Asset Investment Decisions and Capital Rationing

Chapter 17 Asset Investment Decisions and Capital Rationing

LEARNING OBJECTIVES 1.      Evaluate leasing and borrowing to buy using the before- and after-tax costs of debt. 2.      Evaluate asset replacement decisions using equivalent annual cost. 3.      Evaluate investment decisions under single period capital rationing. 4.      Explain the calculation of profitability indexes (PI) for divisible investment projects. 5.      Explain the calculation of the NPV of combinations of non-divisible investment projects. 6.      A discussion of the reasons for capital rationing.

 

1.       Lease or Buy Decisions

1.1       Types of leases

1.1.1    Rather than buying an asset outright, using either available cash resources or borrowed funds, a business may lease an asset.
1.1.2    We distinguish three types of leasing:
(a)        Operating leases – is a lease where the lessor retains most of the risks and rewards of ownership. The lessor is responsible for maintaining asset
(b)        Finance leases – is a lease that transfers substantially all of the risks and rewards of ownership of an asset to the lessee. The lessee is responsible for maintenance
(c)        Sale and leaseback arrangements – a business that owns an asset agrees to sell the asset to a financial institution and lease it back on terms specified in the sale and leaseback agreement.
1.1.3    The NPVs of the financing cash flows for both options of lease and buy are found and compared and the lowest cost option selected.
1.1.4    The finance decision is considered separately from the investment decision. The operating costs and revenues from the investment will be common in each case.
1.1.5    Only the relevant cash flows arising as a result of the type of finance are included in the NPV calculation.

1.2       Attractions of leasing

1.2.1    Attractions to lessor – the lessor invests finance by purchasing assets from suppliers and makes a return out of the lease payments from the lessee. The lessor will get capital allowances on his purchase of the equipment.
1.2.2    Attractions to lessee under finance lease –
(a)        The lessee may not have enough cash to pay for the asset, and would have difficulty obtaining a bank loan to buy it. If so the lessee has to rent the asset to obtain use of it at all.
(b)        Finance leasing may be cheaper than a bank loan.
(c)        The lessee may find the tax relief available advantageous.
1.2.3    Attractions to lessee under operating lease –
(a)        The leased equipment does not have to be shown in the lessee’s published statement of financial position, and so the lessee’s statement of financial position shows no increase in its gearing ratio.
(b)        The equipment is leased for a shorter period than its expected useful life. In the case of high-technology equipment, if the equipment becomes out of date before the end of its expected life, the lessee does not have to keep on using it. The lessor will bear the risk of having to sell obsolete equipment secondhand.

1.3       Lease or buy decisions
(Jun 12)
1.3.1    The decision whether to lease or buy involves two steps:
(a)        The acquisition decision – is the asset worth having? Test by discounting project cash flows at a suitable cost of capital.
(b)        The financing decision – if the asset should be acquired, compare the cash flows of purchasing and leasing or hire-purchase (HP) arrangements. The cash flows can be discounted at an after-tax cost of borrowing.

Question 1 – Purchase or Lease the New Machine AGD Co is a profitable company which is considering the purchase of a machine costing £320,000. If purchased, AGD Co would incur annual maintenance costs of £25,000. The machine would be used for three years and at the end of this period would be sold for £50,000. Alternatively, the machine could be obtained under an operating lease for an annual lease rental of £120,000 per year, payable in advance. AGD Co can claim capital allowances on a 25% reducing balance basis. The company pays tax on profits at an annual rate of 30% and all tax liabilities are paid one year in arrears. AGD Co has an accounting year that ends on 31 December. If the machine is purchased, payment will be made in January of the first year of operation. If leased, annual lease rentals will be paid in January of each year of operation. Required: (a)     Using an after-tax borrowing rate of 7%, evaluate whether AGD Co should purchase or lease the new machine.                                                                                    (12 marks) (b)     Explain and discuss the key differences between an operating lease and a finance lease.                                                                                                                            (8 marks)

