Part 2 – Investment Appraisal

Chapter 4 Capital Budgeting and Basic Investment Appraisal Techniques

I. Payback period and NPV

1. A Option A is correct. The NPV method takes account of the time value of money and risk, uses cash flows rather than profit flows, takes account of all cash flows associated with the project and expresses the wealth created in absolute terms rather than relative terms. It is the method that is most suitable as no other method has all of these attributes.

2. B Lowering the cost of capital will increase the present value of cash inflows, which will in turn increase the NPV and reduce the discounted payback period. The IRR will be unaffected by any change as the cost of capital is only used as a ‘hurdle rate’ and is not used in calculating the IRR.

3. A The net present value method is consistent with maximisation of shareholder wealth.

4. A Year Cumulated discounted cash flows1 $23,1482 $53,1553 $73,0014 $87,702

Disc. Payback = 2 years + [(70,000 – 53,155)/(73,001 – 53,155) x 12 months = 2 years and 10 months approx.

The other options all take the $10,000 paid in year five into account in various formats, although cash flows after the payback are ignored and therefore the $10,000 payment should be ignored.

5. B

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II. IRR

6. A

7. A

8. B9. D A higher cost of capital figure will have no effect on the IRR calculations as it

is only used as a ‘hurdle rate’. It is, however, used in calculating the DPP and a higher figure will lead to a longer payback period.

10. D11. B12. C PI = PV of cash inflows / Initial outlay

Initial outlay = $50m / 2 = $25m

PV of net cash inflows = Annual net cash inflows / r (i.e. perpetuirty)$50m – $25m = $10m / rr = IRR = $10m / $25m = 40%

13. D The IRR will be unaffected by the change in the cost of capital as it is used as a benchmark rather than part of the IRR calculation. The discounted payback method will be affected. A lower cost of capital will result in a decrease in the payback period as discounted cash flows will be higher.

14. A IRR = 146,400 / 732,000 = 20%15. C Statement 1 is not an advantage. The decision rule depends on the shape of

the IRR curve. There could be several IRRs and whether the IRR needs to be higher or lower than the cost of capital depends on the project cash flows.Statement 2 is an advantage. IRR is a discounting technique hence takes into account the time value of money.Statement 3 is a disadvantage. The ‘reinvestment assumption’ is a flaw in IRR. There is no reason to suppose that funds generated early on in a project will be reinvested at the IRR after that point. The funds may well be distributed elsewhere.Statement 4 is an advantage: unlike payback period, the IRR considers all of the future incremental cash flows associated with a decision in its calculation.

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III. Accounting rate of return

16. C Statements 1 and 3 are correct. Statement 2 is incorrect because ARR considers the cash flows through the full time period.

17. A ARR = average annual profits (after depreciation)/average investment.Annual depreciation = cost-residual value/10 = $100,000 per annum.Profits after depreciation = $250,000 – $100,000 = $150,000 per annumAverage investment = $1,250,000 + 250,000/2 = $750,000Therefore, ARR = $150,000/$750,000 = 20%.

DistractersB Using average value of investment as $1,250,000 – 250,000 = $1,000,000150,000/1,000,000 = 15%C Erroneously ignoring depreciation = $250,000/$750,000 = 33%.D Making both of those mistakes $250,000/$1,000,000 = 25%.

18. A The first two statements are correct. Statements 3 and 4 are incorrect. The discount rate reflects the cost of capital which represents the minimum required returns from investors. The payback method takes account of all relevant cash flows when calculating the payback period.

IV. Relevant cash flows

19. B Even if the accountant’s salary was not sunk (eg if they were PLANNING to work on the project next month) the cost should still not feature in the project appraisal as the accountant is paid anyway ie his salary is not incremental.

20. C $000 $000Net profit 180Stocks (30)Debtors (40)

(70)Less: creditors 35 (35)

145

A deducts depreciation and the increase in working capitalB adds the increase in working capitalD deducts depreciation and adds the increase in working capital.

21. C C refers to an opportunity cost that should be taken into account. The other

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costs should be ignored. A is a committed cost, B refers to costs that do not vary with the decision, D refers to a non-cash charge.

22. A The current rental cost is $5,000. The net new rental cost should the project proceed would be ($17,000 + $5,000 – $3,000) = $19,000, so an increment of $19,000 – $5,000 = $14,000.

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Chapter 5 DCF with Inflation and Taxation

I. Inflation

1. D Both statements are incorrect. A business must either exclude inflation from the estimated future cash flows and then apply a discount rate based on the real cost of capital or include inflation in the estimated future cash flows and then apply a discount based on the money cost of capital.

2. A3. B By Fisher’s Equation:

(1 + 6.3%) = (1 + r)(1 + 3%)r = 3.2%

4. A The discount rate must be expressed in real terms i.e. 10%

Option B adds the general rate of inflation to the required rate of return (10 + 3) = 13%

Option C uses a market interest rate based on 3% inflation.Market interest rate = [(1 + r)(1 + h)] – 1[(1·1 x 1·03) – 1] = 0·133= 13·3%

Option D uses a market interest rate based on 5% inflationMarket interest rate = [(1 + r)(1 + h)] – 1[(1·1 x 1·05) – 1] = 0·155= 15·5%

5. B Investors are interested in after-tax returns, hence the first statement is correct. The rate of return will be expressed in money terms if the cash flows are stated in money terms. Hence, the second statement is false.

6. C The payback period will decrease and the IRR increase, because the outflow at time 0 is unaffected by inflation.

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7. D Year 0 1 2$ $ $

Outlay (18,000) Labour 10,000 11,000 Salvage 5,000 Net cash flow (18,000) 10,000 16,000 Discount at 20% 1.000 0.833 0.694 PV (18,000) 8,330 11,104

NPV = 1,434

Money cost of capital = 1.09 × 1.1 – 1 = 19.9%, say 20%8. C The NPV impact of the initial outflow is unaffected.

The revenue flows will be subject to inflation, but then should be discounted at a money rate. The net effect is no change in the PV.The sales proceeds represent a flow of money, not affected by inflation, but this will now be discounted at a money rate, lowering the NPV of the project.

