Investment Appraisal Methods

1.1       Payback period

1.1.1    Time it takes the project to payback its initial investment.
1.1.2    When is useful?

• seeking to claw back cash from investments as quickly as possible
• commonly used for initial screening of investment alternatives

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:

• only select projects which payback within the specified time period
• choose between options on the basis of the fastest payback
• provides a measure of liquidity

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 ($000)	Discounted Cash flow @10% ($000)	Cumulative cash flow ($000)
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
It is simple It is useful in certain situations: Rapidly changing technology Improving investment conditions It favours quick return: Helps company growth Minimizes risk Maximizes liquidity It uses cash flows, not accounting profit.	It ignores overall profitability after the payback period It ignores time value of money It is subjective – no definitive investment signal

 

1.2       Accounting Rate of Return (ARR)                                                         (Pilot, Jun 09)

1.2.1    Also known as ROCE or ROI.
1.2.2    Decision rule:

• ARR > target return or hurdle rate, accept the project
• Take the project with the highest ARR

1.2.3    Calculation of ARR – three version

• Annual basis –

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.

• Total investment basis –

ARR	=	Average annual profit	× 100%
		Initial capital invested

 

• Average investment basis –

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
It is a quick and simple calculation It involves the familiar concept of a percentage return It looks at the entire project life	It is based on accounting profit and not cash flows. It depends on accounting policies and this can make comparison of ARR being difficult. It is a relative measure rather than an absolute measure and hence takes no account of the size of the investment Like the payback method, it ignores the time value of money.

 

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:

•   NPV > 0, the project is financially viable, i.e. accepted.
•   NPV = 0, the project breaks even.
•   NPV < 0, the project is not financially viable, i.e. rejected.

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.

• All acceptable investment project should have positive NPV
• The market value of the company, theoretically at least, increases by the amount of the NPV
• The share price of the company should theoretically increase as well
• Objective of maximizing the wealth of shareholders is usually substituted by the objective of maximizing the share price of a company

 

1.3.6    Advantages and disadvantages of NPV

Advantages	Disadvantages
Considers the time value of money Is an absolute measure of return, i.e. absolute increase in corporate value Is based on cash flows not profits Considers the whole life of the project Should lead to maximization of shareholder wealth Can accommodate changes in discount rate Has a sensible re-investment assumption Can accommodate non-conventional cash flows	It is difficult to explain to managers and relatively complex It requires knowledge of the cost of capital

1.3.7    Why NPV is superior to other methods?

• NPV considers cash flows
• NPV considers the whole life of an investment project
• NPV considers the time value of money
• NPV is an absolute measure of return
• NPV directly links to the objective of maximizing shareholders’ wealth
• NPV offers the correct investment advice
• NPV can accommodate changes in the discount rate
• NPV has a sensible re-investment assumption
• NPV can accommodate non-conventional cash flows

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:

•   IRR > cost of capital, project accepts
•   The higher IRR is the better

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

Considers the time value of money Is a percentage and therefore easily understood Uses cash flows not profits Considers the whole life of the project Means a firm selecting projects where the IRR exceeds the cost of capital should increase shareholders’ wealth.

It is not a measure of absolute increase in company value. Interpolation only provides an estimate and an accurate estimate requires the use of a spreadsheet program It is fairly complicated to calculate Non-conventional cash flows may give rise to multiple IRRs Can offer conflicting advice between IRR and NPV in the evaluation of mutually exclusive projects Assume cash inflows being reinvested at the IRR rate, this is unrealistic when IRR is high.

 

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

Stages	Explanation
Identify investment opportunities	Arise from analysis of strategic choice, business environment, R&D or legal environment, etc. Key requirement is to achieve the organizational objectives.
Screen investment proposals	Select those proposals with best strategic fit and the most appropriate use of economic resources.
Analyse and evaluate investment proposals	Analyse and evaluate which proposal(s) offer the most attractive opportunities to achieve company objectives, e.g. increase shareholder wealth. Investment appraisal plays a key role here, e.g. choose highest NPV among different proposals.
Approve investment proposals	Pass to relevant level of authority for approval. Large proposals approve by board of directors, smaller proposals approve by divisional level.
Implementation	Responsibility for the project is assigned to a project manager or other responsible person. Resources will be available and specific target should be set.
Monitoring	Progress must be monitored to check whether there are any big variances and unforeseen events.
Post-completion audit	To facilitate organizational learning and to improve future investment decisions.

