1.1 Payback period
1.1.1 Time it takes the project to payback its initial investment.
1.1.2 When is useful?
1.1.3 A long payback period is considered risky because it relies on cash flows that are in the distant future.
1.1.4 Decision rule:
1.1.5 General approach:
Year 
Cash flows ($) 
Cumulative cash flows ($) 
0 
(100,000) 
(100,000) 
1 
20,000 
(80,000) 
2 
30,000 
(50,000) 
3 
40,000 
(10,000) 
4 
30,000 
20,000 
5 
40,000 

Payback period = 3 years + 10,000/30,000
= 3.33 years or 3 years 4 months
1.1.6 Discounted payback period:
Year 
Cash flow 
Discounted 
Cumulative cash flow 
0 
(2,000) 
(2,000) 
(2,000) 
1 
600 
545 
(1,455) 
2 
500 
413 
(1,042) 
3 
600 
451 
(591) 
4 
600 
410 
(181) 
5 
300 
186 
5 
6 
200 
113 
118 
The payback period is about 5 years.
1.1.7 Advantages and disadvantages of payback period
Advantages 
Disadvantages 


1.2 Accounting Rate of Return (ARR) (Pilot, Jun 09)
1.2.1 Also known as ROCE or ROI.
1.2.2 Decision rule:
1.2.3 Calculation of ARR – three version
ARR 
= 
Profit for the year 
× 100% 
Asset book value at start of year 
Then, take average of each year’s ARR to find the average ARR.
ARR 
= 
Average annual profit 
× 100% 
Initial capital invested 
ARR 
= 
Average annual profit 
× 100% 
Average capital invested 
Average capital invested 
= 
Initial investment + Scrap value 
2 
1.2.4 Advantages and disadvantages of ARR
Advantages 
Disadvantages 


1.3 Net Present Value (NPV)
1.3.1 PV of cash inflows compare with the PV of cash outflows to obtain a NPV.
1.3.2 The discount rate equals its cost of capital or WACC.
1.3.3 Decision rule:
1.3.4 If the company has two or more mutually exclusive projects under consideration it should choose the one with the highest NPV.
1.3.5 The NPV gives the impact of the project on shareholder wealth.
1.3.6 Advantages and disadvantages of NPV
Advantages 
Disadvantages 


1.3.7 Why NPV is superior to other methods?
1.4 Internal Rate of Return (IRR) (Dec 07, Jun 08, Jun 09, Dec 11)
1.4.1 IRR is defined as the discount rate at which the NPV equals zero. In other words, the IRR represents the breakeven discount rate for the investment.
1.4.2 Decision rule:
1.4.3 Steps in calculating the IRR using linear interpolation:
1. Calculate two NPV at two different discount rates. One must be positive and another one must be negative.
2. Using the following formula to find the IRR
IRR = L +
where:
L = Lower rate of interest
H = Higher rate of interest
NL = NPV at lower rate of interest
NH = NPV at higher rate of interest
1.4.4 Advantages and disadvantages of IRR (Pilot, Jun 10)
Advantages 
Disadvantages 


2. Stages in the Capital Investment Projects
(June 2009)
2.1 Stages can be summarized as follows:
Stages 
Explanation 
Identify investment opportunities 

Screen investment proposals 

Analyse and evaluate investment proposals 

Approve investment proposals 

Implementation 

Monitoring 

Postcompletion audit 

3. Determination of the Cash Flows
3.1 Relevant cash flows
3.1.1 The following principles should be applied when identifying costs that are relevant to a period.
Relevant costs 
Explanation 
Future costs 

Cash flows 

Incremental costs 

Opportunity costs 

3.2 Nonrelevant costs
3.2.1 Other nonrelevant costs:
4. Allowing for Tax, Inflation and Working Capital
4.1 Inflation (Pilot, Jun 08, Jun 09, Dec 10, Jun 11)
4.1.1 Inflation has two impacts on NPV:
4.1.2 Real and money (nominal) interest rate
(1 + i) = (1 + r) (1 + h)
Where h = inflation rate
r = real interest rate
i = nominal interest rate
4.2 Taxation (Pilot, Jun 07, Dec 07, Jun 08, Dec 08, Jun 10, Dec 10, Jun 11, Dec 11)
4.2.1 Taxation has the following two effects on cash flow:
Effects 
Explanation 
Tax on profits 