 

 

Question 2 – Leases You are the manager of a cosmetics store in a busy shopping mall located in Central. The store has five years remaining on its rental lease, with a monthly rent of $100,000, and the next lease payment is due in one month. The mall’s owner plans to sell the property in three years and wants the rent at that time to be high so the mall can be sold for a higher price. The owner has therefore offered you a new five-year lease deal as follows: zero rent for the first 24 months, then $200,000 for the remaining 36 months. Suppose the cost of capital for the store is 12% per annum (1% per month). Required: (a)     Should you accept the new lease? Explain your reasons.                                  (5 marks) (b)     Suppose you want to negotiate with the owner over the new lease payment and you would like to keep the rent at zero for the first 24 months. What new monthly lease payment (for the remaining 36 months) would make you indifferent between the existing and the new leases?                                                                              (5 marks) (HKIAAT PBE Paper III Financial Management June 2006 Q5(a))

Question 3 – Payback, NPV and leases Jackie Consulting is considering whether to buy or lease its office accommodation. The annual rent payable is HK$2.2 billion while the purchase price is HK$37 billion. Assume a 30-year time horizon and that there is no change in the annual rent payable and the price of the office accommodation at the end of 30 years. Discount rate is 3% per annum. Required: (a)        What is the payback period for the purchase?                                                (2 marks) (b)        What is the net present value (NPV) of the purchase?                                    (6 marks) (c)        Discuss some of the limitations of the calculation in (b).                               (6 marks) (d)        Explain why some retail companies prefer to buy their shops rather than lease even where the NPV of the purchase is negative.                                                    (3 marks) (e)        If you are a market leader or leading company, suggest TWO ways, other than purchase, to hedge against an increase in rental expense when a company is leasing its shop from a property developer.                                                                 (3 marks) (Total 20 marks) (HKIAAT PBE Paper II Management Accounting and Finance June 2012 Q4)

 

2.       Asset Replacement Decisions

2.1       Introduction

2.1.1    DCF techniques can assist asset replacement decisions. When an asset is being replaced with an identical asset, the equivalent annual cost method can be used to calculate on optimum replacement cycle.
2.1.2    When an asset is to be replaced by an identical asset, the problem is to decide the optimum interval between replacements. As the asset gets older, it may cost more to maintain and operate, its residual value will decrease, and it may lose some productivity/operating capability.

2.2       Replacement decision

2.2.1    In making a replacement decision the increased costs associated with the purchase and installation of the new machine have to be weighted against the savings from switching to the new method of production. In other words the incremental cash flows are the focus of attention.

2.2.2

EXAMPLE 1

Amtarc plc produces Tarcs with a machine which has a useful life of four more years before it will be sold for scrap, raising $10,000. Q-2000 cost of $800,000 payable immediately. Existing machine secondhand value: $70,000. The Q-2000 will have a life of four years before being sold for scrap for $20,000. Q-2000 has lower raw material wastage and its reduced labour requirements. Selling price and variable overhead will be the same as for the old machine. The accountants have prepared the figures below on the assumption that output will remain constant at last year’s level of 100,000 Tarcs per annum.           Profit per unit of Tarc   Old machine Q-2000   $ $ Sale price 45 45 Costs     Labour (10) (9) Materials (15) (14) Variable overhead (7) (7) Fixed overhead     Factory admin., etc. (5) (5) Depreciation (0.35) (1.95) Profit per Tarc 7.65 8.05       Q-2000 reduces raw material buffer stocks by $120,000. Redundancy payments of $50,000 will be necessary after one year. The required rate of return is 10 per cent. To simplify the analysis sales, labour costs, raw material costs and variable overhead costs all occur on the last day of each year.   Required: Using the NPV method decide whether to continue using the old machine or to purchase the Q-2000. Solution: Note the irrelevant information: Depreciation is not a cash flow The book value of the machine is merely an accounting entry   Savings per Tarc   Old machine Q-2000 Saving   $ $ $ Labour 10 9 1 Materials 15 14 1 Total saving     2   Incremental cash flow table   0 1 2 3 4   $000 $000 $000 $000 $000 Purchase of Q-2000 (800)         Scrap of old machine 70         Raw materials stocks 120         Opportunity cost (old machine)         (10) Redundancy payments   (50)       Sale of Q-2000         20 Annual cost savings   200 200 200 200 Net cash flow (610) 150 200 200 210 Discount at 10% 1.000 0.909 0.826 0.751 0.683 Present value (610.00) 136.35 165.20 150.20 143.43 NPV = ($14,820) The negative NPV indicates that shareholder wealth will be higher if the existing machine is retained.

