Nonuniform Cash Flows

When cash flows are not uniform, the payback computation takes a cumulative form: The cash flows over successive years are accumulated until the amount of net initial investment is recovered. Suppose Venture Law Group is considering purchasing videoconferencing equipment for $150,000. The equipment is expected to provide total cash savings of $340,000 over the next 5 years, due to reduced travel costs and more effective use of associates’ time. The cash savings occur uniformly throughout each year but are not uniform across years.

<p>A table shows cash savings for Venture Law Group</p>

The table depicts cash savings, cumulative cash savings, and net initial investment unrecovered at end of year for years 0 through 5. The details of the table are as follows:

1. Year 0

2. Year 1

3. Year 2

4. Year 3

5. Year 4

6. Year 5

The chart shows that payback occurs during the third year. Straight-line interpolation within the third year reveals that the final $45,000 needed to recover the $150,000 investment (that is, $150,000− $ 105,000 recovered by the end of year 2) will be achieved three-quarters of the way through year 3, during which $60,000 of cash savings occur:

Payback period=2  years+($45,000$60,000×1  year)=2.75  years

It is relatively simple to adjust the payback method to incorporate the time value of money by using a similar cumulative approach. The discounted payback method calculates the amount of time required for the discounted expected future cash flows to recoup the net initial investment in a project. For the videoconferencing example, we can modify the preceding chart by discounting the cash flows at the 8% required rate of return.

<p>A table shows cash savings for Venture Law Group after discounting cash flows at the 8 percent required rate of return</p>

The table depicts cash savings, present value of 1 dollar discounted at 8 percent, discounted cash savings, cumulative discounted cash savings, and net initial investment unrecovered at end of year for years 0 through 5. The details of the table are as follows:

1. Year 0

2. Year 1

3. Year 2

4. Year 3

5. Year 4

6. Year 5

The fourth column shows the present values of the future cash savings. It is evident from the chart that discounted payback occurs between years 3 and 4. At the end of the third year, $8,925 of the initial investment is still unrecovered. Comparing this to the $62,475 in present value of savings achieved in the fourth year, straight-line interpolation reveals that the discounted payback period is exactly one-seventh of the way into the fourth year:

Discounted payback period=3 years+($8,925$62,475×1 year)=3.14 years

The discounted payback does incorporate the time value of money, but is still subject to the other criticism of the payback method—that cash flows beyond the discounted payback period are ignored, resulting in a bias toward projects with high short-run cash flows. Companies such as Hewlett-Packard value the discounted payback method (Hewlett-Packard refers to it as “breakeven time”) because they view longer-term cash flows as inherently unpredictable in high-growth industries, such as technology.

Finally, the videoconferencing example has a single cash outflow of $150,000 in year 0. When a project has multiple cash outflows occurring at different points in time, these outflows are first aggregated to obtain a total cash-outflow figure for the project. For computing the payback period, the cash flows are simply added, with no adjustment for the time value of money. For calculating the discounted payback period, the present values of the outflows are added instead.

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