e) (i) IRR
Since the IRR of this project is less than the required rate of return, it should not be undertaken. Therefore, the ball and crane should not be bought.
(ii) An alternative approach to this problem would be to discount the cash flows at 10%. Since the project has a negative NPV at 10% (the desired rate of return), the project would not be accepted.
Answer 16 GERRARD
Net
Year end Machinery Receipts Paper Salary cash flow
(a) and (b)
Year end Net Discount PV Discount PV
cash flow factors 12% factors 14%
$000 $000 $000
0 (58.0) 1.000 (58.00) 1.000 (58.00) 1 (3.5) 0.893 (3.13) 0.877 (3.07)
2 21.5 0.797 17.14 0.769 16.53
3 21.5 0.712 15.31 0.675 14.51
4 21.5 0.636 13.67 0.592 12.73
5 29.5 0.567 16.73 0.519 15.31
–—— –——
NPV = 1.72 NPV = (1.99)
–—— –——
(c) In view of the project’s positive NPV at 12%, expansion is (just) worthwhile. The IRR of the project is approximately 13% (i.e. half way between 12 & 14%) or
IRR = 12% + 172 172 199
.
. + . (14 – 12)% = 12.9% This gain indicates that the project is worthwhile.
Answer 17 CARTER LTD
(a) (i) Net present value
Time Cash flow 10% factor Present value
$ $
0 (32,000) 1 (32,000)
1 – 15 5,000 7.606 38,030
———
Positive NPV 6,030
———
In view of the positive NPV the project should be undertaken.
.
(ii) Internal rate of return
The internal rate of return is calculated by finding a 15 year cumulative discount factor as follows.
15 year factor @ IRR =
flow cash Annual
Investment =
000
,
5
000
,
32
= 6.4IRR = 13%
(b) (i) Book value of $2,000
This information does not affect the NPV as a book value is not a cash flow. (ii) Reduced project duration to ten years
Revised NPV calculation
10% Present
Time Cash flow factor value
$ $
0 Net investments (32,000) 1 (32,000) 1 – 10 Net savings 5,000 6.145 30,725
———
Negative NPV (1,275)
———
The reduction in the project duration means that it is no longer worthwhile.
(iii) Changes in allocation and apportionment
This information does not affect the NPV as allocation and apportionment are arbitrary. The cash flows are unchanged.
(iv) Revised scrap values
With the existing equipment having a scrap value of $2,000 in 15 years’ time, if the project is undertaken this $2,000 in year 15 will be forgone.
The NPV will therefore be reduced be reduced by the present value of $2,000 discounted for 15 years.
NPV = $6,030 – ($2,000 × 0.239) = $5,552
The project will still be accepted though the NPV is reduced.
Answer 18 ABC Project A
Cash flows
Time 0 1 2 3 4 5
$ $ $ $ $ $ Equipment – cost (95,000) (95,000) (95,000)
Deluxe – net cash inflow (W1) 80,000 80,000 88,000 96,800 106,480 Existing – lost cash contribution
(W2) (7,500) (7,500) (8,250) (9,075) (9,985)
——— ——— ——— ——— ——— ———–
Net cash flow (95,000) (22,500) (22,500) 79,750 87,725 96,495 DF @ 17% 1 0.855 0.731 0.624 0.534 0.456 PV (95,000) (19,237) (16,448) 49,794 46,845 44,002
Project B
Time Description Cash flow 17% DF PV
$ $
0 Patent rights (320,000) 1 (320,000) 1 – 5 Reduction in labour 70,000 3.199 223,930 Expected increase in sales (W3) 27,600 3.199 88,292 ———– NPV = (7,778)
———–
Project C
Time Description Cash flow 17% DF PV
$ $
0 – 4 Rental (50,000) 1 + 2.743 = 3.743 (187,150) 2 – 5 IT bureau costs saved 90,000 3.199 – 0.855 210,960
1 Training (10,000) 0.855 (8,550)
½ Consultant (5,000) 0.925 (W4) (4,625)
1 Consultant (5,000) 0.855 (4,275)
———– NPV = 6,360 ———–
Projects A and C are worth considering further as they show a positive NPV at the company’s required rate of return.