Question 4 – Replacement decision PBE Company is a car washing company in Fo Tan. The existing car washing machine has been used for a number of years and its performance is deteriorating. PBE has two alternatives: to remodel the car washing machine or to install a new one. The revenue and cost information of the car washing machine on the cash basis is as follows:   New machine Old machine   HK$ HK$ Annual revenue 900,000 700,000 Annual cost 300,000 250,000 Annual net cash inflow 600,000 450,000 The new car washing machine costs HK$3,000,000 and can be used for 10 years. Its salvage value is HK$700,000. The machine requires replacement of brushes at the end of 6 years and the expense is HK$500,000. If the old washing machine is sold now, it can be sold for HK$400,000. The existing car washing machine can be remodeled at a cost of HK$1,750,000 but it needs to replace the brushes at the end of year 6 at a cost of HK$800,000. The discount rate is 10% per annum. Required: (a)     Calculate the NPV of the new machine scenario.                                             (5 marks) (b)     Calculate the NPV of the old machine scenario (assuming there is no salvage value at the end of year 10).                                                                                            (5 marks) (c)     Based on your answer in part (a) and (b) above, advise management of your recommendation of preference with reasons.                                                    (2 marks) (d)     Give TWO qualitative consideration in the decision.                                       (4 marks) (e)     What are the possible reasons for getting an incorrect conclusion in the above NPV analysis?                                                                                                            (4 marks) (Total 20 marks) (HKIAAT PBE Paper II Management Accounting and Finance December 2011 Q3)

2.3       Replacement cycles
(Jun 16)
2.3.1    Assets such as vehicles are often replaced on a regular cycle, say every two or three years, depending on the comparison between the benefit to be derived by delaying the replacement decision and the cost in terms of higher maintenance costs.

2.3.2

Equivalent Annual Cost Method (Annual Equivalent Annuity)

The equivalent annual cost method is the quickest method to use in a period of no inflation. Step 1:    Calculate the present value of costs for each replacement cycle over one cycle only. Step 2:    Turn the present value of costs for each replacement cycle into an equivalent annual cost (an annuity). The equivalent annual costs is calculated as follows. Equivalent annual cost = PV of costs Annuity factor for the number of years in the cycle

 

 

2.3.3

EXAMPLE 2

Consider the case of a car rental firm which is considering a switch to a new type of car. The cars cost £10,000 and a choice has to be made between four alternative (mutually exclusive) projects. Project 1 is to sell the cars on the secondhand market after one year for £7,000. Project 2 is to sell after two years for £5,000. Projects 3 and 4 are three-year and four-year cycles and will produce £3,000 and £1,000 respectively on the secondhand market. The cost of maintenance rises from £500 in the first year to £900 in the second, £1,200 in the third and £2,500 in the fourth. The car are not worth keeping for more than four years because of the bad publicity associated with breakdowns. The revenue streams and other costs are unaffected by which cycle is selected. We will focus on achieving the lowest present value of the costs. Equivalent Annual Cost Method Thus, Project 3 requires the lowest equivalent annual cash flow and is the optimal replacement cycle.