 

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	Future cost arises as a direct consequence of a decision. Sunk costs should not be included because it is past and so irrelevant to any decision.
Cash flows	Future costs which are in the form of cash should be included. So depreciation should be ignored because it is not cash spending.
Incremental costs	Increase in costs results from making a particular decision.
Opportunity costs	It is the value of a benefit foregone as a result of choosing a particular course of action.

 

3.2       Non-relevant costs

3.2.1    Other non-relevant costs:

• Committed costs – they are future cash flow but will be incurred anyway, regardless of what decision will be taken.
• Interest costs – they have already been included in the discount rate, if counted, it will be double counted.

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:

•     Specific inflation – cash flow rises by the rate of inflation
•     General inflation – cost of capital (or discount rate) rises by the rate of inflation.

4.1.2    Real and money (nominal) interest rate

• It has the following relationship between real interest rate and nominal interest rate under Fisher’s equation.                                                                                             (Pilot, Jun 10)

(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	Calculate the taxable profits (before capital allowances) and calculate tax at the rate given. The effect of taxation will not necessarily occur in the same year, often one year in arrears in the examination.
Tax benefits from WDAs	Normally 25% writing-down allowances on plant and machinery (can be straight-line) Remember the balancing allowance or balancing charge in the final year.

 

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:

•     Initial investment is a cost at the start of the project, i.e. cash outflow.
•     If increasing during the project, the increase is a relevant cash outflow.
•     Working capital is released at the end of the project and treated as cash inflow.

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 The following draft appraisal of a proposed investment project has been prepared for the finance director of OKM Co by a trainee accountant. The project is consistent with the current business operations of OKM Co. 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 2.      Selling price: $12/unit (current price terms), selling price inflation is 5% per year 3.      Variable cost: $7/unit (current price terms), variable cost inflation is 4% per year 4.      Fixed overhead costs: $500,000/year (current price terms), fixed cost inflation is 6% per year 5.      $200,000/year of the fixed costs are development costs that have already been incurred and are being recovered by an annual charge to the project 6.      Investment financing is by a $2 million loan at a fixed interest rate of 10% per year 7.      OKM Co can claim 25% reducing balance capital allowances on this investment and pays taxation one year in arrears at a rate of 30% per year 8.      The scrap value of machinery at the end of the four-year project is $250,000 9.      The real weighted average cost of capital of OKM Co is 7% per year 10.    The general rate of inflation is expected to be 4·7% per year Required: (a)     Identify and comment on any errors in the investment appraisal prepared by the trainee accountant.                                                                                                             (5 marks) (b)     Prepare a revised calculation of the net present value of the proposed investment project and comment on the project’s acceptability.                                                       (12 marks) (c)     Discuss the problems faced when undertaking investment appraisal in the following areas and comment on how these problems can be overcome: (i)      assets with replacement cycles of different lengths; (ii)     an investment project has several internal rates of return; (iii)    the business risk of an investment project is significantly different from the business risk of current operations.                                                                             (8 marks) (25 marks) (ACCA F9 Financial Management June 2010 Q3)

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 non-viable.

5.4       Adjusted payback                                                                                 (Jun 09, Jun 11)

5.4.1    Payback can be adjusted for risk:

•   Higher risk project should require shortening the payback period.
•   Putting the focus on cash flows that are more certain (less risky) because they are nearer in time.

5.4.2    Discounted payback:

•   Adjusted for risk by discounting future cash flows with a risk-adjusted discount rate.
•   The normal payback period target can be applied to the discounted cash flows, which will have decreased in value due to discounting.
•   The overall effect is similar to reducing the payback period with undiscounted cash flows.

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 Umunat plc is considering investing $50,000 in a new machine with an expected life of five years. The machine will have no scrap value at the end of five years. It is expected that 20,000 units will be sold each year at a selling price of $3·00 per unit. Variable production costs are expected to be $1·65 per unit, while incremental fixed costs, mainly the wages of a maintenance engineer, are expected to be $10,000 per year. Umunat plc uses a discount rate of 12% for investment appraisal purposes and expects investment projects to recover their initial investment within two years. Required: (a)     Explain why risk and uncertainty should be considered in the investment appraisal process.                                                                                                                (5 marks) (b)     Calculate and comment on the payback period of the project.                           (4 marks) (c)     Evaluate the sensitivity of the project’s net present value to a change in the following project variables: (i)      sales volume; (ii)     sales price; (iii)    variable cost; and discuss the use of sensitivity analysis as a way of evaluating project risk. (10 marks) (d)     Upon further investigation it is found that there is a significant chance that the expected sales volume of 20,000 units per year will not be achieved. The sales manager of Umunat plc suggests that sales volumes could depend on expected economic states that could be assigned the following probabilities: Economic state Poor Normal Good Probability 0.3 0.6 0.1 Annual sales volume (units) 17,500 20,000 22,500 Calculate and comment on the expected net present value of the project.         (6 marks) (25 marks) (ACCA 2.4 Financial Management and Control December 2004 Q5)

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

•             The benefits of leasing vs purchasing (with a loan) can be assessed by an NPV approach:

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.