WORKINGS
Project A
(1) De-luxe net cash inflow
Year 1 2 3 4 5
Demand (units) 10,000 10,000 11,000 12,100 13,310 Net cash inflow (@ $8) 80,000 80,000 88,000 96,800 106,480
(2) Loss of cash contribution on existing project
Year 1 2 3 4 5
Reduction in demand (units)
(15% of demand in W1) 1,500 1,500 1,650 1,815 1,997
Contribution lost (@ $5) 7,500 7,500 8,250 9,075 9,985
Project B
(3) Expected increase in contribution from increased sales
0.8 × 5,000 + 0.2 × 3,000 = 4,600 units
Project C
(4) Discount factor for a flow taking place in six months’ time
= 17 . 11 = 0.925
Answer 19 MOORGATE COMPANY (a) Ex-rights price
$ 4 existing shares × $3.00 12.00 1 rights share × $2.00 2.00 –––––
14.00 –––––
The theoretical value of Moorgate’s shares ex-rights is
5
14.00
= $2.80(b) Value of right
Value of right = $(2.80 – 2.00) = $0.80
One right enables a holder to buy for $2.00 a share which will eventually sell for $2.80. The value of the right to buy one share is, therefore, $0.80. Four existing shares are needed to buy one additional share. Thus, the value of the rights attaching to each existing share is $0.20.
(c) Chairman’s views
The chairman is correct. The shareholder should either exercise his rights or sell them (subject to (d) below).
(i) If he sells all rights
$ Wealth before rights issue
Value of shares 1,000 × $3.00 3,000 –––––– Wealth after rights issue
(ii) If he exercises one half of his rights and sells the other half
$ Wealth before rights issue
Value of shares 1,000 × $3.00 3,000 –––––– Wealth after rights issue
Value of old shares 1,000 × $2.80 2,800 Value of new shares
4
500 × $2.80 350
Cash from sale of rights 500 × $0.20 100 –––––– 3,250 Less Cost of purchasing new shares 125 × $2 (250)
–––––– 3,000 –––––– (iii) If he does nothing
$ Wealth before rights issue
Value of shares 1,000 × $3.00 3,000 Wealth after rights issue
Value of shares 1,000 × $2.80 (2,800) ––––––
Reduction in wealth 200
–––––– (d) Shareholder wealth
It is possible that the shareholder, whether exercising the rights or selling them, will suffer a reduction in wealth.
The above analysis is based on the assumption that the funds to be raised by the new issue of shares will be invested in the business to earn a rate of return comparable to the return on the existing funds. The capital market, in valuing the share of Moorgate after the rights issue, has to make some assumption as to how profitably the new funds are to be used. For example, if the new funds were squandered the overall return on equity funds would fall, and the price would drop below the $2.80 calculated above.
Alternatively, if the sales are to be used to finance a highly profitable investment and the capital market does not initially appreciate this point, then the market in arriving at a price of $2.80 ex-rights would be undervaluing the share. When the true earning potential of the company were realised, the share price would rise. However, by then it might be too late for the shareholder referred to in the question.
Answer 20 GREINER LTD
REPORT
To Mr and Mrs Greiner From XYZ Ltd
Date Today
Subject Proposed entry onto the Stock Exchange
With reference to your recent enquiry, we set out below information regarding
(a) the necessary steps to be taken prior to obtaining a quotation, and
(b) the methods of raising finance from the market and advice as to which should be used.
(a) Steps prior to obtaining a quotation (i) Review of current situation
Before approaching the sponsoring brokers, a detailed review of the company’s current situation should be made. This will include consideration of the following areas.
(i) Management. Is there sufficient financial expertise within the company to cope with the demands of being a public company? The meetings and information-gathering involved with obtaining a quotation will take up an excessive amount of your time. It is possible that further staff may be required to aid with the running of the business during this period.
(ii) Contractual relationships. It may be necessary to formalise trading relationships with the company’s major suppliers and customers, and to review the debt collection procedure if this has caused problems in the past.
(iii) Directors’ contracts. The terms of your appointments as directors should be clearly laid out in the form of service contracts. Prospective shareholders will want to be sure that remuneration and other benefits are of a reasonable level.
(iv) Accounting systems. These must be in good order to enable management to be confident of their ability to supply sufficiently accurate information at the required time.
(ii) Appointment of professional team
The full professional team required to take a company to the market comprises a sponsoring broker, a reporting accountant and a solicitor. The broker will take overall responsibility for the co-ordination of the various stages leading up to the quotation. It is important that you feel confident in the broker’s ability to handle the work and that good working relationships can be maintained before, during and after the flotation.
(iii) Information-gathering and presentation
The reporting accountant will thus be obliged to carry out a detailed review of the financial records of the company and will solicit any other information he may require from yourselves or your employees.
Once the long-form report has been drafted and agreed upon by all parties, the sponsor will prepare the prospectus, and preliminary clearance for the quotation will be obtained from the Stock Exchange.
The finalisation of the prospectus may take several meetings between yourselves and the professionals; it is essential that all legal requirements are met and that the document is carefully and accurately worded.
Appended to the prospectus will be the accountant’s short-form report, containing a profits record of the company, a balance sheet, and other statements similar in content to those contained in the annual accounts.
(iv) The final stages
Once the prospectus and other necessary documentation have been completed, they will be submitted by the sponsor to the Stock Exchange for approval.
(b) Methods of raising equity on the Stock Exchange There are two main methods.