Question 5 – EAC Fortune Garment Manufacturing Ltd must choose between two models of sewing machines. The Deluxe model costs $20,000 and lasts for four years, with annual maintenance expenses of $2,000 paid at each year-end. The Economy model costs $15,000 and lasts for three years, with annual maintenance expenses of $1,500 paid at each year-end. The appropriate discount rate is 15% per annum. Required: (a)     Use the equivalent annual cost method to determine which model should be chosen. (6 marks) (b)     State TWO assumptions in the analysis above.                                                  (4 marks) (HKIAAT Paper III Financial Management June 2004 Q6(a))

 

 

 

Question 6 – EAC (a)     Suppose you are operating an old machine that will last 2 more years before it is given up. It costs $12,000 per year to operate. You can replace it now with a new machine, which costs $25,000 but is much more efficient ($8,000 per year in operating costs) and will last for 5 years. The cost of capital is 6%. Required: (i)      What is Equivalent Annual Cost (EAC) analysis and when it is applied? (4 marks) (ii)     What is the equivalent annual cost of the new machine?                         (6 marks) (iii)    What is your conclusion and the rationale behind it?                              (2 marks) (b)     What is underpricing of IPO? Why is there underpricing?                               (4 marks) (c)     Inflation rate in main cities in China is about 7% in early 2008. Point out the measurements used to indicate inflation and why the rate of inflation has been a bit high in China in recent years.                                                                            (4 marks) (Total 20 marks) (HKIAAT PBE Paper III Financial Management June 2008 Q2)

Question 7 – EAC In NPV analysis, Equivalent Annual Cost (EAC) is commonly used to evaluate the feasibility of a project. Required: (a)     In what situation should the EAC be used?                                                       (3 marks) (b)     A company is operating an old machine that will last 2 more years before it is discarded. It costs HK$12,000 per year to operate. The company can replace the old machine with a new machine which costs HK$25,000. The new machine is much more efficient and its operating cost is HK$8,000 per year. Its useful life can last for 5 years. The cost of capital is 6%. Required: (i)      Calculate the annuity factor and show the formula.                                  (2 marks) (ii)     What is the equivalent annual cost of the new machine?                          (5 marks) (iii)    Should the old machine be replaced by the new machine now? Explain your answer.                                                                                                       (3 marks) (c)     Point out TWO important assumptions in the calculation of part (b).               (3 marks) (d)     Besides the EAC method, briefly describe any TWO non-discounting methods for investment appraisal.                                                                                          (4 marks) (HKIAAT PBE Paper II Management Accounting and Finance June 2016 Q4)

3.       Capital Rationing

3.1       Soft and hard capital rationing

3.1.1    Capital rationing occurs when funds are not available to finance all wealth-enhancing projects. There are two types of capital rationing:
(a)        Soft capital rationing – is internal management-imposed limits on investment expenditure. Such limits may be linked to the firm’s financial control policy.
(b)       Hard capital rationing – relates to capital from external sources. Agencies (e.g. shareholders and bank) external to the firm will not supply unlimited amounts of investment capital, even though positive NPV projects are identified.
3.1.2    Soft capital rationing may arise for one of the following reasons.
(a)        Management may be reluctant to issue additional share capital because of concern that this may lead to outsiders gaining control of the business.
(b)       Management may be unwilling to issue additional share capital if it will lead to a dilution of earnings per share.
(c)        Management may not want to raise additional debt capital because they do not wish to be committed to large fixed interest payments.
(d)       Management may wish to limit investment to a level that can be financed solely from retained earnings.
(e)        Capital expenditure budgets may restrict spending.
3.1.3    Hard capital rationing may arise for one of the following reasons.
(a)        Raising money through the stock market may not be possible if share prices are depressed.
(b)       There may be restrictions on bank lending.
(c)        Lending institutions may consider an organization to be too risky to be granted further loan facilities.
(d)       The costs associated with making small issues of capital may be too great.