Tax benefits from WDAs 

4.3 Working capital (Jun 08, Dec 08, Jun 11, Dec 11)
4.3.1 New project requires an additional investment in working capital.
4.3.2 The treatment of working capital is as follows:
4.4 General layout of cash flow preparation
4.4.1 The general layout can be shown as follows:
Year 
0 
1 
2 
3 
4 

$000 
$000 
$000 
$000 
$000 
Sales 

X 
X 
X 

Costs 

(X) 
(X) 
(X) 

Operating cash flows 

X 
X 
X 

Taxation 


(X) 
(X) 
(X) 
Tax benefit of CAs 


X 
X 
X 
Capital expenditure and scrap value 
(X) 


X 

Working capital changes 
(X) 
(X) 
(X) 
(X) 
X 
Net cash flows 
(X) 
X 
X 
X 
X 
Discount factor 
X 
X 
X 
X 
X 
Present value 
(X) 
X 
X 
X 
X 
Question 1 Net present value = 1,645,000 – 2,000,000 = ($355,000) so reject the project. The following information was included with the draft investment appraisal: 1. The initial investment is $2 million Required: (a) Identify and comment on any errors in the investment appraisal prepared by the trainee accountant. (5 marks) 
5. Project Appraisal and Risk
5.1 Risk and uncertainty (Dec 07, Jun 11)
5.1.1 Risk refers to the situation where probabilities can be assigned to a range of expected outcomes, so it can be quantified.
5.1.2 Uncertainty refers to the situation where probabilities cannot be assigned to expected outcomes, so it is unquantifiable. It can only be described.
5.2 Probability analysis (Dec 2007, Jun 11)
5.2.1 It refers to the assessment of the separate probabilities of a number of specified outcomes of an investment project.
5.2.2 The NPV from combinations of future economic conditions could be assessed and linked to the joint probabilities of those combinations. The expected NPV could be calculated.
5.2.3 The expected value (EV) is the weighted average of all possible outcomes, with the weightings based on the probability estimates.
EV =
Where: p = the probability of an outcome
x = the value of an outcome
5.3 Sensitivity analysis (Dec 07, Jun 11, Dec 11)
5.3.1 Sensitivity analysis assesses how the NPV of an investment project is affected by changes in project variables. The purpose is to identify the key or critical variables so that management can concern more.
5.3.2 The change in one variable required to make the NPV to be zero.
5.3.3 Or alternatively, the change in NPV arising from a fixed change in the given project variable.
5.3.4 However, sensitivity analysis does not assess the probability of changes in project variables.
5.3.5 A simple approach to deciding which variables the NPV is particularly sensitive to is to calculate the sensitivity of each variable:
Sensitivity 
= 
NPV 
% 
PV of project variable 
5.3.6 The lower the percentage, the more sensitive is NPV to that project variable as the variable would need to change by a smaller amount to make the project nonviable.
5.4 Adjusted payback (Jun 09, Jun 11)
5.4.1 Payback can be adjusted for risk:
5.4.2 Discounted payback:
5.5 Simulation
5.5.1 An analysis of how changes in more than one variable (e.g. market share and sales price) may affect the NPV of a project.
Question 2 Required: (a) Explain why risk and uncertainty should be considered in the investment appraisal process. (5 marks)
Calculate and comment on the expected net present value of the project. (6 marks) 
6. Asset Investment Decisions
6.1 Lease or buy (Dec 09)
6.1.1 DCF techniques can also be used to assess whether to finance an investment with a lease or a bank loan.
6.1.2 Numerical analysis
Step 1: the cost of leasing (payments, lost capital allowances and lost scrap revenue)
Step 2: the benefits of leasing (savings on loan repayments = PV of loan = initial outlay)
Step 3: discounting at the after tax cost of debt
Step 4: calculate the NPV – if positive it means that the lease is cheaper than the after tax cost of a loan.
6.1.3 Finance lease:
6.1.4 Operating lease:
6.1.5 Attractions of finance lease for lessee:
6.1.6 Attractions of operating lease for lessee:
6.1.7 Attractions of operating lease for lessor:
Question 3 Purchasing the machine outright Leasing
General Required: (a) Calculate the net present value at 31 December 2008, using the after tax cost of capital, for: Calculate the revised net present values of the three options for the turbine given capital rationing. Advise whether your recommendation in (a) would change. 
6.2 Asset replacement
6.2.1 NPV can be applied to situations of assets replacement.
6.2.2 Compare the purchase cost with the cost savings or benefits,
6.3 Replacement cycles (Dec 09, Jun 10)
6.3.1 How frequently should an asset be replaced? The equivalent annual cost (EAC) or annual equivalent annuity (AEA) can be used for evaluation.
EAC = 
NPV of costs 
Annuity factor for the number of years in the cycle 
The best decision is to choose the option with the lowest EAC.
6.3.2 Is it worth paying more for an asset that has a longer expected life? The equivalent annual benefit (EAB) can be applied.
EAB = 
NPV of project 
