# Payback and discounted payback

In the Study Guide for Paper FFM, reference E3(a) requires candidates to not only be able to calculate the payback and discounted payback, but also to be able to discuss the usefulness of payback as a method of investment appraisal.

Recent Paper FFM exam sittings have shown that candidates are not studying payback in sufficient depth or breadth to answer exam questions successfully. This article aims to help candidates with this.

Candidates should note that payback is not only examined within the Paper FFM syllabus, but also the Paper F9 syllabus.

#### Payback

Definition
Payback is defined as the length of time it takes the net cash revenue / cash cost savings of a project to payback the initial investment.

From the definition, it can be seen that only cash flows should be included within the calculation – specifically, only relevant cash flows should be included within the calculation, so items such as depreciation should be excluded.

Calculation
Let’s use the following example:

An organisation is considering a project which has an initial investment of \$40,000 and is expected to generate profit after depreciation but before tax of \$12,500 each year for eight years. Depreciation will be on a straight line basis over the life of the project.

The first step is to determine the cash flows from the project.  In this case, we are given the profit figure so need to adjust for depreciation of (\$40,000/8 years) \$5,000 per year, to give an annual cash flow of (\$12,500 + \$5,000) \$17,500.

The second step is to calculate the payback period and the easiest way of completing the calculation is often via a table:

TimeCash flowCumulative
cash flow
0(40,000)

(40,000)

1

17,500

(22,500)

2

17,500

(5,000)

3

17,500

12,500

It can be seen from the table that the cumulative cash flow becomes positive in year three. If cash flows arise at the end of the year, the payback period will be three years. If however cash flows arise during the year, payback will arise during year three, and more precisely (5,000/17,500 x 12) three months (to the nearest month) through the year, so giving a payback of two years and three months.

In this example, the same net cash inflow arises every year, starting in year one, and so a short cut is available:

Payback = initial investment / net cash inflow
Payback = (40,000) / 17,500 = 2.29 years

So if the cash flow arises at the end of the year, payback is three years, and if cash flow arises during the year, the payback is two years and (0.29 x 12) three months (to the nearest month).

As well as ensuring that the cash flows rather than the profits are used within the calculation, candidates also need to ensure that they consider the timing of the cash flows.

Using the previous example, how would the answer change if the first cash inflow did not arise until year three?

The cumulative cash flow table would become:

TimeCash flowCumulative
cash flow
0(400,000)(40,000)
10(40,000)
20(40,000)
317,500(22,500)
417,500(5,000)
517,50012,500

We can see that the payback period is either five years if cash flows arise at the end of the year or four years and (5,000/17,500 x 12) three months (to the nearest month) if cash flows arise during the year.

Usefulness
Payback is often used as a first screening method for an investment – ie the first question that is often asked with a new project is: ‘When will the initial cost be paid back?’ An organisation may have a target payback period, with any project taking longer than the target period being rejected.

Payback also provides more focus on the earlier cash flows arising from a project, as these are both more certain and more important if an organisation has liquidity concerns.

Two other advantages are that payback is easy to calculate and to understand.

There are, however, disadvantages associated with the payback method of investment appraisal:

• Cash flows after the payback period are ignored, therefore the effect of the whole project on the cash flows of the organisation are not considered.
• A target is required, which can be difficult to set and is arbitrary.
• The increase / decrease in wealth of the investor arising from the project is not considered – the net present value of the project would need to be calculated to assess the effect on shareholder wealth, for example.
• The time value of money is not considered.

This last disadvantage will be overcome if the discounted payback is calculated rather than the payback period.

#### Discounted Payback

Definition
The discounted payback is defined as the length of time it takes the discounted net cash revenue/cost savings of a project to payback the initial investment.

Calculation
The discounted payback calculation takes into account the time value of money by discounting each cash flow before the cumulative cash flow is calculated, and determines the time at which the net present value becomes positive.

Let’s use the first example, but expand it by including the fact that the organisation has a cost of capital of 10%.

Again, the first step would be to ensure that the cash flows are identified, which we have already done – \$17,500 per year.

The second step is to complete the cumulative cash flow table, but now extra columns are required for the discount factor and the discounted cash flow:

TimeCash flowDiscounted factorDiscounted cash flowCumulative discounted cash flow
0(40,000)1(40,000)(40,000)
117,5000.90915,908(24,092)
217,5000.82614,455(9,637)
317,5000.75113,1433,506

From the table above, it is evident that the payback period is three years.

Note that here an assumption is that the cash flows arise at the end of the year so the answer is a whole number of years.

Usefulness
The time value of money is considered when using discounted payback, but otherwise the points made previously regarding the usefulness of payback hold for discounted payback as well.

#### Conclusion

Candidates need to be able to perform the calculations for payback and discounted payback, as well as understand how useful these measures, as a method of investment appraisal, can be. It is hoped that this article will help candidates with both of these elements.

Written by a member of the Paper FFM examining team