 

3.2       Relaxation of capital constraints

3.2.1    If an organization adopts a policy that restricts funds available for investment (soft capital rationing), the policy may be less than optimal. The organization may reject projects with a positive NPV and forgo opportunities that would have enhanced the market value of the organization.
3.2.2    A company may be able to limit the effects of hard capital rationing and exploit new opportunities.
(a)        It may seek joint venture partners with which to share projects.
(b)       As an alternative to direct investment in a project, the company may be able to consider a licensing or franchising agreement with another enterprise, under which the licensor/franchisor company would receive royalties.
(c)        It may be possible to contract out parts of a project to reduce the initial capital outlay required.
(d)       The company may seek new alternative sources of capital, for example:
(i)        Venture capital
(ii)       Debt finance secured on the assets of the project
(iii)      Sale and leaseback of property or equipment
(iv)      Grant aid
(v)       More effective capital management

3.3       Single period capital rationing

3.3.1    The simplest and most straightforward form of rationing occurs when limits are placed on finance availability for only one year.
3.3.2    There are two possibilities with this single-period rationing situation.
(a)        Divisible projects – The nature of the proposed projects is such that it is possible to undertake a fraction of a total project. For instance, if a project is established to expand a retail shop by opening a further 100 shops, it would be possible to take only 30% (that is 30 shops) or any other fraction of the overall project.
(b)       Indivisible projects – with some projects it is impossible to take a fraction. The choice is between undertaking the whole of the investment or none of it (for instance, a project to build a ship, or a bridge or an oil platform).
3.3.3    When capital rationing occurs in a single period, projects are ranked in terms of profitability index.

 

3.3.4	Profitability Index
	Profitability index is the ratio of the PV of the project’s future cash flows (not including the capital investment) divided by the present value of the total capital investment. PI = PV of future cash flows Initial investment

 

3.3.5

EXAMPLE 3

Suppose that ABC Co is considering four projects, W, X, Y and Z. Relevant details are as follows. Project Investment required PV of cash inflows NPV PI Ranking as per NPV Ranking as per PI   $ $ $       W (10,000) 11,240 1,240 1.12 3 1 X (20,000) 20,991 991 1.05 4 4 Y (30,000) 32,230 2,230 1.07 2 3 Z (40,000) 43,801 3,801 1.10 1 2 Without capital rationing all four projects would be viable investments. Suppose, however, that only $60,000 was available for capital investment. Let us look at the resulting NPV if we select projects in the order of ranking per NPV.   By NPV: Project Priority Outlay NPV   Z 1st 40,000 3,801   Y (balance)* 2nd 20,000 1,487 (2/3 of $2,230)     60,000 5,288   By PI: Project Priority Outlay NPV   W 1st 10,000 1,240   Z 2nd 40,000 3,801   Y 3rd 10,000 743 (1/3 of $2,230)     60,000 5,784   * Projects are divisible. By spending the balancing $20,000 on project Y, two thirds of the full investment would be made to earn two thirds of the NPV.

 

Question 8 – PI A company is experiencing capital rationing in year 0, when only $60,000 of investment finance will be available. No capital rationing is expected in future periods, but none of the three projects under consideration by the company can be postponed. The expected cash flows of the three projects are as follows. Project Year 0 Year 1 Year 2 Year 3 Year 4   $ $ $ $ $ A (50,000) (20,000) 20,000 40,000 40,000 B (28,000) (50,000) 40,000 40,000 20,000 C (30,000) (30,000) 30,000 40,000 10,000 The cost of capital is 10%. Required: Decide which projects should be undertaken in year 0, in view of the capital rationing, given that projects are divisible.