Annuity factor for the life of project 
The best decision is to choose the option with the highest equivalent annual benefit.
Question 4
Original cost, maintenance costs and resale values are expressed in current prices. That is, for example, maintenance for a two year old oven would cost $800 for maintenance undertaken now. It is expected that maintenance costs will increase at 10% per annum and oven replacement cost and resale values at 5% per annum. The money discount rate is 15%. Required: (a) Calculate the preferred replacement policy for the ovens in a choice between a two year or three year replacement cycle. (12 marks) 
6.3 Capital rationing (Dec 09, Dec 11)
6.3.1 In a perfect capital market, a company can raise funds as and when it needs them.
6.3.2 However, in practice, it is not the case. The capital available is always to be limited or rationed. There are two types of rationing:
6.3.3 External (hard) capital rationing:
6.3.4 Internal (soft) capital rationing:
6.3.5 Single period capital rationing
PI = 
PV of future cash flows 
Initial investment 
6.3.6 Multiperiod capital rationing
6.3.7 Practical steps to deal with capital rationing include:
Question 5 Project 1
Project 2 Project 3 Basril plc has a money cost of capital of 12% and taxation should be ignored. Required: (a) Determine the best way for Basril plc to invest the available funds and calculate the resultant NPV: 
Additional Examination Style Questions
Question 6 – WACC, NPV and Projectspecific Discount Rate
Rupab Co is a manufacturing company that wishes to evaluate an investment in new production machinery. The machinery would enable the company to satisfy increasing demand for existing products and the investment is not expected to lead to any change in the existing level of business risk of Rupab Co.
The machinery will cost $2·5 million, payable at the start of the first year of operation, and is not expected to have any scrap value. Annual beforetax net cash flows of $680,000 per year would be generated by the investment in each of the five years of its expected operating life. These net cash inflows are before taking account of expected inflation of 3% per year. Initial investment of $240,000 in working capital would also be required, followed by incremental annual investment to maintain the purchasing power of working capital.
Rupab Co has in issue five million shares with a market value of $3·81 per share. The equity beta of the company is 1·2. The yield on shortterm government debt is 4·5% per year and the equity risk premium is approximately 5% per year.
The debt finance of Rupab Co consists of bonds with a total book value of $2 million. These bonds pay annual interest before tax of 7%. The par value and market value of each bond is $100.
Rupab Co pays taxation one year in arrears at an annual rate of 25%. Capital allowances (taxallowable depreciation) on machinery are on a straightline basis over the life of the asset.
Required:
(a) Calculate the aftertax weighted average cost of capital of Rupab Co. (6 marks)
(b) Prepare a forecast of the annual aftertax cash flows of the investment in nominal terms, and calculate and comment on its net present value. (8 marks)
(c) Explain how the capital asset pricing model can be used to calculate a projectspecific discount rate and discuss the limitations of using the capital asset pricing model in investment appraisal. (11 marks)
(25 marks)
(ACCA F9 Financial Management December 2008 Q3)
Question 7 – NPV and Projectspecific Cost of Equity
CJ Co is a profitable company which is financed by equity with a market value of $180 million and by debt with a market value of $45 million. The company is considering two investment projects, as follows.
Project A
This project is an expansion of existing business costing $3·5 million, payable at the start of the project, which will increase annual sales by 750,000 units. Information on unit selling price and costs is as follows:
Selling price: 
$2.00 per unit (current price terms) 
Selling costs: 
$0.04 per unit (current price terms) 
Variable costs: 
$0.80 per unit (current price terms) 
Selling price inflation and selling cost inflation are expected to be 5% per year and variable cost inflation is expected to be 4% per year. Additional initial investment in working capital of $250,000 will also be needed and this is expected to increase in line with general inflation.
Project B
This project is a diversification into a new business area that will cost $4 million. A company that already operates in the new business area, GZ Co, has an equity beta of 1·5. GZ Co is financed 75% by equity with a market value of $90 million and 25% by debt with a market value of $30 million.
Other information
CJ Co has a nominal weighted average aftertax cost of capital of 10% and pays profit tax one year in arrears at an annual rate of 30%. The company can claim capital allowances (taxallowable depreciation) on a 25% reducing balance basis on the initial investment in both projects.
