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Capital Investment Appraisal

February 20th 2007

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Learning Objectives• To understand the nature and importance of

investment decision-making in organisations• To understand the concept of the time value of money

and how to calculate discount factors • To identify the four investment appraisal methods

and how to evaluate investment proposals using these methods ***

• To summarise advantages and disadvantages of these methods both in theory and practice

• To make recommendations based on your analyses

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Recommended Readings• Drury C (2001) Management Accounting for Business

Decisions 2nd Edition. Thomson. (Chapter 9)• Gowthorpe C (2003) Business Accounting and Finance for

Non-Specialists. Thomson. (Chapter 21)• McLaney E and Atrill P (2002) Accounting: An Introduction,

2nd edition. Prentice Hall: Europe. (Chapter 14)• Cashmore C (2002) ‘Cut to the Chase’, CIMA Insider,

September.• Dugdale D & Jones C (1991) ‘Discordant voices: accountants’

views of investment appraisal’ Management Accounting, November.

• Dugdale D (1992) ‘Is there a ‘correct’ method of investment appraisal?’ Management Accounting, May.

• Scarlett B (2002) ‘That Sinking Feeling’, CIMA Insider, September.

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Nature & Importance • Nature

– Long-term rather than short-term– Large investment rather than small investment– More complicated from concerns of future cash

flows and/or time value of money

• Importance– Large amounts of resources are often involved:

business strategy, profitability, and survive – Difficult to “bail out”, once an investment made– Close relationship with shareholders: wealth

maximisation

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Methods of Investment Appraisal• Payback period

– The length of time: cash proceeds recover the initial capital expenditure

• Accounting Rate of Return (ARR)– A return measurement by using average annual profits

• Net Present Value (NPV)– The present value of the net cash inflows less the initial

investment

• Internal Rate of Return (IRR)– A return measurement takes into account the time value of

money

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Example There are two optional projects for your

company to choose. However, you can only choose one of them. The data for the initial investments are in the following table. You are required to calculate:– Payback period– ARR– NPV– IRR, and– Your recommendation

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Data for the Projects

Project A Project B

Initial investment £100,000 £100,000

Cash inflows

Year 1 £45,000 £30,000

Year 2 £40,000 £30,000

Year 3 £35,000 £44,000

Year 4 £30,000 £46,000

• The depreciation is £20,000 per year.

• The residual value for both projects is the same, £20,000.

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Payback Period

• The Payback period = the point in time at which cash flows turn from negative to positive

Project A Cash flows Cumulated cash flow

Year 0 -100,000 -100,000

Year 1 45,000 -55,000

Year 2 40,000 -15,000

Year 3 35,000 +20,000

Year 4 50,000 +70,000

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Payback Period

• Payback period (A) = change in cash flow required to reach zero/total cash flow in year

=15,000/35,000 = 0.43 + 2 years = 2.43 years

• Payback period (B) = 40,000/44,000 = 0.91 + 2 years = 2.91 years

• Which project is the better one based on payback period?

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Payback Period

Project B Cash flows Cumulated cash flow

Year 0 -100,000 -100,000

Year 1 30,000 -70,000

Year 2 30,000 -40,000

Year 3 44,000 +4,000

Year 4 66,000 +70,000

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ARRStep 1: calculate annual profit

– Annual profit = net cash inflow - depreciation

Step 2: calculate average profit– Average profit = total profits / number of years

Step 3: calculate average capital invested– Average capital invested = (initial cost + residual

value) /2

Step 4: calculate ARR– ARR = average profit/average capital invested x

100

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ARR• Project A

– Average profit = (25,000 + 20,000 + 15,000 + 10,000)/4 = 70,000/4 = 17,500

– Average capital invested = (100,000+20,000) /2 = 60,000

– ARR = 17,500/60,000 x 100 = 29%

• Project B– Average profit = (10,000 + 10,000 + 24,000 + 26,000)/4 =

17,500

– Average capital invested = (100,000 + 20,000)/2 = 60,000

– ARR = 17,500/60,000 x 100 = 29%

• Which project is the better one?