3.4       Problems with the profitability index method

3.4.1    Problems –
(a)        The approach can only be used if projects are divisible. If the projects are not divisible a decision has to be made by examining the absolute NPVs of all possible combinations of complete projects that can be undertaken within the constraints of the capital available. The combination of projects which remains at or under the limit of available capital without any of them being divided, and which maximizes the total NPV, should be chosen.
(b)        The selection criterion is fairly simplistic, taking no account of the possible strategic value of individual investments in the context of the overall objectives of the organization.
(c)        The method is of limited use when projects have differing cash flow patterns. These patterns may be important to the company since they will affect the timing and availability of funds. With multi-period capital rationing, it is possible that the project with the highest PI is the slowest in generating returns.
(d)        The PI ignores the absolute size of individual projects. A project with a high index might be very small and therefore only generate a small NPV.

3.5       Single period rationing with non-divisible projects

3.5.1    If the projects are not divisible then the method shown above may not result in the optimal solution. Another complication which arises is that there is likely to be a small amount of unused capital with each combination of projects. The best way to deal with this situation is to use trial and error and test the NPV available from different combinations of projects. This can be a laborious process if there are a large number of projects available.

3.5.2

EXAMPLE 4

ABC Co has capital of $95,000 available for investment in the forthcoming period. The directors decide to consider projects P, Q and R only. They wish to invest only in whole projects, but surplus can be invested. Which combination of projects will produce the highest NPV at a cost of capital of 20%?     Project Investment required PV of inflows at 20%   $000 $000 P 40 56.5 Q 50 67.0 R 30 48.8 Solution: The investment combinations we need to consider are the various possible pairs of projects P, Q and R. Projects Required investment PV of inflows NPV from projects   $000 $000 $000 P and Q 90 123.5 33.5 P and R 70 105.3 35.3 Q and R 80 115.8 35.8 The highest NPV will be achieved by undertaking projects Q and R and investing the unused funds of $15,000 externally.

3.6       Multi-period capital rationing

3.6.1    A situation where there is a shortage of funds in more than one period is known as multi-period capital rationing. This makes the analysis more complicated because we have multiple limitations and multiple outputs. In such a situation we must employ a linear programming model to identify the profit maximizing mix of investments.

Examination Style Questions

Question 9 – Purchase of New Machine Outright or by Leasing
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)

Question 10 – Replacement Cycles
(a)     Explain and illustrate (using simple numerical examples) the Accounting Rate of Return and Payback approaches to investment appraisal, paying particular attention to the limitations of each approach.                                                                                                                              (8 marks)
(b)     (i)      Explain the differences between NPV and IRR as methods of Discounted Cash Flow analysis.                                                                                                                     (7 marks)
(ii)     A company with a cost of capital of 14% is trying to determine the optimal replacement cycle for the laptop computers used by its sales team. The following information is relevant to the decision:

The cost of each laptop is $2,400. Maintenance costs are payable at the end of each full year of ownership, but not in the year of replacement, e.g. if the laptop is owned for two years, then the maintenance cost is payable at the end of year 1.

 

 

Interval between replacement (years)	Trade-in value ($)	Maintenance cost
1	1,200	Zero
2	800	$75 (payable at end of year 1)
3	300	$150 (payable at end of year 2)

Required:

Ignoring taxation, calculate the equivalent annual cost of the three different replacement cycles, and recommend which should be adopted. What other factors should the company take into account when determining the optimal cycle?
(10 marks)
(Total 25 marks)

Question 11 – Replacement Cycles and Capital Rationing
Cavic Ltd services custom cars and provides its clients with a courtesy car while servicing is taking place. It has a fleet of 10 courtesy cars which it plans to replace in the near future. Each new courtesy car will cost £15,000. The trade-in value of each new car declines over time as follows:

Age of courtesy car (years)	1	2	3
Trade-in value (£/car)	11,250	9,000	6,200

Servicing and parts will cost £1,000 per courtesy car in the first year and this cost is expected to increase by 40% per year as each vehicle grows older. Cleaning the interior and exterior of each courtesy car to keep it up to the standard required by Cavic’s clients will cost £500 per car in the first year and this cost is expected to increase by 25% per year.