(i) Placing
This is the most favoured method for small issues, in part because the costs are likely to be lower than those of an offer for sale.
In a placing the shares are not offered generally to the public but are placed in the hands of a group of large investing institutions, possibly via an issuing house.
As a placing involves only a limited number of prospective investors, substantial savings may be made in printing of the prospectus, allotment letters, application forms, etc, as well as in advertising.
The general cost of a placing of the size being considered will be in the range $50,000 – $120,000.
(ii) Offer for sale
This involves the issuing house or broker buying the shares from the directors and selling them on to the public at a predetermined price.
The offer for sale has to be advertised, under Stock Exchange rules, in a leading newspaper. Just before the prospectus is made available to prospective investors, the documentation will be filed with the Registrar of Companies and the company re-registered as a public company.
A press conference will be arranged to promote the company and the flotation and hopefully gain some favourable press comment which will assist a successful launch of the shares.
You will then be able to realise part of your investment in the company as well as raising the additional amount of finance required.
The costs of an offer for sale typically range between $200,000 and $500,000.
Where the sale of shares to be issued is in excess of $3 million, an offer for sale is the method encouraged by the Stock Exchange. This is because an offer for sale gives as large a number of investors as possible the chance to invest in the security being offered. It therefore helps to ensure that there is a wide distribution of shareholders and a good trading market once they have been issued.
For the size of issue involved with Greiner Ltd, however, a placing is strongly recommended, principally due to the lower costs involved.
Answer 21 MR FIDELIO
All sources of finance to a business fall into one of two categories. The first is equity, the second debt. The essential difference between the two is that the providers of equity capital become owners of the business: they participate in running the business, share in the profits and bear the risk. The providers of debt finance have merely lent money to the firm, they usually have a fixed return and some form of security over the company’s assets. Mr Fidelio and Aida Ltd will have to consider both categories in their search for the required finance.
There are three significant differences between Mr Fidelio and Aida with respect to their ability to raise long-term finance. Firstly, Mr Fidelio has no “track record” to support his request for funds.
Secondly, he does not have very much in the way of “mortgageable assets” to offer as security for his loan. Finally, Mr Fidelio wishes to raise a very high proportion of the total funds required. Of the $250,000 he needs he is only able to provide 20% from his personal resources. No investor would be prepared to bear so much of the risk of the enterprise without an opportunity to share in the potential return, i.e. some form of equity would be required. It is equally likely that the providers of such funds would require some say in the running of the business.
Possible sources of finance for Mr Fidelio are as follows.
(a) Enterprise Investment Scheme
Tax relief is given to individual investors in new equity in unquoted trading companies. Obviously Mr Fidelio would lose some control of the business and would need to form a company. In order to retain at least half of the shares Mr Fidelio would probably also need debt finance.
(b) Venture capital trusts
Tax relief is given to investors in listed investment trust companies who invest at least 70% of their funds in unquoted trading companies. Hence investment trust companies may provide equity and debt finances. Again, Mr Fidelio would have to set up a company.
(c) Loan guarantee scheme
(d) Venture capital funds
$200,000 is probably too small an amount for venture capitalists such as 3i to be interested. (e) Leasing
Leasing provides an alternative to borrowing to fund the acquisition of fixed assets like plant and machinery.
(f) Government grants/EU grants
Various grants are available from the above, particularly for high-tech industries (into which category electronic components may fall). Mr Fidelio should contact the DTI (Department of Trade and Industry) to see what is available.
Aida Ltd has a major advantage over Fidelio in raising debt finance and that is that it presumably owns a considerable amount of mortgageable assets. It could raise a fixed interest loan from an institutional investor such as an insurance company or a pension fund by giving a mortgage on its property. It is unlikely that such an investor would be prepared to advance more than 60-70% of the valuation so, if Aida wishes to raise the whole $2 million this way, it would have to mortgage some of its existing properties as well as the new site. Alternatively, if Aida were prepared to give up the freehold interest on the site, it could negotiate a sale and leaseback arrangement with an institutional investor. The ease with which this sort of arrangement could be set up would depend on the quality of the new site. However, this type of arrangement is very popular at this time, particularly for the retail warehouse type of development that Aida is considering.
As far as equity is concerned Aida has a number of options.
(a) Private placing of shares if its articles so allow.
(b) Rights issue to existing shareholders, if they have sufficient funds.
(c) (a) and (b) above maintain the existing limited status of Aida. If neither source of equity funds is available, Aida could consider becoming a plc and obtaining a listing. Much depends on the company’s size but assuming it is a relatively small (in terms of value), then a listing on the Alternative Investment Market at the same time as a new issue of shares (e.g. via a placing) would provide it with the necessary funds. The downside is the cost of listing and increased scrutiny of the company’s activities by external investors and the Stock Exchange.