•             Alternative method – to evaluate the NPV of the cost of the loan and the NPV of the cost of the lease separately, and to choose the cheapest option.

6.1.3    Finance lease:

•             Transfer substantially all of the risks and rewards of ownership to lessee.
•             Lessee can use the asset for all or most of its useful economic life.
•             It cannot be cancelled or with severe financial penalties even when cancelled. Therefore, it is a kind of medium- to long-term source of debt finance.
•             Leased asset must be capitalized together with the amount of obligations for the lease payments.

6.1.4    Operating lease:

•             It’s renal agreement and the lease period is shorter than the asset’s useful economic life.
•             Maintenance and similar costs are borne by the lessor.
•             Cancelled without penalty at short notice. It can avoid the obsolescence problem, so suitable for high-tech assts.
•             No need to be capitalized and no liabilities need to be recognized.

6.1.5    Attractions of finance lease for lessee:

•             Not enough cash and also difficult to obtain bank loan.
•             Interest may be cheaper than a bank loan.
•             Having tax relief such as the interest expenses and depreciation allowance (but refer to the examination question, it may not have).

6.1.6    Attractions of operating lease for lessee:

•             No effect on assets and liabilities, so no increase in its gearing ratio.
•             Can have the up-to-date assets at all time because the lessee can replace with no cost.
•             Higher flexibility with cancellation at short notice
•             Suitable for small companies who may find it difficult to raise debt
•             Cheaper than borrow to buy
•             Off-balance sheet financing

6.1.7    Attractions of operating lease for lessor:

•             Leased asset can be recovered if the lessee default on lease rentals
•             Lessor can take advantage of bulk buying
•             Lessor can have access to lower cost finance by virtue of being a much larger company.
•             Enjoy tax benefits such as depreciation allowance and other allowable expenses.

Question 3 Leaminger Inc has decided it must replace its major turbine machine on 31 December 2008. The machine is essential to the operations of the company. The company is, however, considering whether to purchase the machine outright or to use lease financing. Purchasing the machine outright The machine is expected to cost $360,000 if it is purchased outright, payable on 31 December 2008. After four years the company expects new technology to make the machine redundant and it will be sold on 31 December 2012 generating proceeds of $20,000. Capital allowances for tax purposes are available on the cost of the machine at the rate of 25% per annum reducing balance. A full year’s allowance is given in the year of acquisition but no writing down allowance is available in the year of disposal. The difference between the proceeds and the tax written down value in the year of disposal is allowable or chargeable for tax as appropriate. Leasing The company has approached its bank with a view to arranging a lease to finance the machine acquisition. The bank has offered two options with respect to leasing which are as follows:   Finance lease Operating lease Contract length (years) 4 1 Annual rental $135,000 $140,000 First rent payable 31 December 2009 31 December 2008 General For both the purchasing and the finance lease option, maintenance costs of $15,000 per year are payable at the end of each year. All these rentals (for both finance and operating options) can be assumed to be allowable for tax purposes in full in the year of payment. Assume that tax is payable one year after the end of the accounting year in which the transaction occurs. For the operating lease only, contracts are renewable annually at the discretion of either party. Leaminger Inc has adequate taxable profits to relieve all its costs. The rate of corporation tax can be assumed to be 30%. The company’s accounting year-end is 31 December. The company’s annual after tax cost of capital is 10%. Required: (a)     Calculate the net present value at 31 December 2008, using the after tax cost of capital, for: (i)      purchasing the machine outright (ii)     using the finance lease to acquire the machine (iii)    using the operating lease to acquire the machine. Recommend the optimal method.                                                                     (12 marks) (b)     Assume now that the company is facing capital rationing up until 30 December 2009 when it expects to make a share issue. During this time the most marginal investment project, which is perfectly divisible, requires an outlay of $500,000 and would generate a net present value of $100,000. Investment in the turbine would reduce funds available for this project. Investments cannot be delayed. Calculate the revised net present values of the three options for the turbine given capital rationing. Advise whether your recommendation in (a) would change. (5 marks) (c)     As their business advisor, prepare a report for the directors of Leaminger Inc that assesses the issues that need to be considered in acquiring the turbine with respect to capital rationing.                                                                                                 (8 marks) (Total 25 marks) (Adapted ACCA Paper 2.4 Financial Management and Control December 2002 Q4)

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,

• Cost savings or benefits > purchase cost, replace the old one.