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The Time Value of Money• What a difference between £1 now and £1 in a year’s

time? • Factors change the value of money

– Interest cost– Inflation– Other risks to materialise the money

• For example: the annual interest rate is 10%, I lend you £1 now and will get back after 1 year, how much worth of that £1 in a year’s time?– ? x (1+10%) = £1– ? = £0.91

• 10% is called “cost of capital”; “?” is called the “discount factor”

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NPV

• Assume that your company’s cost of capital is 10%

• Discount factors at 10% are:– Year 1 0.909– Year 2 0.826– Year 3 0.751– Year 4 0.683

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NPV

Project A Cash flow Discount factor Dis.d cash flow

Year 0 -100,000 1.00 (100,000)

Year 1 45,000 0.909 40,905

Year 2 40,000 0.826 33,040

Year 3 35,000 0.751 26,285

Year 4 50,000 0.683 34,150

NPV £34,380

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NPVProject B Cash flow Discount factor Dis.d cash flow

Year 0 -100,000 1.00 (100,000)

Year 1 30,000 0.909 27,270

Year 2 30,000 0.826 24,780

Year 3 44,000 0.751 33,044

Year 4 66,000 0.683 45,078

NPV £30,172

• Which project is the better one based on NPV?

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IRR• IRR: the discount rate when the net present value is zero

• Project A

– NPV = £34,380 when the discount rate is 10%

– NPV = ? When the discount rate is 25%

Project A Cash flow Discount factor Dis.d cash flow

Year 0 -100,000 1.00 (100,000)

Year 1 45,000 0.800 36,000

Year 2 40,000 0.640 25,600

Year 3 35,000 0.512 17,920

Year 4 50,000 0.410 20,500

NPV £20

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IRR• Project B

– NPV = £30,172 when the discount rate is 10%

– NPV = ? When the discount rate is 25%

Project B Cash flow Discount factor Dis.d cash flow

Year 0 -100,000 1.00 (100,000)

Year 1 30,000 0.800 24,000

Year 2 30,000 0.640 19,200

Year 3 44,000 0.512 22,258

Year 4 66,000 0.410 27,060

NPV -7,482

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IRR• Project A: IRR = 25%

• Project B

– Total change in NPV = 30,172 + 7,482 = 37,654

– Total change in discount rate = 25% - 10% = 15%

– IRR = 10% + 30,172/37,654 x15 = 22%

• Which project is better?

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Project Selection

Methods Single project Choice of projects A or B?

Payback less than the target period

Shortest payback period

A

ARR Above the target rate

With the highest ARR

N/A

NPV A positive NPV With the highest NPV

A

IRR Higher than the target rate (cost of capital)

With the highest IRR A

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Advantages & Disadvantages

Method Advantages Disadvantages

Payback • simple and easy to understand and use

• objective – using cash flows

• liquidity – commercially realistic

• cautious & risk averse – ignores later cash flows

• ignores the time value of money

• ignores cash flows after the payback period

ARR • simple and easy to understand and use

• aids internal and external comparisons

• looks at the whole life of the project

•A useful tool to measure divisional managerial performance

• subjective – profit, not cash flows

• ignores the time value of money

• difficulty in use when with same ARR and various project sizes

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Advantages & Disadvantages

Method Advantages Disadvantages

NPV • takes account of the time value of money

• concerns of shareholder wealth

• takes account of risk

• looks at the whole life of the project

• difficult to be understood by managers

• adverse effects on accounting profits in the short run

• how to choose discount rate?

IRR • takes account of the time value of money

• easy to be understood by managers

• difficult to use in choosing projects of varying sizes

• difficult to choose when have the same IRR

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Tips of Exam Question

• How to use four methods based on examples

• How to interpret and compare your calculations

• How to select the best choice

• How to distinguish advantages and disadvantages of four methods