II. Taxation

9. A Year WDV DA Tax benefits Discount at PV$ $ $ 15% $

2014 2,000,000 x 25% = 500,000 x 30% = 150,000 0.870 130,500 2015 1,500,000 - 350,000 = 1,150,000 x 30% = 345,000 0.756 260,820

391,320

10. B Year WDV DA Tax benefits Discount at PV$ $ $ 10% $

2012 90,000 x 25% = 22,500 x 30% = 6,750 0.909 6,136 2013 67,500 x 25% = 16,875 x 30% = 5,063 0.826 4,182 2014 50,625 x 25% = 12,656 x 30% = 3,797 0.751 2,851 2015 37,969 - 25,000 = 12,969 x 30% = 3,891 0.683 2,657

15,826

11. B $PV of perpetuity of cash inflows ($20,000 / 10%) 200,000PV of perpetuity of tax paid [($20,000 × 30%) / 10% × 0.909] (54,540)

After tax PV 145,460

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III. Incorporating working capital

12. C 0 1 2 3Cash inflows 100,000 125,000 105,000 Working capital 10,000 12,500 10,500 Incremental working capital (10,000) (2,500) 2,000 10,500 Discount at 10% 1.000 0.909 0.826 0.751 Present value (10,000) (2,273) 1,652 7,886

PV of working capital (2,735)

13. A The working capital required will inflate year on year, then the inflated amount will be ‘returned’ at the end of the project:

0 1 2Working capital required 100,000 110,000 - Incremental working capital (100,000) (10,000) 110,000 Discount at 12% 1.000 0.893 0.797 Present value (100,000) (8,930) 87,670

PV of working capital (21,260)

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Answer 1(a)(i) Calculation of NPVYear 0 1 2 3 4 Marks

$000 $000 $000 $000 $000Sales revenue 1,236 1,485 2,623 1,013 [2]Variable costs (499) (606) (1,080) (421) [1]Fixed costs (177) (184) (191) (199) [1]Initial investment (2,000)

Net cash flow (2,000) 560 696 1,351 393

Discount at 10% 1.000 0.909 0.826 0.751 0.683

Present values (2,000) 509 575 1,015 268

NPV = $367,000 [1 mark]

(a)(ii) Calculation of IRRYear 0 1 2 3 4 Marks

$000 $000 $000 $000 $000Net cash flow (2,000) 560 696 1,351 393

Discount at 20% 1.000 0.833 0.694 0.579 0.482

Present values (2,000) 466 483 782 189

NPV = (79,000)

[3 marks]

(a)(iii) Calculation of ARRYear 1 2 3 4

$000 $000 $000 $000Net cash flow 560 696 1,351 393

Less: Depreciation ($2m/4) (500) (500) (500) (500)

Profit after depreciation 60 196 851 (107)

Average profit = (60 + 196 + 851 – 107) / 4 = 250Average investment = 2,000 / 2 = 1,000ARR = 250 / 1,000 × 100% = 25% [3 marks]

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(b)The investment proposal has a positive net present value (NPV) of $366,722 and is therefore financially acceptable. The results of the other investment appraisal methods do not alter this financial acceptability, as the NPV decision rule will always offer the correct investment advice. [1 mark]

The internal rate of return (IRR) method also recommends accepting the investment proposal, since the IRR of 18·2% is greater than the 10% return required by PV Co. If the advice offered by the IRR method differed from that offered by the NPV method, the advice offered by the NPV method would be preferred. [1 mark]

The calculated return on capital employed of 25% is less than the target return of 30%, but as indicated earlier, the investment proposal is financially acceptable as it has a positive NPV. The reason why PV Co has a target return on capital employed of 30% should be investigated. This may be an out-of-date hurdle rate which has not been updated for changed economic circumstances. [2 marks]

Answer 2(a)Errors in the original investment appraisalInflation was incorrectly applied to selling prices and variable costs in calculating contribution, since only one year’s inflation was allowed for in each year of operation.

[1 mark]The fixed costs were correctly inflated, but included $200,000 per year before inflation that was not a relevant cost. Only relevant costs should be included in investment appraisal.

[1 mark]Straight-line accounting depreciation had been used in the calculation, but this depreciation method is not acceptable to the tax authorities. The approved method using 25% reducing balance capital allowances should be used.

[1 mark]Interest payments have been included in the investment appraisal, but these are allowed for by the discount rate used in calculating the net present value.

[1 mark]The interest rate on the debt finance has been used as the discount rate, when the nominal weighted average cost of capital should have been used to discount the calculated nominal after-tax cash flows. [1 mark]

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(b)Nominal weighted average cost of capital = 1·07 × 1·047 = 1·12, i.e. 12% per year

[1 mark]NPV calculationYear 1 2 3 4 5 Marks

$000 $000 $000 $000 $000Contribution 1,330 2,264 3,010 1,600 [3]Fixed costs (318) (337) (357) (379) [1]

Taxable cash flow 1,012 1,927 2,653 1,221

Taxation (304) (578) (796) (366)

CA tax benefits 150 112 84 178 [3]

After-tax cash flows 1,012 1,773 2,187 509 (188)

Scrap value 250 [1]

After-tax cash flows 1,012 1,773 2,187 759 (188)

Discount at 12% 0.893 0.797 0.712 0.635 0.567 [1]

Present values 904 1,413 1,557 482 (107)

$ Marks

PV of future cash flows 4,249Less: initial investment (2,000)NPV 2,249 [1]

The net present value is positive and so the investment is financially acceptable.[1 – 2 marks]

Alternative NPV calculation using taxable profit calculation

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Capital allowance (CA) tax benefitsYear WDV Depreciation Tax Tax benefit

$ Allowance rate $1 2,000,000 × 25% = 500,000 × 30% = 150,000 2 1,500,000 × 25% = 375,000 × 30% = 112,500 3 1,125,000 × 25% = 281,250 × 30% = 84,375 4 843,750 - 250,000 = 593,750 × 30% = 178,125

(Balancing allowance)(c)(i)Asset replacement decisions1. The problem here is that the net present value investment appraisal method may offer

incorrect advice about when an asset should be replaced. The lowest present value of costs may not indicate the optimum replacement period.

2. The most straightforward solution to this problem is to use the equivalent annual cost method. The equivalent annual cost of a replacement period is found by dividing the

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present value of costs by the annuity factor or cumulative present value factor for the replacement period under consideration. The optimum replacement period is then the one that has the lowest equivalent annual cost.

[2 – 3 marks](Other solutions that could be discussed are the lowest common multiple method and the limited time horizon method.)

(c)(ii)Multiple internal rates of return1. An investment project may have multiple internal rates of return if it has

unconventional cash flows, that is, cash flows that change sign over the life of the project. A mining operation, for example, may have initial investment (cash outflow) followed by many years of successful operation (cash inflow) before decommissioning and environmental repair (cash outflow). This technical difficulty makes it difficult to use the internal rate of return (IRR) investment appraisal method to offer investment advice.

2. One solution is to use the net present value (NPV) investment appraisal method instead of IRR, since the non-conventional cash flows are easily accommodated by NPV. This is one area where NPV is considered to be superior to IRR.

[2 – 3 marks](c)(iii)Projects with significantly different business risk to current operations1. Where a proposed investment project has business risk that is significantly different

from current operations, it is no longer appropriate to use the weighted average cost of capital (WACC) as the discount rate in calculating the net present value of the project.

2. WACC can only be used as a discount rate where business risk and financial risk are not significantly affected by undertaking an investment project.

3. Where business risk changes significantly, the capital asset pricing model should be used to calculate a project-specific discount rate which takes account of the systematic risk of a proposed investment project.

[3 – 4 marks]

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Answer 3(a)Net present value evaluation of new confectionery investmentYear 1 2 3 4 5 Marks

$000 $000 $000 $000 $000Sales 3,605 8,488 11,474 16,884 [2]Variable cost (2,019) (5,093) (6,884) (10,299) [2]Fixed costs (1,030) (1,910) (3,060) (4,277) [1]

Taxable cash flow 556 1,485 1,530 2,308

Taxation (167) (446) (459) (692) [1.5]CA tax benefits 150 113 84 253 [2.5]Working capital (23) (23) (24) 820 [2]

After-tax cash flows 533 1,445 1,173 2,753 (439)

Discount at 12% 0.893 0.797 0.712 0.636 0.567 [1]

Present values 476 1,152 835 1,751 (249)

$000Sum of PV 3,965

Working capital (750) [1]Initial investment (2,000)

NPV 1,215 [1]

Comment:The proposed investment in the new product is financially acceptable, as the NPV is positive. [1 mark]

Examiner’s note:Including capital allowance tax benefits by subtracting capital allowances, calculating tax liability and then adding back the capital allowances is also acceptable.

