# Discounted payback

Discounted payback is a variant of the payback method of investment appraisal.

Under discounted payback, the amounts of money arising in different time periods are discounted to their present values.

Example

A proposal requires an initial investment of \$100m at Time 0 years,

and will then pay out annual amounts of \$10m, \$20m, \$30m, \$40m, \$50m and \$60m,

at future Times 1 to 6 years respectively.

The relevant cost of capital is 10% per year.

The cumulative discounted net cash flow and discounted payback period are calculated as follows:

Discounted cash flows:

Time 0: (100) x 1.100

= \$(100)m.

Time 1: 10 x 1.10-1

= \$9.09m.

Time 2: 20 x 1.10-2

= \$16.53m.

Time 3: 30 x 1.10-3

= \$22.54m.

Time 4: 40 x 1.10-4

= \$27.32m.

Time 5: 50 x 1.10-5

= \$31.05m.

Cumulative discounted cash flows:

Time 0: (100).

Time 1: (100) + 9.09

= \$(90.91)m.

Time 2: (90.91) + 16.53

= \$(74.38)m.

Time 3: (74.38) + 22.54

= \$(51.84)m.

Time 4: (51.84) + 27.32

= \$(24.52)m.

Time 5: (24.52) + 31.05

= +\$6.53m.

The initial investment has paid back by the end of 5 years, so the payback period to the nearest whole year is 5 years.

It is also possible to calculate a more refined estimate using interpolation between 4 years and 5 years. Interpolation assumes that the cash flows arise evenly over the course of the 5th year.

This method removes some of the problems of the simple payback method. But it still leaves significant problems and simplifying assumptions.