Cavic Ltd has a cost of capital of 10%. Ignore taxation and inflation.

Required:

(a)     Using the equivalent annual cost method, calculate whether Cavic Ltd should replace its fleet after one year, two years, or three years.                                                                           (12 marks)
(b)     Discuss the causes of capital rationing for investment purposes.                        (4 marks)
(c)     Explain how an organisation can determine the best way to invest available capital under capital rationing. Your answer should refer to the following issues:
(i)      single-period capital rationing;
(ii)     multi-period capital rationing;
(iii)    project divisibility;
(iv)    the investment of surplus funds.                                                                  (9 marks)
(Total 25 marks)
(ACCA Paper 2.4 Financial Management and Control December 2006 Q2)

Question 12 – Purchase of New Machine
Trecor Co plans to buy a new machine to meet expected demand for a new product, Product T. This machine will cost $250,000 and last for four years, at the end of which time it will be sold for $5,000. Trecor Co expects demand for Product T to be as follows:

Year	1	2	3	4
Demand (units)	35,000	40,000	50,000	25,000

The selling price for Product T is expected to be $12.00 per unit and the variable cost of production is expected to be $7.80 per unit. Incremental annual fixed production overheads of $25,000 per year will be incurred. Selling price and costs are all in current price terms.

Selling price and costs are expected to increase as follows:

	Increase
Selling price of Product T:	3% per year
Variable cost of production:	4% per year
Fixed production overheads:	6% per year

Other information

Trecor Co has a real cost of capital of 5.7% and pays tax at an annual rate of 30% one year in arrears. It can claim capital allowances on a 25% reducing balance basis. General inflation is expected to be 5% per year.

Trecor Co has a target return on capital employed of 20%. Depreciation is charged on a straight-line basis over the life of an asset.

Required:

(a)     Calculate the net present value of buying the new machine and comment on your findings (work to the nearest $1,000).                                                                                                  (13 marks)
(b)     Calculate the before-tax return on capital employed (accounting rate of return) based on the average investment and comment on your findings.                                                         (5 marks)
(c)     Discuss the strengths and weaknesses of internal rate of return in appraising capital investments.   (7 marks)
(ACCA F9 Financial Management Pilot Paper Q4)

Question 13 – Purchase of New Machine and IRR
Duo Co needs to increase production capacity to meet increasing demand for an existing product, ‘Quago’, which is used in food processing. A new machine, with a useful life of four years and a maximum output of 600,000 kg of Quago per year, could be bought for $800,000, payable immediately. The scrap value of the machine after four years would be $30,000. Forecast demand and production of Quago over the next four years is as follows:

Year	1	2	3	4
Demand (units)	1.4 million	1.5 million	1.6 million	1.7 million

Existing production capacity for Quago is limited to one million kilograms per year and the new machine would only be used for demand additional to this.

The current selling price of Quago is $8.00 per kilogram and the variable cost of materials is $5.00 per kilogram. Other variable costs of production are $1.90 per kilogram. Fixed costs of production associated with the new machine would be $240,000 in the first year of production, increasing by $20,000 per year in each subsequent year of operation.

Duo Co pays tax one year in arrears at an annual rate of 30% and can claim capital allowances (tax-allowable depreciation) on a 25% reducing balance basis. A balancing allowance is claimed in the final year of operation.

Duo Co uses its after-tax weighted average cost of capital when appraising investment projects. It has a cost of equity of 11% and a before-tax cost of debt of 8·6%. The long-term finance of the company, on a market-value basis, consists of 80% equity and 20% debt.