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(b)The proposal to use a four-year time horizon The finance director believes that cash flows are too uncertain after four years to be

included in the net present value calculation, even though sales will continue beyond four years.

While it is true that uncertainty increases with project life, cutting off the analysis after four years will underestimate the value of the investment to the extent that cash flows after the cut-off point are ignored.

Furthermore, since the new confectionery line is expected to be popular, cash flows after year four could be substantial, increasing the extent of the undervaluation.

Artificially terminating the evaluation after four years has accelerated the recovery of working capital and has also led to a large balancing allowance. These increased cash flows, which arise in years four and five respectively, will overestimate the value of the investment.

[1 – 2 marks]

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The value of cash flows after the fourth year of operationThe approach here should be to calculate the present value of the expected future cash flows beyond year four. If the before-tax cash flows are assumed to be constant and if the one-year delay in tax liabilities is ignored, the year four present value of future cash flows beyond year four can be estimated using a perpetuity approach. If inflation in year five is ignored, the year four present value of cash flows from year five onwards will be:

2,308,000 × (1 – 0·3)/0·12 = $13,463,000The year zero present value of these cash flows = 13,463,000 × 0·636 = $8,562,468

If one year’s inflation is included:2,308,000 × 1·03 × (1 – 0·3))/0·12 = $13,867,000The year zero present value of these cash flows = 13,867,000 × 0·636 = $8,819,000

[Calculation: 1 – 2 marks]Although these calculations ignore the capital allowance tax benefits (which will decrease each year) and the incremental investment in working capital (which will increase slightly each year), the present value of cash flows after year four is still substantial.

[Discussion: 1 – 2 marks](c)Examiner note: only THREE ways of incorporating risk into investment appraisal were required to be discussed.

Risk and uncertaintyRisk in investment appraisal refers to the attachment of probabilities to the possible outcomes from an investment project and therefore represents a quantified assessment of the variability of expected returns. Uncertainty cannot be quantified by attaching probabilities and although the terms are often used interchangeably, the difference is important in investment appraisal.

Sensitivity analysisThis assesses the sensitivity of project NPV to changes in project variables. It calculates the relative change in a project variable required to make the NPV zero, or the relative change in NPV for a fixed change in a project variable. Only one variable is considered at a time. When the sensitivities for each variable have been calculated, the key or critical variables can be identified. These show where assumptions may need to be checked and where managers could focus their attention in order to increase the likelihood that the project will deliver its calculated benefits. However, since sensitivity analysis does not incorporate probabilities, it cannot be described as a way of incorporating risk into investment appraisal, although it is often described as such.

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Probability analysisThis approach involves assigning probabilities to each outcome of an investment project, or assigning probabilities to different values of project variables. The range of net present values that can result from an investment project is then calculated, together with the joint probability of each outcome. The net present values and their joint probabilities can be used to calculate the mean or average NPV (the expected NPV or ENPV) which would arise if the investment project could be repeated a large number of times. Other useful information that could be provided by the probability analysis includes the worst outcome and its probability, the probability of a negative NPV, the best outcome and its probability, and the most likely outcome. Managers could then make a decision on the investment that took account more explicitly of its risk profile.

Risk-adjusted discount rateIt appears to be intuitively correct to add a risk premium to the ‘normal’ discount rate to assess a project with greater than normal risk. The theoretical approach here would be to use the capital asset pricing model (CAPM) to determine a project-specific discount rate that reflected the systematic risk of an investment project. This can be achieved by selecting proxy companies whose business activities are the same as the proposed investment project: removing the effect of their financial risk by ungearing their equity betas to give an average asset beta; regearing the asset beta to give an equity beta reflecting the financial risk of the investing company; and using the CAPM to calculate a project-specific cost of equity for the investment project.

Adjusted paybackPayback can be adjusted for risk, if uncertainty is considered to be the same as risk, by shortening the payback period. The logic here is that as uncertainty (risk) increases with the life of the investment project, shortening the payback period for a project that is relatively risky will require it to pay back sooner, putting the focus on cash flows that are more certain (less risky) because they are nearer in time.

Payback can also be adjusted for risk by discounting future cash flows with a risk-adjusted discount rate, i.e. by using the discounted payback method. The normal payback period target can be applied to the discounted cash flows, which will have decreased in value due to discounting, so that the overall effect is similar to reducing the payback period with undiscounted cash flows.

[2 – 3 marks per method]

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Answer 4(a)Net present value of investment in new machinery

0 1 2 3 4 5 Marks$000 $000 $000 $000 $000 $000

Sales 6,084 6,327 6,580 6,844 [2]Variable costs (2,374) (2,504) (2,642) (2,787) [1]Contribution 3,710 3,823 3,938 4,056 Fixed costs (263) (276) (289) (304) [1]Operating cash flow Step 1 3,448 3,547 3,649 3,752 Taxation Step 2 (690) (709) (730) (750) [1.5]CA tax benefits (W1) Step 3 250 188 141 372 [3.5]Initial investment Step 4 (5,000) 250 [1]Working capital (W2) Step 5 (500) (24) (25) (26) (27) [1]Net cash flow (5,500) 3,424 3,083 3,102 3,387 (378) Discount at 12% 1.000 0.893 0.797 0.712 0.636 0.567 [1]PV (5,500) 3,057 2,457 2,208 2,154 (215)

NPV = 4,162 [1]

As the net present value of $4·162 million is positive, the expansion can be recommended as financially acceptable. [1]

Examiner comment on working capital changesSome candidates had difficulty calculating the incremental working capital investment, which was needed because the working capital was subject to the general rate of inflation. The new machine was planned to be replaced at the end of four years and so production to meet the increased demand would continue. Working capital should not therefore have been recovered at the end of the four-year life of the new machine, although students who did recover the working capital were not penalised.

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W1 CA tax benefitsYear WDV CA Tax rate Tax benefits

$000 $000 $0001 5,000 x 25% 1,250 x 20% = 250 2 3,750 x 25% 938 x 20% = 188 3 2,813 x 25% 703 x 20% = 141 4 2,109 - 250 = 1,859 x 20% = 372

(Balancing allowance)

W2 Working capital requirement0 1 2 3 4

$000 $000 $000 $000 $000Total working capital (500) (524) (548) (574) (601) Working capital requirement (500) (24) (25) (26) (27)

(b)A nominal (money terms) approach to investment appraisal discounts nominal cash flows with a nominal cost of capital. Nominal cash flows are found by inflating forecast values from current price estimates, for example, using specific inflation. Applying specific inflation means that different project cash flows are inflated by different inflation rates in order to generate nominal project cash flows. [2 – 3 marks]

A real terms approach to investment appraisal discounts real cash flows with a real cost of capital. Real cash flows are found by deflating nominal cash flows by the general rate of inflation. The real cost of capital is found by deflating the nominal cost of capital by the general rate of inflation, using the Fisher equation:(1 + real discount rate) × (1 + inflation rate) = (1 + nominal discount rate)

[2 – 3 marks]The net present value for an investment project does not depend on whether a nominal terms approach or a real terms approach is adopted, since nominal cash flows and the nominal discount rate are both discounted by the general rate of inflation to give real cash flows and the real discount rate, respectively. Both approaches give the same net present value.