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 Bread Products Ltd is considering the replacement policy for its industrial size ovens which are used as part of a production line that bakes bread. Given its heavy usage each oven has to be replaced frequently. The choice is between replacing every two years or every three years. Only one type of oven is used, each of which costs $24,500. Maintenance costs and resale values are as follows: Year Maintenance per annum Resale value   $ $ 1 500   2 800 15,600 3 1,500 11,200 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) (b)     Identify the limitations of Net Present Value techniques when applied generally to investment appraisal.                                                                                        (13 marks) (25 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:

• Cannot raise external finance due to too risky.
• Financial risk – the company’s gearing may be seen as too high.
• Business risk – lenders may be uncertain on the company’s future profits whether it can meet the interest and principal payments

6.3.4    Internal (soft) capital rationing:

• Managers impose restrictions on the funds. The reasons are as follows:
• Managers may not want to raise new external finance, for example
• Not wish to raise new debt to increase future interest payments
• Not wish to issue new equity to avoid dilution of control.
• Managers may prefer slower organic growth in order to remain in control of the growth process and so avoid rapid growth.
• Managers may want to make capital investments compete for funds in order to week out weaker or marginal projects.

6.3.5    Single period capital rationing

• Rationing occurs when limits are placed for only one year or one period.
• Two types of single-period rationing:
• Divisible projects – a proportion rather than the whole investment can be undertaken and use profitability index (PI) to rank the project for priority.

PI =	PV of future cash flows
	Initial investment

• Indivisible projects – use trial and error to find the affordable combination that maximizes NPV

6.3.6    Multi-period capital rationing

• Limits are placed for more than one period, in this case, linear programming should be employed. More complex linear programming problems require the use of computers.

6.3.7    Practical steps to deal with capital rationing include:

• Leasing
• Entering into a joint venture with a partner
• Delaying projects to a later period
• Raising new capital if possible

Question 5 Basril plc is reviewing investment proposals that have been submitted by divisional managers. The investment funds of the company are limited to $800,000 in the current year. Details of three possible investments, none of which can be delayed, are given below. Project 1 An investment of $300,000 in work station assessments. Each assessment would be on an individual employee basis and would lead to savings in labour costs from increased efficiency and from reduced absenteeism due to work-related illness. Savings in labour costs from these assessments in money terms are expected to be as follows: Year 1 2 3 4 5 Cash flows ($000) 85 90 95 100 95 Project 2 An investment of $450,000 in individual workstations for staff that is expected to reduce administration costs by $140,800 per annum in money terms for the next five years. Project 3 An investment of $400,000 in new ticket machines. Net cash savings of $120,000 per annum are expected in current price terms and these are expected to increase by 3·6% per annum due to inflation during the five-year life of the machines. 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: (i)       on the assumption that each of the three projects is divisible; (ii)      on the assumption that none of the projects are divisible.                      (10 marks) (b)     Explain how the NPV investment appraisal method is applied in situations where capital is rationed.                                                                                                           (3 marks) (c)     Discuss the reasons why capital rationing may arise.                                         (7 marks) (d)     Discuss the meaning of the term ‘relevant cash flows’ in the context of investment appraisal, giving examples to illustrate your discussion.                                    (5 marks) (25 marks) (ACCA 2.4 Financial Management and Control December 2003 Q3)

 

Additional Examination Style Questions

Question 6 – WACC, NPV and Project-specific 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 before-tax 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 short-term 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 (tax-allowable depreciation) on machinery are on a straight-line basis over the life of the asset.

Required:

(a)     Calculate the after-tax weighted average cost of capital of Rupab Co.               (6 marks)
(b)     Prepare a forecast of the annual after-tax 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 project-specific 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 Project-specific 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 after-tax 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 (tax-allowable depreciation) on a 25% reducing balance basis on the initial investment in both projects.

Risk-free 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 four-year 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 project-specific 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 life-cycle 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 (tax-allowable depreciation), which SC Co can claim on a straight-line basis over the four-year life of the proposed investment. The new machine is expected to have no scrap value at the end of the four-year period.

SC Co uses a nominal (money terms) after-tax 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 four-year 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 straight-line 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 after-tax 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 four-year time-horizon, 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 (tax-allowable 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 after-tax 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 four-year time horizon, and calculate and discuss a value that could be placed on after-tax cash flows arising after the fourth year of operation, using a perpetuity approach. Assume, for this part of the question only, that before-tax 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 after-tax 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)