Required:

(a)     Calculate the net present value of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000).                                                               (13 marks)
(b)     Calculate the internal rate of return of buying the new machine and advise on the acceptability of the proposed purchase (work to the nearest $1,000).
(4 marks)
(c)     Explain the difference between risk and uncertainty in the context of investment appraisal, and describe how sensitivity analysis and probability analysis can be used to incorporate risk into the investment appraisal process.                                                                                                  (8 marks)
(Total 25 marks)
(ACCA F9 Financial Management December 2007 Q2)

Question 14 – Lease or Buy, Equivalent Annual Cost and Capital Rationing
ASOP Co is considering an investment in new technology that will reduce operating costs through increasing energy efficiency and decreasing pollution. The new technology will cost $1 million and have a four-year life, at the end of which it will have a scrap value of $100,000.

A licence fee of $104,000 is payable at the end of the first year. This licence fee will increase by 4% per year in each subsequent year.

The new technology is expected to reduce operating costs by $5·80 per unit in current price terms. This reduction in operating costs is before taking account of expected inflation of 5% per year.

Forecast production volumes over the life of the new technology are expected to be as follows:

Year	1	2	3	4
Production (units per year)	60,000	75,000	95,000	80,000

If ASOP Co bought the new technology, it would finance the purchase through a four-year loan paying interest at an annual before-tax rate of 8·6% per year.

Alternatively, ASOP Co could lease the new technology. The company would pay four annual lease rentals of $380,000 per year, payable in advance at the start of each year. The annual lease rentals include the cost of the licence fee.

If ASOP Co buys the new technology it can claim capital allowances on the investment on a 25% reducing balance basis. The company pays taxation one year in arrears at an annual rate of 30%. ASOP Co has an after-tax weighted average cost of capital of 11% per year.

Required:

(a)     Based on financing cash flows only, calculate and determine whether ASOP Co should lease or buy the new technology.                                                                                                 (11 marks)
(b)     Using a nominal terms approach, calculate the net present value of buying the new technology and advise whether ASOP Co should undertake the proposed investment.
(6 marks)
(c)     Discuss and illustrate how ASOP Co can use equivalent annual cost or equivalent annual benefit to choose between new technologies with different expected lives.
(3 marks)
(d)     Discuss how an optimal investment schedule can be formulated when capital is rationed and investment projects are either:
(i)      divisible; or
(ii)     non-divisible.                                                                                              (5 marks)
(Total 25 marks)
(ACCA F9 Financial Management December 2009 Q1)

Question 15 – PI and capital rationing
ABC Co is a highly geared company that wishes to expand its operations. Six possible capital investments have been identified, but the company only has access to a total of $620,000. The projects are not divisible and may not be postponed until a future period. After the project’s end it is unlikely that similar investment opportunities will occur.

Expected net cash inflows (including salvage value)

Project	Year 1	Year 2	Year 3	Year 4	Year 5	Initial outlay
	$	$	$	$	$	$
A	70,000	70,000	70,000	70,000	70,000	246,000
B	75,000	87,000	64,000			180,000
C	48,000	48,000	63,000	73,000		175,000
D	62,000	62,000	62,000	62,000		180,000
E	40,000	50,000	60,000	70,000	40,000	180,000
F	35,000	82,000	82,000			150,000

Projects A and E are mutually exclusive. All projects are believed to be of similar risk to the company’s existing capital investments.

Any surplus funds may be invested in the money market to earn a return of 9% per year. The money market may be assumed to be an efficient market.
ABC Co’s cost of capital is 12% a year.

Required:

(a)     (i)    Calculate the expected net present value for each of the six projects.
(ii)   Calculate the expected profitability index associated with each of the six projects.
(iii)  Rank the projects according to both of these investment appraisal methods. Explain briefly why these rankings differ.
(12 marks)
(b)     Give reasoned advice to ABC Co recommending which projects should be selected.
(7 marks)
(c)     A director of the company has suggested that using the company’s normal cost of capital might not be appropriate in a capital rationing situation. Explain whether you agree with the director. (6 marks)
(Total 25 marks)