Tutorial note for illustrative purposes:The real after-tax cost of capital of HDW Co can be found as follows:1·12/1·047 = 1·07, i.e. the real after-tax cost of capital is 7%.

The following illustration deflates nominal net cash flows (NCF) by the general rate of inflation (4·7%) to give real NCF, which are then discounted by the real cost of capital (7%).

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Allowing for rounding, the illustration shows that the present values of the real cash flows are the same as the present values of the nominal cash flows, and that the real terms approach NPV of $4·154 million is the same as the nominal terms approach NPV of $4·161 million. The two approaches produce identical NPVs and offer the same investment advice.

(c)Identification of two financial objectives A listed company such as HDW Co is likely to have a range of financial objectives.

Maximisation of shareholder wealth is often suggested to be the primary financial objective, and this can be substituted by the objective of maximising the company’s share price.

Other financial objectives that might be used by HDW Co could relate to earnings per share (for example, a target EPS value for a given period), operating profit (for example, a target level of profit before tax or PBIT), revenue (for example, a desired increase in revenue or sales) and so on. These examples of financial objectives can all be quantified, so that progress towards meeting them can be measured over time. [1 mark]

Discussion of support for objectives of planned investment The investment in the new machine will enable HDW Co to meet increased demand

for its products and the company expects to be able to sell all of the increased production at a profit. This will lead to increased revenue and operating profit (profit before interest and tax), so financial objectives relating to these accounting figures will be supported.

Whether a financial objective relating to increasing earnings per share (EPS) will be supported will depend on how the investment is financed. For example, raising equity finance by issuing new shares will dilute (decrease) EPS, while raising debt finance will increase interest payments, which will also dilute EPS.

The investment in the new machine has a positive net present value (NPV), so the market value of the company is expected to increase by the amount of the NPV. This

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increases the wealth of shareholders irrespective of how the investment is financed, since financing costs were accounted for by the discount rate (whether nominal or real). The investment in the new machine will therefore support the objective of shareholder wealth maximisation.

[5 marks]

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Chapter 6 Project Appraisal and Risk

I. Sensitivity analysis

1. D The sensitivity to a change in sales volume = 100 × 1,300/24,550 = 5·3%2. B Cash flow 10% factor PV

Year $ $0 Machine cost (280,000) 1.000 (280,000)

1 - 5 Contribution 200,000 3.791 758,200 1 - 5 Fixed costs (95,000) 3.791 (360,145)

118,055

PV of contribution must fall by $118,055Sale volume must fall by 118,055 / 758,200 = 15.57%Fall in sales volume = 50,000 units × 15.57% = 7,785 units

3. A To force an NPV = 0, the 4 year annuity factor, AF1-4 = 110,000/40,000 = 2.75Proof: the NPV calculation would be (2.75 × 40,000) – 110,000 = 0From tables, the 4-year annuity factor closest to 2.75 is 17%.In terms of sensitivity: (17 – 10)/10 = 70% sensitivity

II. Probability Analysis and Expected Value

4. D Beta should be rejected as it offers higher risk than Alpha for a lower return. Delta should be rejected as it offers a lower return than Alpha for the same level of risk.

5. D The expected value criterion is irrespective of risk.6. B The IRR (C) and the cost of the initial investment (A) are independent of the

risk of the project. The lower the risk of the project, the less (not greater) is the required rate of return (D).

7. C Statement 1 is false. As an average the expected value probably won’t actually occur in any single event so it does not represent a probable outcome. It is more appropriate for repeated events (for example expected sales each year for many years). By the same logic statement 3 is true.Statement 2 is true. Expected values fail to show the spread of possible values, therefore hiding the best/worst outcomes from the decision making process.Statement 4 is false. Risk is calculable (known or estimated probabilities

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and/or outcomes), uncertainty is not (either probabilities or some outcomes are unknown).

8. B Expected sales = (20,000 × 0.6) + (25,000 × 0.4) = 22,000 unitsExpected sales price = ($10 × 0.3) + ($15 × 0.7) = $13.50So expected revenue = 22,000 units × $13.50 = $297,000Expected margin = (30% × 0.5) + (40% × 0.5) = 35% therefore costs will be 1 – 35% = 65%So expected cost = 65% × $297,000 = $193,050

III. Simulation

9. B10. B A is incorrect. There is no decision rule with simulations – it is not an

‘optimising’ techniqueB is a clear advantage that simulations have over sensitivity analysisC is incorrect. The input variables and distributions are estimatesD has some validity potentially, but is not necessarily the case

Answer 5(a)The investment appraisal process is concerned with assessing the value of future cash flows compared to the cost of investment.

1. Since future cash flows cannot be predicted with certainty, managers must consider how much confidence can be placed in the results of the investment appraisal process. They must therefore be concerned with the risk and uncertainty of a project. Uncertainty refers to the situation where probabilities cannot be assigned to future cash flows. Uncertainty cannot therefore be quantified and increases with project life: it is usually true to say that the more distant is a cash flow, the more uncertain is its value.

[1 mark]2. Risk refers to the situation where probabilities can be assigned to future cash flows,

for example as a result of managerial experience and judgement or scenario analysis. Where such probabilities can be assigned, it is possible to quantify the risk associated with project variables and hence of the project as a whole. [2 marks]

3. If risk and uncertainty were not considered in the investment appraisal process,

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managers might make the mistake of placing too much confidence in the results of investment appraisal, or they may fail to monitor investment projects in order to ensure that expected results are in fact being achieved.

4. Assessment of project risk can also indicate projects that might be rejected as being too risky compared with existing business operations, or projects that might be worthy of reconsideration if ways of reducing project risk could be found in order to make project outcomes more acceptable.

[2 marks](b)Contribution per unit = 3·00 – 1·65 = $1·35 per unitTotal annual contribution = 20,000 × 1·35 = $27,000 per yearAnnual cash flow after fixed costs = 27,000 – 10,000 = $17,000 per yearPayback period = 50,000/17,000 = 2·9 years [2 marks](assuming that cash flows occur evenly throughout the year)

Discussion of payback period:1. The payback period calculated is greater than the maximum payback period used by

Umunat plc of two years and on this basis should be rejected. Use of payback period as an investment appraisal method cannot be recommended, however, because payback period does not consider all the cash flows arising from an investment project, as it ignores cash flows outside of the payback period. Furthermore, payback period ignores the time value of money.

2. The fact that the payback period is 2·9 years should not therefore be a reason for rejecting the project. The project should be assessed using a discounted cash flow method such as net present value or internal rate of return, since the project as a whole may generate an acceptable return on investment.

