What is the project’s payback period?

The project pays for itself after 41/2 years. At the end of that period the project produces net cash flows of £100,000 equal to the cost of the original investment.

The payback method has universal appeal because of its simplicity and the fact that it tends to favour less risky capital projects. Projects that take too long to pay for themselves are riskier and this method tends to reject these.

Accounting rate of return

This method establishes the relationship between the capital cost of a project and the profits accruing. The accounting rate of return is calculated by the following formula.

Average annual profit

------------------------------- x 100

Average cost of investment

An average profit is calculated over the life of the project. The average cost of investment is calculated by adding the initial cost of the investment and the value at the end of its useful life divided by two.

Example:

A company has two alternative projects A and B, each involving an outlay of £500,000 and £600,000

Each project has an economic life of 5 years. Project A has a residual value of £50,000. Annual profits before depreciation is £200,000 before depreciation.

	Project A	Project B
	£	£
Initial outlay	500,000	600,000
Annual profits (Yr. 1-5)	1,000,000	1,000,000
Less depreciation (Yr. 1-5)	500,000	550,000
	----------	----------
Profits after depreciation	500,000	450,000
	---------	---------
Average net profit	100,000	90,000
	----------	--------
Accounting rate of return	40%	28%

The ARR method is easy to administer and is understood by business in general because of is similarity with the return on investment (ROCE) ratio.

The main disadvantage with payback and accounting rate of return is both ignore the time value of money. Money has a value in time, namely, a rate of interest. If £1 is invested for 1 year at a rate of interest of 10% the investment grows to £1.10 at the end of year 1. If £1.10 is invested in year 2 the investment

grows to £1.21 at the end of year 2. This process is called compounding which is represented by the formula £1(1 + r)n.

The opposite of compounding is discounting. This answers the question ‘ what is £1 receivable in a year’s time worth in today’s value?’ In present value terms £1 receivable in a years time (assuming the rate of interest is 10%) is £0.909. The formula for discounting is: £1

-----------

(1 + r)n

Investment appraisal compares the cash outflows with the cash returns from the project and these cash flows take place over a lengthy period of time.

Discounting allows all the cash flows to be converted to present day values which permits meaningful comparison. The following investment appraisal methods employ the discounting of cash flows.

Net Present Value

A particular rate of interest is used to discount future flows of cash to present values. The discount rate used might reflect the cost of obtaining capital, or a target rate/cut-off rate,or a risk-adjusted rate. Once the future cash flows are discounted to present-day values they are totalled and compared with the cost of the project. If the discounted cash flows exceed the cost the difference is the net cash flow. In general, if the NPV is positive the project is worth considering.

Example:

A company wishes to evaluate a capital project based on the following information. The initial outlay is £100,000 and the project has an economic life of 5 years and realises £5,000 when it is sold at the end of year 5. The profits after depreciation have been estimated as year 1-3 £10,000 and £15,000 in the final two years. The rate of interest is 10%.

Year	Cash flow	Discount factor	Present value	Cumulative PV
	£		£	£
	(100,000)		(100,000)
	29,000	0.909	26,361	26,361
	29,000	0.826	23,954	50,315
	29,000	0.751	22,939	73,254
	34,000	0.683	23,222	94,476
	34,000	0.621	21,114	117,590
	5,000	0.564	2,820	120,410
			---------
			NPV =20,410
			--------

Since theNPV is +£20,410, the project is worthwhile.

Discounted payback

In the calculation of the NPV in the previous example a column records the cumulative present value of the cash flows. Since the payback method is criticised for ignoring the time value of money it is possible to remedy this shortcoming by using the discounted cash flows to ascertain the payback period.

In this example, the payback period is just over 4years. There is a shortfall of £5,524 which has to be generated in year 5.

£5,524 365 days

--------- x = 17 days

£117,590