Riskfree rate of return: 4%
Equity risk premium: 6%
General rate of inflation: 4·5% per year
Directors’ views on investment appraisal
The directors of CJ Co require that all investment projects should be evaluated using either payback period or return on capital employed (accounting rate of return). The target payback period of the company is two years and the target return on capital employed is 20%, which is the current return on capital employed of CJ Co. A project is accepted if it satisfies either of these investment criteria.
The directors also require all investment projects to be evaluated over a fouryear planning period, ignoring any scrap value or working capital recovery, with a balancing allowance (if any) being claimed at the end of the fourth year of operation.
Required:
(a) Calculate the net present value of Project A and advise on its acceptability if the project were to be appraised using this method. (12 marks)
(b) Critically discuss the directors’ views on investment appraisal. (7 marks)
(c) Calculate a projectspecific cost of equity for Project B and explain the stages of your calculation. (6 marks)
(25 marks)
(ACCA F9 Financial Management December 2010 Q1)
Question 8 – NPV, IRR and Maximization of Shareholders’ Wealth
SC Co is evaluating the purchase of a new machine to produce product P, which has a short product lifecycle due to rapidly changing technology. The machine is expected to cost $1 million. Production and sales of product P are forecast to be as follows:
Year 
1 
2 
3 
4 
Production and sales (units/year) 
35,000 
53,000 
75,000 
36,000 
The selling price of product P (in current price terms) will be $20 per unit, while the variable cost of the product (in current price terms) will be $12 per unit. Selling price inflation is expected to be 4% per year and variable cost inflation is expected to be 5% per year. No increase in existing fixed costs is expected since SC Co has spare capacity in both space and labour terms.
Producing and selling product P will call for increased investment in working capital. Analysis of historical levels of working capital within SC Co indicates that at the start of each year, investment in working capital for product P will need to be 7% of sales revenue for that year.
SC Co pays tax of 30% per year in the year in which the taxable profit occurs. Liability to tax is reduced by capital allowances on machinery (taxallowable depreciation), which SC Co can claim on a straightline basis over the fouryear life of the proposed investment. The new machine is expected to have no scrap value at the end of the fouryear period.
SC Co uses a nominal (money terms) aftertax cost of capital of 12% for investment appraisal purposes.
Required:
(a) Calculate the net present value of the proposed investment in product P.
(12 marks)
(b) Calculate the internal rate of return of the proposed investment in product P.
(3 marks)
(c) Advise on the acceptability of the proposed investment in product P and discuss the limitations of the evaluations you have carried out. (5 marks)
(d) Discuss how the net present value method of investment appraisal contributes towards the objective of maximising the wealth of shareholders. (5 marks)
(Total 25 marks)
(ACCA F9 Financial Management June 2008 Q4)
Question 9 – NPV, IRR and Comparison of Investment Appraisal Methods
Charm plc, a software company, has developed a new game, ‘Fingo’, which it plans to launch in the near future. Sales of the new game are expected to be very strong, following a favourable review by a popular PC magazine. Charm plc has been informed that the review will give the game a ‘Best Buy’ recommendation. Sales volumes, production volumes and selling prices for ‘Fingo’ over its fouryear life are expected to be as follows.
Year 
1 
2 
3 
4 
Sales and production (units) 
150,000 
70,000 
60,000 
60,000 
Selling price (£ per game) 
£25 
£24 
£23 
£22 
Financial information on ‘Fingo’ for the first year of production is as follows:
Direct material cost 
£5.40 per game 
Other variable production cost 
£6.00 per game 
Fixed costs 
£4.00 per game 
Advertising costs to stimulate demand are expected to be £650,000 in the first year of production and £100,000 in the second year of production. No advertising costs are expected in the third and fourth years of production. Fixed costs represent incremental cash fixed production overheads. ‘Fingo’ will be produced on a new production machine costing £800,000. Although this production machine is expected to have a useful life of up to ten years, government legislation allows Charm plc to claim the capital cost of the machine against the manufacture of a single product. Capital allowances will therefore be claimed on a straightline basis over four years.