[2 marks](c)Calculation of project net present valueAnnual cash flow = ((20,000 × (3 – 1·65)) – 10,000 = $17,000 per yearNet present value = (17,000 × 3·605) – 50,000 = 61,285 – 50,000 = $11,285

[2 marks]Alternatively: PV (£)Sales revenue (20,000 × 3.00 × 3.605) 216,300Variable costs (20,000 × 1.65 × 3.605) (118,965)Contribution 97,335Initial investment (50,000)

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Fixed costs (10,000 × 3.605) (36,050)NPV 11,285

Sensitivity of NPV to sales volumeSales volume giving zero NPV = ((50,000/3·605) + 10,000)/1·35 = 17,681 unitsThis is a decrease of 2,319 units or 11·6%Alternatively, sales volume decrease = 100 × 11,285/97,335= 11·6%

[2 marks]Sensitivity of NPV to sales priceSales price for zero NPV = (((50,000/3·605) + 10,000)/20,000) + 1·65 = £2·843This is a decrease of 15·7p or 5·2%Alternatively, sales price decrease = 100 × 11,285/216,300 = 5·2%

[2 marks]Sensitivity of NPV to variable costVariable cost must increase by 15·7p or 9·5% to £1·81 to make the NPV zero.Alternatively, variable cost increase = 100 × 11,285/118,965 = 9·5%

[1 marks]Discussion of sensitivity analysis:1. Sensitivity analysis evaluates the effect on project net present value of changes in

project variables. The objective is to determine the key or critical project variables, which are those where the smallest change produces the biggest change in project NPV.

2. It is limited in that only one project variable at a time may be changed, whereas in reality several project variables may change simultaneously. For example, an increase in inflation could result in increases in sales price, variable costs and fixed costs.

3. Sensitivity analysis is not a way of evaluating project risk, since although it may identify the key or critical variables, it cannot assess the likelihood of a change in these variables. In other words, sensitivity analysis does not assign probabilities to project variables.

4. Where sensitivity analysis is useful is in drawing the attention of management to project variables that need careful monitoring if a particular investment project is to meet expectations.

5. Sensitivity analysis can also highlight the need to check the assumptions underlying the key or critical variables.

[3 marks](d)

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Expected value of sales volume:(17,500 × 0·3) + (20,000 × 0·6) + (22,500 × 0·1) = 19,500 units [1 mark]Expected NPV = (((19,500 × 1·35) – 10,000) × 3·605) – 50,000 = $8,852 [1 mark]

Discussion of ENPV:1. Since the expected net present value is positive, the project appears to be

acceptable. From earlier analysis we know that the NPV is positive at 20,000 per year, and the NPV will therefore also be positive at 22,500 units per year.

The NPV of the worst case is:(((17,500 × 1·35) – 10,000) × 3·605) – 50,000 = ($882)

The NPV of the best case is:(((22,500 × 1·35) – 10,000) × 3·605) – 50,000 = $23,452

2. There is thus a 30% chance that the project will produce a negative NPV, a fact not revealed by considering the expected net present value alone.

3. The expected net present value is not a value that is likely to occur in practice: it is perhaps more useful to know that there is a 30% chance that the project will produce a negative NPV (or a 70% chance of a positive NPV), since this may represent an unacceptable level of risk as far as the managers of Umunat plc are concerned.

4. It can therefore be argued that assigning probabilities to expected economic states or sales volumes has produced useful information that can help the managers of Umunat to make better investment decisions.

5. The difficulty with this approach is that probability estimates of project variables or future economic states are likely to carry a high degree of uncertainty and subjectivity.

[4 marks]

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Answer 6(a)Expected number of barrels extracted

EstimateExpected no. of barrels

(millions)1 30m × 100% × 0.1 32 30m × 40% × 0.5 63 30m × 25% × 0.4 3

12

Expected net oil revenueYear $m2 4m × $(85 – 5) 3203 4m × $(75 – 5) 2804 4m × $(100 – 5) 380

980[4 marks]

Residual value of equipment:$125m – (12m × $8) = $29m [2 marks]

Expected NPVYear 0 1 2 3 4 Marks

$m $m $m $m $mNet oil receipts 320.0 280.0 380.0

License payment (40.0) [1]Equipment (125.0) 29.0 [1]Operating costs (120.0) (160.0) (160.0) (160.0) [1]

Net cash flows (165.0) (120.0) 160.0 120.0 249.0

Discount rate 1.000 0.877 0.769 0.675 0.592

Present value (165.0) (105.2) 123.0 81.0 147.4

ENPV = $81.2m [1 mark]

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(b)NPV of worst possible outcomePredicted net oil revenueYear $m2 [(0.25 × 30m)/3] × $(85 – 5) 200.03 [(0.25 × 30m)/3] × $(75 – 5) 175.04 [(0.25 × 30m)/3] × $(100 – 5) 237.5

612.5[2 marks]

Residual value of equipment:$125m – (7.5m × $8) = $65m [1 mark]

Year 0 1 2 3 4

$m $m $m $m $mNet oil receipts 200.0 175.0 237.5

License payment (40.0)

Equipment (125.0) 65.0

Operating costs (120.0) (160.0) (160.0) (160.0)

Net cash flows (165.0) (120.0) 40.0 15.0 142.5

Discount rate 1.000 0.877 0.769 0.675 0.592

Present value (165.0) (105.2) 30.8 10.1 84.4

NPV = (144.9m) [2 marks]

(c)The calculations in (a) above show that the ENPV of the investment project is positive and so acceptance of the project is expected to enhance shareholder wealth. However, the calculations in (b) reveal that if the worst possible outcome occurs, the company will make a significant loss. Moreover the probability of making a loss is quite high. The final decision to go ahead should reflect the shareholders’ attitude towards risk.

[2 marks](d)A problem of the ENPV approach, however, is that it does not reveal the ‘downside’ risk associated with the project. We saw in (c) above that the ENPV of the project was positive but the downside risk was high. It is therefore useful to provide managers with information concerning downside risk where this method is being employed. [1 mark]

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The expected value represents a weighted average where the probabilities are used as weights. In practice, the expected value may not reflect any of the possible outcomes of the project, as is the case in this question. It can be argued that, where a company has a portfolio of projects, this is not a serious problem. Where, however, the company makes a large, one-off, project, the ENPV approach may not be suitable. [2 marks]

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Chapter 7 Asset Investment Decisions and Capital Rationing

I. Lease or Buy

1. C2. A Statement 1 is incorrect: Lessee’s acquire the risk and responsibility of

ownership with finance leases.Statement 2 is correct: Finance leases are accounted for as an asset and a payable – on the statement of financial position.Statement 3 is incorrect: Finance leases have a primary period covering all or most of the useful economic life of the asset.

3. C Interest should not be included as a cash flow as it is part of the discount rate.As a financing decision the alternatives should be assessed at the after tax cost of borrowing – the risk associated with each is the risk of borrowing (or not), and not related to what is done with the asset.

Answer 7(a)Evaluation of purchase versus leasing compares the net cost of each financing alternative using the after-tax cost of borrowing.