Answer 22 COST OF CAPITAL
(a) Cost of debt (pre-corporation tax)
(i)
price) market (or proceeds Issue
payment interest
Annual =
10010 = 10%
(ii)
85
(iii) We need to find the IRR by the following cash flows.
t0 t1 t2 t3
$(74) $10 $10 $110
By trial and error, NPV of the four cash flows at
25% NPV = – $74 + 1.440 × $10 + 0.512 × $110 = – $3.28
20% NPV = – $74 + 1.528 × $10 + 0.579 × $110 = $4.97
∴ kd = 20% +
28 . 3 97 . 4
97 . 4
+ × (25% – 20%)
= 23%
(iv) As redeemable at current market price, then
100
10 = 10%
(v) Irredeemable
655 = 7.7%
(b) Cost of debt (post-corporation tax) (i) 10% (1 – 0.35) = 6.5%
(ii) 11.76% (1 – 0.35) = 7.64%
(iii) We need to find the IRR by the following cash flows.
t0 t1 t2 t3
$(74) $6.5 $6.5 $106.5
(Note This assumes no lag in corporation tax payment.)
By trial and error,
15% NPV = – $74 + 1.626 × $6.5 + 0.658 × $106.5 = $6.646
20% NPV = – $74 + 1.528 × $6.5 + 0.579 × $106.5 = – $2.405
∴ kb = 15% +
405 . 2 646 . 6
646 . 6
+ × (20% – 15%)
= 19%
(iv) 10% × (1 – 0.35) = 6.5%
(c) Cost of equity
(i) ke = 150
5 .
7 × 100
= 5%
(ii) ke =
15 165
15
− × 100
= 10%
(iii) ke =
120 ) 05 . 0 1 ( 24× +
× 100 + 5
= 26%
(iv) ke = 10
5 .
1 × 100
= 15%
(d) Dividend valuation model
(i) No growth, hence Po =
ke
D
=
0.1 50,000 0.10×
= $50,000
Per share Po = 0.1010
= $1.00
(ii) No growth, hence Po = 0.15500
= $3,333
Per share Po = 1,0003,333
(iii) Constant growth Po =
(a) Six-monthly gross redemption yield
This is found as the IRR of the following cash flows.
Initial capital cost Market value $110.43
Interest Nine payments of $7 due half-yearly
Redemption One payment of $100 in nine half-years’ time
(b) Redemption date and effective annual gross redemption yield
Kelly plc will presumably choose the option which minimises the effective cost (based on similar IRR calculations) of the bond
(i) Redeem 19X8
PV at 10% PV at 5%
$ $
Market value (110.15) (110.15)
Six interest payments of $7 30.49 35.53
One payment of $100 56.40 74.60
Market value (110.15) (110.15)
Ten interest payments of $7 43.02 54.05
One payment of $100 38.60 61.40
Therefore Kelly will redeem the bond in July 19X8. The effective annual gross redemption yield is (1.05)2 – 1 = 10.25%.
(c) Price of debentures on 1 July 19X5
The value at 1 October 19X5 is the present value, at 6%, of two cash flows.
(i) Interest Nine interest payments of $3 plus $3 due on 1 October 19X5.
(ii) Redemption payment $100 in nine half years’ time.
PV of capital = 9 (1.06)100
= $59.19
Value at 1 July =
1.0296 59.19) (23.41+
= $80.23
(d) Factors influencing the market price of issued corporate debentures
The market price of a corporate debenture will be equal to the present value of the expected future interest payments plus the present value of the amount due on redemption. Since the coupon rate of the bond and the terms for redemption will be known with certainty, the price is largely a function of the discount rate applied to the future cash flows.
Generally it is agreed that the discount rate used to capitalise an anticipated cash flow stream is a function of the risk-free rate and a premium for risk. The risk-free rate is often taken to be the return on government debt. Strictly speaking, government debt is not risk-free; it is default-free. Whist there is no realistic possibility that the government will not meet its obligations to pay interest and redemption of capital, there is a risk for the holders of government debt, since their returns, in real terms, are influenced by the rate of inflation.
Therefore, the required return from a corporate debenture, and hence its market value, is a function of
the true “risk-free” rate a premium for inflation a premium for risk. Each of these will now be considered in turn. (i) The “risk-free” rate
Even in the absence of risk and inflation, all investors require a return to persuade them to forgo current consumption in return for future consumption. It is felt that if investors are prepared to forgo a certain amount of current consumption at a given interest rate, in order to persuade them to make more funds available it will be necessary to offer a higher “risk-free” rate. Therefore it seems likely that the “risk-free” rate will, in part at least, be a function of the demand and supply of investment funds. An increase in the demand for funds, e.g. resulting from a rise in the government’s budget deficit, is likely to result in an increase in the risk-free rate.
(ii) A premium for inflation