Charm plc pays tax on profit at a rate of 30% per year and tax liabilities are settled in the year in which they arise. Charm plc uses an aftertax discount rate of 10% when appraising new capital investments. Ignore inflation.
Required:
(a) Calculate the net present value of the proposed investment and comment on your findings. (11 marks)
(b) Calculate the internal rate of return of the proposed investment and comment on your findings. (5 marks)
(c) Discuss the reasons why the net present value investment appraisal method is preferred to other investment appraisal methods such as payback, return on capital employed and internal rate of return. (9 marks)
(Total 25 marks)
(ACCA Paper 2.4 Financial Management and Control June 2006 Q5)
Question 10 – NPV and Discussion with Risk Incorporation
BRT Co has developed a new confectionery line that can be sold for $5·00 per box and that is expected to have continuing popularity for many years. The Finance Director has proposed that investment in the new product should be evaluated over a fouryear timehorizon, even though sales would continue after the fourth year, on the grounds that cash flows after four years are too uncertain to be included in the evaluation. The variable and fixed costs (both in current price terms) will depend on sales volume, as follows.
Sales volume (boxes) 
less than 1 million 
1 – 1.9 million 
2 – 2.9 million 
3 – 3.9 million 
Variable costs ($ per box) 
2.8 
3.00 
3.00 
3.05 
Total fixed costs ($) 
1 million 
1.8 million 
2.8 million 
3.8 million 
Forecast sales volumes are as follows.
Year 
1 
2 
3 
4 
Demand (boxes) 
0.7 million 
1.6 million 
2.1 million 
3.0 million 
The production equipment for the new confectionery line would cost $2 million and an additional initial investment of $750,000 would be needed for working capital. Capital allowances (taxallowable depreciation) on a 25% reducing balance basis could be claimed on the cost of equipment. Profit tax of 30% per year will be payable one year in arrears. A balancing allowance would be claimed in the fourth year of operation.
The average general level of inflation is expected to be 3% per year and selling price, variable costs, fixed costs and working capital would all experience inflation of this level. BRT Co uses a nominal aftertax cost of capital of 12% to appraise new investment projects.
Required:
(a) Assuming that production only lasts for four years, calculate the net present value of investing in the new product using a nominal terms approach and advise on its financial acceptability (work to the nearest $1,000). (13 marks)
(b) Comment briefly on the proposal to use a fouryear time horizon, and calculate and discuss a value that could be placed on aftertax cash flows arising after the fourth year of operation, using a perpetuity approach. Assume, for this part of the question only, that beforetax cash flows and profit tax are constant from year five onwards, and that capital allowances and working capital can be ignored. (5 marks)
(c) Discuss THREE ways of incorporating risk into the investment appraisal process.
(7 marks)
(25 marks)
(ACCA F9 Financial Management June 2011 Q1)
Question 11
Warden Co plans to buy a new machine. The cost of the machine, payable immediately, is $800,000 and the machine has an expected life of five years. Additional investment in working capital of $90,000 will be required at the start of the first year of operation. At the end of five years, the machine will be sold for scrap, with the scrap value expected to be 5% of the initial purchase cost of the machine. The machine will not be replaced.
Production and sales from the new machine are expected to be 100,000 units per year. Each unit can be sold for $16 per unit and will incur variable costs of $11 per unit. Incremental fixed costs arising from the operation of the machine will be $160,000 per year.
Warden Co has an aftertax cost of capital of 11% which it uses as a discount rate in investment appraisal. The company pays profit tax one year in arrears at an annual rate of 30% per year. Capital allowances and inflation should be ignored.
Required:
(a) Calculate the net present value of investing in the new machine and advise whether the investment is financially acceptable. (7 marks)
(b) Calculate the internal rate of return of investing in the new machine and advise whether the investment is financially acceptable. (4 marks)
(c) (i) Explain briefly the meaning of the term ‘sensitivity analysis’ in the context of investment appraisal; (1 mark)
(ii) Calculate the sensitivity of the investment in the new machine to a change in selling price and to a change in discount rate, and comment on your findings. (6 marks)
(d) Discuss the nature and causes of the problem of capital rationing in the context of investment appraisal, and explain how this problem can be overcome in reaching the optimal investment decision for a company. (7 marks)
(25 marks)
(ACCA F9 Financial Management December 2011 Q1)
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