Borrowing to buy evaluationYear 0 1 2 3 4 Marks

£000 £000 £000 £000 £000Purchase and sale (320) 50 [2]CA tax benefits 24 18 39 [3]Maintenance costs (25) (25) (25) [1]Main. Costs benefits 8 8 8 [1]

Net cash flow (320) (25) 7 51 47

Discount factor (7%) 1.000 0.935 0.873 0.816 0.763

Present value (320) (23) 6 42 36

PV of borrowing to buy = –£259,000 [1 mark]

Workings: Capital allowance tax benefits

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Balancing allowance = (320,000 – 50,000) – (80,000 + 60,000) = £130,000

Leasing evaluationYear 0 1 2 3 4 Marks

£000 £000 £000 £000 £000Lease rentals (120) (120) (120) [1]Lease rentals tax

benefits 36 36 36 [1]

Net cash flows (120) (120) (84) 36 36

Discount factors (7%) 1.000 0.935 0.873 0.816 0.763

Present values (120) (112) (73) 29 27

PV of leasing = –£249,000 [1 mark]

On financial grounds, leasing is to be preferred as it is cheaper by £10,000. Note that the first lease rental is taken as being paid at year 0 as it is paid in the first month of the first year of operation. [1 mark]

An alternative form of evaluation combines the cash flows of the above two evaluations. Because this evaluation is more complex, it is more likely to lead to computational errors.

The PV of –£12,000 indicates that leasing would be £12,000 cheaper than borrowing. The difference between this and the previous evaluation is due to rounding.

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(b)Finance lease:1. A finance lease exists when the substance of the lease is that the lessee enjoys

substantially all of the risks and rewards of ownership, even though legal title to the leased asset does not pass from lessor to lessee.

2. A finance lease is therefore characterised by one lessee for most, if not all, of its useful economic life, with the lessee meeting maintenance and similar regular costs.

3. A finance lease cannot be cancelled, once entered into, without incurring severe financial penalties. A finance lease therefore acts as a kind of medium- to long-term source of debt finance which, in substance, allows the lessee to purchase the desired asset.

4. This ownership dimension is recognised in the statement of financial position, where a finance-leased asset must be capitalised (as a non-current asset), together with the amount of the obligations to make lease payments in future periods (as a liability).

[4 – 5 marks]Operating lease:5. In contrast, an operating lease is a rental agreement where several lessees are expected

to use the leased asset and so the lease period is much shorter than the asset’s useful economic life.

6. Maintenance and similar costs are borne by the lessor, with this cost being reflected in the lease rentals charged.

7. An operating lease can usually be cancelled without penalty at short notice. This allows the lessee to ensure that only up-to-date assets are leased for use in business operations, avoiding the obsolescence problem associated with the rapid pace of technological change in assets such as personal computers and photocopiers.

8. Because the substance of an operating lease is that of a short-term rental agreement, operating leases do not require to be capitalised in the statement of financial position, allowing companies to take advantage of this form of ‘off-balance sheet financing’.

[4 – 5 marks]

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Answer 8(a)In order to evaluate whether Spot Co should use leasing or borrowing, the present value of the cost of leasing is compared with the present value of the cost of borrowing.

LeasingThe lease payments should be discounted using the cost of borrowing of Spot Co. Since taxation must be ignored, the before-tax cost of borrowing must be used. The 7% interest rate of the bank loan can be used here.

The five lease payments will begin at year 0 and the last lease payment will be at the start of year 5, i.e. at the end of year 4. The appropriate annuity factor to use will therefore be 4·387 (1·000 + 3·387).

Present value of cost of leasing = 155,000 x 4·387= $679,985

BorrowingThe purchase cost and the present value of maintenance payments will be offset by the present value of the future scrap value. The appropriate discount rate is again the before-tax cost of borrowing of 7%.

The cheaper source of financing is leasing, since the present value of the cost of leasing is $98,540 less than the present value of the cost of borrowing.

(b)Operating leasing can act as a source of short-term finance, while finance leasing can act as a source of long-term finance.

Operating leasing offers a solution to the obsolescence problem, whereby rapidly aging assets can decrease competitive advantage. Where keeping up-to-date with the latest technology is essential for business operations, operating leasing provides equipment on short-term contracts which can usually be cancelled without penalty to the lessee. Operating leasing can also provide access to skilled maintenance, which might otherwise need to be bought in by

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the lessee, although there will be a charge for this service.

Both operating leasing and finance leasing provide access to non-current assets in cases where borrowing may be difficult or even not possible for a company. For example, the company may lack assets to offer as security, or it may be seen as too risky to lend to. Since ownership of the leased asset remains with the lessor, it can be retrieved if lease rental payments are not forthcoming.

ACCA Marking Scheme

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II. Asset Replacement Decision

4. B Year 0 1 2 3$ $ $ $

Outlay (10,000) Running costs (3,000) (5,000) (7,000) Disposal value 2,000 Net cash flow (10,000) (3,000) (5,000) (5,000) Discount at 10% 1.000 0.909 0.826 0.751 PV (10,000) (2,727) (4,130) (3,755)

NPV = (20,612) Annual factor 2.487

EAC = (8,288)

5. C Net present cost of 1 year cycle = 20,000 – (10,000 × 0.909) = $10,910 costNet present cost of 2 year cycle = 20,000 – [(8,000 – 5,000) × 0.826] = $17,522 costEAC 1 year cycle = $10,910 / 0.909 = 12,002EAC 2 year cycle = $17,522 / 1.736 = 10,093The 2-year cycle should be chosen with an equivalent annual cost of $10,093

6. C The NPVs cannot be directly compared as they relate to different time periods. Equivalent annual benefits (EAB) should be compared. This is similar in principle to equivalent annual cost.EAB Gas = $50,000 / AF1-5 = 50,000 / 3.993 = $12,522 paEAB Electric = $68,000 / AF1-7 = 68,000 / 5.206 = $13,062 paTherefore electric should be chosen as its equivalent annual benefit is higher.

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Answer 9(a)Net present value evaluation of investmentAfter-tax weighted average cost of capital = (11 × 0.8) + (8.6 × (1 – 0.3) × 0.2) = 10%[2 marks]

Year 1 2 3 4 5 Marks$000 $000 $000 $000 $000

Contribution 440 550 660 660 [2]Fixed costs (240) (260) (280) (300) [1]

Taxable cash flow 200 290 380 360

Taxation - (60) (87) (114) (108) [1]CA tax benefits - 60 45 34 92 [3]Scrap value - - - 30 - [1]

After-tax cash flows 200 290 338 310 (16)

Discount at 10% 0.909 0.826 0.751 0.683 0.621 [1]

Present values 182 240 254 212 (10)

$000 Marks

PV of future benefits 878Less: initial investment (800)NPV 78 [1]

The net present value is positive and so the investment is financially acceptable. However, demand becomes greater than production capacity in the fourth year of operation and so further investment in new machinery may be needed after three years. The new machine will itself need replacing after four years if production capacity is to be maintained at an increased level. It may be necessary to include these expansion and replacement considerations for a more complete appraisal of the proposed investment.

A more complete appraisal of the investment could address issues such as the assumption of constant selling price and variable cost per kilogram and the absence of any consideration of inflation, the linear increase in fixed costs of production over time and the linear increase in demand over time. If these issues are not addressed, the appraisal of investing in the new machine is likely to possess a significant degree of uncertainty.

