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Worked Example: Payback period

A company is considering an investment in a project to acquire new equipment costing $80 000. The equipment would have a five-year life and no residual value at the end of that time. The straight-line method of depreciation is used. The expected profits after depreciation from investing in the equipment are as follows:

What is the payback period for the investment?

Solution

The payback period is calculated from the cumulative annual profits before depreciation and we have been given profit after depreciation. Annual depreciation is $16 000, and the profit before depreciation each year is found simply by adding back the $16 000 to the annual profit estimate.

Year Investment Profit before

depreciation Cumulative profit before depreciation

Payback occurs when the cumulative profits stop being negative and start to be positive. This will happen some time during Year 3 (or after three years if cash flows are assumed to arise at the end of each year).

If it is assumed that profits each year arise at an even rate throughout the course of the year, the payback period can be calculated in years and months:

LO 1.4

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Y = the number of complete years before payback. This is the year before the one in which payback occurs.

B = the cumulative profits before depreciation at the beginning of the payback year, ignoring the negative value.

E = the cumulative profits before depreciation at the end of the payback year.

In this example:

6.2 Disadvantages of the payback method

There are a number of drawbacks to the payback method:

(a) The choice of a maximum payback period for an investment is arbitrary and subjective.

(b) It ignores all cash flows after the end of the payback period, and so is not concerned with the total expected returns from the investment.

For example, suppose that the maximum payback period that a company selects for its investments is four years, and it is considering two mutually exclusive projects, X and Y, each costing $80 000.

Project X would be expected to make total profits of $100 000 and pay back within two years.

Project Y would be expected to make total profits of $500 000, but only pay back after five years.

On the basis of payback alone, project X would be preferred, despite its lower total profitability.

(c) It ignores time value of money.

(d) If the objective of a company is to maximise the wealth of its shareholders, it would be wrong to ignore the future profits from an investment after an arbitrary cut-off date for payback. Using a payback cut-off limit is inconsistent with shareholder wealth maximisation.

(e) The payback method ignores the timing of cash flows within the payback period and the time value of money (a concept incorporated into the DCF appraisal methods that are considered later). This means that it does not take account of the fact that $1 today is worth more than $1 in one year's time (see Section 7).

(f) The method is unable to distinguish between projects with the same payback period.

(g) It may lead to excessive investment in short-term projects.

6.3 The payback method in practice

Despite the theoretical limitations of the payback method, it is widely used in practice. There are a number of reasons for this:

(a) It is simple to calculate and simple to understand, and this may be important when management resources are limited. It is similarly helpful in communicating information about minimum requirements to managers responsible for submitting projects.

(b) It is a particularly useful approach for ranking projects where a firm faces liquidity constraints and requires a fast repayment of investments.

(c) It is appropriate in situations where risky investments are made in uncertain markets that are subject

LO 1.9

LO 1.9

Question 4: Payback period

A company carries out capital project appraisal using payback. It will not undertake any project unless the payback is within three years.

A project is currently being considered. It would involve expenditure of $150 000 on an asset. The project's life would be five years and at the end of this time the asset would have no residual value. A working capital investment of $15 000 would be required.

The annual profits before depreciation from the project would be:

Year $

(a) What is the payback period for the project?

(b) On the basis of the company's investment criterion, would this project be undertaken?

(The answer is at the end of the chapter)

7 The time value of money

Section overview

• The concept of time value of money recognises that $1 today is worth more than $1 at a future time, because money can be reinvested to earn more money over time.

Definition

The time value of money describes the concept that the earlier cash is received, the greater value it has to the recipient. Conversely, the later a cash payment is made, the less the cost to the payer.

Investors put money into shares in the expectation of getting back, over time, an amount in excess of their original investment. The idea of investing cash to make more money should be a familiar concept to you.

If you put money into a deposit account, you will expect to get your money back with interest. If the interest is not high enough, you will look somewhere else to invest.

In the same way, an investor buying shares expects a return in the form of dividends plus the eventual disposal price of the shares when he decides to sell them. If the expected returns are not high enough to justify the purchase price of the shares, he will not buy the shares, but put his money into another investment instead.

The same principle applies to investments by companies. The cash returns from long-term investments should be sufficient to provide an adequate return; otherwise, the investment should not be undertaken.

The required return on an investment consists of three elements, for any investor:

(a) An opportunity cost. This is the return that could be obtained by investing in something else.

In financial management, the opportunity cost of an investment is usually expressed in terms of the return that could be obtained by putting money into a risk-free (and inflation-proof) investment.

(b) An amount to cover inflation. Inflation erodes the value of money over time, and an investor will expect the return on investment to cover the effect of inflation as well as to provide a ‘real’ return.

(c) An amount to reward the investor for the risk in the investment. Higher returns are expected from investments with a higher risk element.

An investment return is expressed as a percentage of the amount invested for each year of investment.

The longer the investment, the greater the required return. This too should be a familiar idea to you. If you put cash into a deposit account, you will expect to earn interest, and the longer you keep the money on deposit, the more interest you will expect to earn.

We must therefore recognise that if a capital investment is to be worthwhile, it must earn at least a minimum profit or return so that the size of the return will compensate the investor (the business) for the length of time which the investor must wait before the profits are made. For example, if a company could invest $60 000 now to earn revenue of $63 000 in one week's time, a profit of $3 000 in seven days would be a very good return. If it takes three years to earn the revenue, however, the return would be very low.

When capital expenditure projects are evaluated, it is therefore appropriate to decide whether the investment will make enough profits to allow for the 'time value' of capital tied up.

The time value of money reflects people's time preference for $1 now over $1 at some time in the future. Discounted cash flow (DCF) is an evaluation technique which takes into account the time value of money.

8 Discounted cash flow techniques

Section overview

In DCF, expected future cash flows (inflows and outflows) are converted into a present value equivalent amount.

• The present value of a future cash flow is the amount that would have to be invested now, at the organisation's cost of capital, to earn the future cash flow at the future time.

• The cost of capital used in DCF is the cost of funds that a company raises and uses, and the return that investors expect to be paid for putting funds into the company.

Definition

Discounted cash flow, (DCF), is an investment appraisal technique which takes into account both the timings of cash flows and also total profitability over a project's life.

Two important points about DCF are as follows:

(a) Like payback, DCF looks at the cash flows of a project, not the accounting profits (as discussed in Section 5).

(b) DCF takes account of the time value of money (as discussed in Section 7).

The timing of cash flows is taken into account by discounting them.

The effect of discounting is to give a bigger value per $1 for cash flows that occur earlier: $1 earned after one year will be worth more than $1 earned after two years, which in turn will be worth more than $1 earned after five years, and so on.

8.1 Compounding

Suppose that a company has $10 000 to invest, and wants to earn a return of 10 per cent per annum (compound interest) on its investments. This means that if the $10 000 could be invested at 10 per cent, the value of the investment with interest would build up as follows:

Formula to learn

The formula for the future value of an investment plus accumulated interest after n time periods is:

FV = PV (1 + r)n

where: FV is the future value of the investment with interest.

PV is the initial or 'present' value of the investment.

r is the compound rate of return per time period, expressed as a proportion (so 10% = 0.10, 5% = 0.05 and so on).

n is the number of time periods.