Reading: Payback Rule

As we have just seen, the standard payback rule ignores the time value of money (the fact that investors require a certain risk-adjusted rate of return). To cure this problem, we could measure a project's payback based on the present values of all future cash flows, rather than the future value of these cash flows. That's what the Discounted Payback or Modified Payback does.

Example 6

Let's consider the following example of a project with an initial investment of 1'000 today and subsequent annual cash flows of 200 for the next 10 years. We assume a cost of capital of 10% and we assume that the relevant payback period is 5 years (all projects with payback ≤ 5 years will be accepted):

The payback of the project is just 5 years and we would accept the project based on the payback rule. However, when we just look at the first five year of the project, the cash flows it generates are insufficient to cover the cost of capital!

To see this, the second row in the table above shows the present value of each future cash flow, assuming a cost of capital of 10%. For example, the present value of year 4's cash flow is \( PV(C_4) = \frac{200}{1.1^4}=137\). When we now compute the cumulative present value of the project cash flows over the first five years, we see that it is negative:

\( \text{Cumulative PV}_{Y0-Y5} = -1'000+182+165+...+124 = -242 \)

Put differently, solely considering the first 5 years, the project destroys value. Alternatively, we could compute the discounted payback to see whether the project is able to recover the initial investment of 1'000 when we take the time value into consideration. To do so, we compute the cumulative present value over the duration of the project: 

From before, we already know that the cumulative PV over the first 5 years is -242. Now we simply repeat the procedure for all other years. The result is shown in the last row of the table above. 

In terms of present values, the project has a payback of 8 years. The discounted payback therefore is 8 years.

Discussion

The discounted payback is much better than the standard payback rule because it takes into consideration the time value of money. 

• Standard projects like the one considered in Example 6 above only have a discounted payback if their NPV is positive.
• In fact, the cumulative PV at the end of the project horizon (Y10 in the example above) indicates the NPV of the project (remember that the NPV is the sum of the present value of each project cash flow)!
• Therefore, the discounted payback rule does much better than the simple payback rule and more often leads to the dame investment decision as the NPV rule.

However, the rule is complex to apply and very often still misleading:

• Fist, it is not clear how to set the cutoff period for the discounted payback. Many managers will find it hard to come up with a sensible definition. 
• For normal investment projects, as we have seen, the existence of a discounted payback implies that the project has positive NPV. Therefore, a reasonable rule could be that the discounted payback occurs within the project's useful technical life. 
• Even with such a cutoff, the discounted payback rule will not solve the other challenges that we have discussed before, namely the inability to choose among projects with different sizes and the fact that it ignores all the cash flows after the (discounted) payback period.

All these issues constitute major flaws of the rule. Just as an illustration, assume that the project considered in Example 6 above has dismantling costs of 1'000 in year 10 instead of a positive cash inflow of 200:

The project still has a discounted payback of 8 years. In total, however, the project destroys value because of the significant dismantling costs. The discounted payback rule is unable to make that distinction!