[1 – 2 marks]

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WorkingsAnnual contribution

Capital allowance (CA) tax benefits

(b)Internal rate of return evaluation of investmentYear 1 2 3 4 5

$000 $000 $000 $000 $000After-tax cash flows 200 290 338 310 (16)

Discount at 20% 0.833 0.694 0.579 0.482 0.402

Present values 167 201 196 149 (6)

$000 Marks

PV of future benefits 707Less: initial investment (800)NPV (93) [1]

IRR = [2 marks]

The investment is financially acceptable since the internal rate of return is greater than the cost of capital used for investment appraisal purposes. However, the appraisal suffers

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from the limitations discussed in connection with net present value appraisal in part (a).[1 – 2 marks]

(c)Risk and uncertainty1. Risk refers to the situation where probabilities can be assigned to a range of expected

outcomes arising from an investment project and the likelihood of each outcome occurring can therefore be quantified.

2. Uncertainty refers to the situation where probabilities cannot be assigned to expected outcomes.

3. Investment project risk therefore increases with increasing variability of returns, while uncertainty increases with increasing project life. The two terms are often used interchangeably in financial management, but the distinction between them is a useful one.

[2 – 3 marks]

Sensitivity analysis1. Sensitivity analysis assesses how the net present value of an investment project is

affected by changes in project variables.2. Considering each project variable in turn, the change in the variable required to

make the net present value zero is determined, or alternatively the change in net present value arising from a fixed change in the given project variable. In this way the key or critical project variables are determined.

3. However, sensitivity analysis does not assess the probability of changes in project variables and so is often dismissed as a way of incorporating risk into the investment appraisal process.

[2 – 3 marks]Probability analysis1. Probability analysis refers to the assessment of the separate probabilities of a

number of specified outcomes of an investment project. For example, a range of expected market conditions could be formulated and the probability of each market condition arising in each of several future years could be assessed.

2. The net present values arising from combinations of future economic conditions could then be assessed and linked to the joint probabilities of those combinations. The expected net present value (ENPV) could be calculated, together with the probability of the worst-case scenario and the probability of a negative net present value. In this way, the downside risk of the investment could be determined and incorporated into the investment decision.

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[2 – 3 marks]

Answer 10(a)Calculation of net present value (NPV)As nominal after-tax cash flows are to be discounted, the nominal after-tax weighted average cost of capital of 7% must be used.

Year 1 2 3 4 5 Marks$000 $000 $000 $000 $000

Sales 1,300 2,466 3,622 2,018 [2]Variable cost (513) (1,098) (1,809) (1,035) [1]

Contribution 787 1,368 1,813 983

Fixed costs (105) (115) (125) (125) [0.5]

Taxable cash flow 682 1,253 1,688 858

Taxation (205) (376) (506) (257) [1]CA tax benefits 113 84 63 160 [4]

After-tax cash flow 682 1,161 1,396 415 (97)

Scrap value 100 [0.5]

Net cash flow 682 1,161 1,396 515 (97)

Discount at 7% 0.935 0.873 0.816 0.763 0.713 [0.5]

Present values 638 1,014 1,139 393 (69)

$000Present value of cash inflows 3,115

Cost of machine (1,500) [0.5]

NPV 1,615 [1]

Project 1 has a positive NPV of $1,615,000 and so it is financially acceptable to Ridag Co. However, the discount rate used here is the current weighted average after-tax cost of capital. As this is a recently-developed product, it may be appropriate to use a project-specific discount rate that reflects the risk of the new product launch. [1 mark]

WorkingsSales revenue

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Variable cost

Capital allowance tax benefits

*843,750 – 210,938 – 100,000 = $532,812

(b)Calculation of equivalent annual cost for machine 1Since taxation and capital allowances are to be ignored, and where relevant all information relating to project 2 has already been adjusted to include future inflation, the correct discount rate to use here is the nominal before-tax weighted average cost of capital of 12%.Year 0 1 2 3 4

$ $ $ $ $Maintenance costs (25,000) (29,000) (32,000) (35,000)

Investment and scrap (200,000) 25,000

Net cash flow (200,000) (25,000) (29,000) (32,000) (10,000)

Discount at 12% 1.000 0.893 0.797 0.712 0.636

Present values (200,000) (22,325) (23,113) (22,784) (6,360)

Present value of cash flows $274,582

Cumulative present value factor 3.037

Equivalent annual cost = 274,582/3.037 = $90,412 [2 marks]

Calculation of equivalent annual cost for machine 2

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Year 0 1 2 3$ $ $ $

Maintenance costs (15,000) (20,000) (25,000)

Investment and scrap (225,000) 50,000

Net cash flow (225,000) (15,000) (20,000) 25,000

Discount at 12% 1.000 0.893 0.797 0.712

Present values (225,000) (13,395) (15,940) 17,800

Present value of cash flows $236,535

Cumulative present value factor 2.402

Equivalent annual cost = 236,535/2.402 = $98,474 [2 marks]

The machine with the lowest equivalent annual cost should be purchased and calculation shows this to be Machine 1. If the present value of future cash flows had been considered alone, Machine 2 (cost of $236,535) would have been preferred to Machine 1 (cost of $274,582). However, the lives of the two machines are different and the equivalent annual cost method allows this to be taken into consideration. [2 marks]

(c)Within the context of investment appraisal, risk relates to the variability of returns and so it can be quantified, for example by forecasting the probabilities related to future cash flows. From this point of view, risk can be differentiated from uncertainty, which cannot be quantified. Uncertainty can be said to increase with project life, while risk increases with the variability of returns. [1 mark]

It is commonly said that risk can be included in the investment appraisal process by using sensitivity analysis, which determines the effect on project net present value of a change in individual project variables. The analysis highlights the project variable to which the project net present value is most sensitive in relative terms. However, since sensitivity analysis changes only one variable at a time, it ignores interrelationships between project variables.

While sensitivity analysis can indicate the key or critical variable, it does not indicate the likelihood of a change in the future value of this variable, i.e. sensitivity analysis does not indicate the probability of a change in the future value of the key or critical variable. For this reason, given the earlier comments on risk and uncertainty, it can be said that sensitivity analysis is not a method of including risk in the investment appraisal process.

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[2 – 3 marks]Probability analysis, as its name implies, attaches probabilities to the expected future cash flows of an investment project and uses these to calculate the expected net present value (ENPV). The ENPV is the average NPV that would be expected to occur if an investment project could be repeated a large number of times. The ENPV can also be seen as the mean or expected value of an NPV probability distribution. Given the earlier discussion of risk and uncertainty, it is clear that probability analysis is a way of including a consideration of risk in the investment appraisal process. It is certainly a more effective way of considering the risk of investment projects than sensitivity analysis.

A weakness of probability analysis, however, lies in the difficulty of estimating the probabilities that are to be attached to expected future cash flows. While these probabilities can be based on expert judgement and previous experience of similar investment projects, there remains an element of subjectivity which cannot be escaped.

[2 – 3 marks]

III. Capital Rationing

7. A Both statements are correct. The profitability index approach assumes that projects are divisible. Where capital rationing extends over more than one period, linear programming should be used rather than the profitability index approach.

