CFA Level 1: Calculate Discounted Payback Period

Discounted Payback Period Calculation

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Question

A project requires an initial outlay of 650. It also needs capital spending of 700 at the end of year 1 and 900 at the end of year 2. It has no revenues for the first 2 years but receives 1,200 in year 3, 1,600 in year 4 and 2,300 in year 5. The project's cost of capital is 10%. The discounted payback period equals ________.

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A. B. C. D.

B

The cash flows of the project starting at the end of year 1 are:

-700, -900, +1,200, +1,600, +2,300

The discounted payback period is defined as the expected number of years that would be required to recover the original investment using discounted cash flows.

The discounted cash flow at the end of year N is obtained by dividing that year's cash flow by 1.1N, since the project's cost of capital is 10%. Using this, the discounted cash flows are:

-636, -744, +902, +1,093, +1,428.

Recovery occurs in the 5th year. At the beginning of the 5th year, the outstanding balance equals 650 + 636 + 744 - 902 - 1093 = 35. Therefore, the discounted payback period = 4 + 35/1428 = 4.02 years.

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