8. A Investment Initial outlay

PV of net cash inflows

PI Ranking

$m $mKurai 186 211 1.1 4Barisan 65 84 1.3 2Carnic 100 120 1.2 3Flinders 50 71 1.4 1

9. B The NPV approach is consistent with the objective of maximising shareholder wealth.

10. B Statement 1 is true and Statement 2 is false. The profitability index should only be used to rank projects where the projects are divisible.

11. B Since projects are divisible all $500,000 can be invested, hence projects 2, 4 and 3 would be invested in fully, which require $450,000 and earning NPV of $135,000. The remaining $50,000 would be invested in 1/6 of project 1,

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giving a further $10,000 NPV.

Option A ignores the fact that capital is rationed. Option C assumes projects are not divisible. Option D selects the two highest NPVs that consist of the entire $500,000.

12. A

Option B ranks the projects according to the discounted future cash flows before deducting the initial outlay.Option C ranks the projects according to their NPV’s.Option D ranks the projects according to the PI based on undiscounted cash flows.

13. CProject Investment

outlayPV of net cash

inflowsPI

$m $mJapura 40 48 1.2Branco 45 64 1.4Tapajos 60 66 1.1Napo 70 92 1.3

14. B Initial outlay ($40m/4·0) = $10mCash inflows (20% × $10m) = $2mOption A calculates the initial outlays as (20% × $40m) = $8mThe cash inflows are 20% × $8m = $1·6mOption C calculates the cash inflows as ($10m/0·20) = $50mOption D calculates the initial outlay as (4·0 × $40m) = $160mThe cash inflows are (20% × $160m) = $32m

15. C Leo Taurus PiscesTotal present value 560 370 330Initial outlay 450 285 240PI 1.24 1.30 1.38

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Ranking 3 2 1

16. D Leasing may be possible. A joint venture partner may provide additional funding. Although delaying projects will probably reduce their NPV (time value of money, and competitor response), this may be better than not investing at all.

Answer 11(a)(i)Analysis of projects assuming they are divisible.

DF @ 12% Project 1 PV at 12% Project 3 PV at 12%$ $ $ $

Initial investment 1.000 (300,000) (300,000) (400,000) (400,000)Year 1 0.893 85,000 75,905 124,320 111,018Year 2 0.797 90,000 71,730 128,795 102,650Year 3 0.712 95,000 67,640 133,432 95,004Year 4 0.636 100,000 63,600 138,236 87,918Year 5 0.567 95,000 53,865 143,212 81,201

32,740 77,791

[1 mark] [2 marks]

Project 2 NPV at 12% = (140,800 x 3.605) – 450,000 = $57,584 [1 mark]

Profitability indexRanking

Project 1 (332,740 / 300,000) 1.11 3Project 2 (507,584 / 450,000) 1.13 2Project 3 (477,791 / 400,000) 1.19 1

[2 marks]

The optimum investment schedule involves investment in projects 3 and 2:Project PI Ranking Investment NPV

3 1.19 1 400 77,7912 1.13 2 400 51,186 (57,584 × 400/450)

800 128,977

[2 marks]

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(a)(ii)Projects Investment NPV

1 + 2 750,000 90,324 (32,740 + 57,584)1 + 3 700,000 110,531 (32,740 + 77,791)

The optimum combination is now projects 1 and 3. [2 marks]

(b)1. The NPV decision rule requires that a company invest in all projects that have a

positive net present value. This assumes that sufficient funds are available for all incremental projects, which is only true in a perfect capital market. [2 marks]

2. When insufficient funds are available, that is when capital is rationed, projects cannot be selected by ranking by absolute NPV. Choosing a project with a large NPV may mean not choosing smaller projects that, in combination, give a higher NPV. Instead, if projects are divisible, they can be ranked using the profitability index in order make the optimum selection. If projects are not divisible, different combinations of available projects must be evaluated to select the combination with the highest NPV.

[1 mark]

(c)The NPV decision rule, to accept all projects with a positive net present value, requires the existence of a perfect capital market where access to funds for capital investment is not restricted. In practice, companies are likely to find that funds available for capital investment are restricted or rationed.

Hard capital rationing:1. Hard capital rationing is the term applied when the restrictions on raising funds

are due to causes external to the company.2. For example, potential providers of debt finance may refuse to provide further funding

because they regard a company as too risky. This may be in terms of financial risk, for example if the company’s gearing is too high or its interest cover is too low, or in terms of business risk if they see the company’s business prospects as poor or its operating cash flows as too variable.

3. In practice, large established companies seeking long-term finance for capital investment are usually able to find it, but small and medium-sized enterprises will

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find raising such funds more difficult.[3 marks]

Soft capital rationing1. Soft capital rationing refers to restrictions on the availability of funds that arise

within a company and are imposed by managers. There are several reasons why managers might restrict available funds for capital investment.

2. Managers may prefer slower organic growth to a sudden increase in size arising from accepting several large investment projects. This reason might apply in a family-owned business that wishes to avoid hiring new managers.

3. Managers may wish to avoid raising further equity finance if this will dilute the control of existing shareholders.

4. Managers may wish to avoid issuing new debt if their expectations of future economic conditions are such as to suggest that an increased commitment to fixed interest payments would be unwise.

5. One of the main reasons suggested for soft capital rationing is that managers wish to create an internal market for investment funds. It is suggested that requiring investment projects to compete for funds means that weaker or marginal projects, with only a small chance of success, are avoided. This allows a company to focus on more robust investment projects where the chance of success is higher. This cause of soft capital rationing can be seen as a way of reducing the risk and uncertainty associated with investment projects, as it leads to accepting projects with greater margins of safety.

[4 marks](d)When undertaking the appraisal of an investment project, it is essential that only relevant cash flows are included in the analysis. If non-relevant cash flows are included, the result of the appraisal will be misleading and incorrect decisions will be made. A relevant cash flow is a differential (incremental) cash flow, one that changes as a direct result of an investment decision. [2 marks]

Examples of relevant cash flowsIf current fixed production overheads are expected to increase, for example, the additional fixed production overheads are a relevant cost and should be included in the investment appraisal. Existing fixed production overheads should not be included.

A new cash flow arising as the result of an investment decision is a relevant cash flow. For example, the purchase of raw materials for a new production process and the net cash flows

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arising from the production process are both relevant cash flows.

The incremental tax effects arising from an investment decision are also relevant cash flows, providing that a company is in a tax-paying position. Direct labour costs, for example, are an allowable deduction in calculating taxable profit and so give rise to tax benefits: tax liabilities arising on incremental taxable profits are also a relevant cash flow.

One area where caution is required is interest payments on new debt used to finance an investment project. They are a differential cash flow and hence relevant, but the effect of the cost of the debt is incorporated into the discount rate used to determine the net present value. Interest payments should not therefore be included as a cash flow in an investment appraisal.

Market research undertaken to determine whether a new product will sell is often undertaken prior to the investment decision on whether to proceed with production of the new product. This is an example of a sunk cost. These are costs already incurred as a result of past decisions, and so are not relevant cash flows.

[3 marks]

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