# An investment project costs $13,000 and has annual cash flows of$3,333 for six years. a. What is...

## Question:

An investment project costs $13,000 and has annual cash flows of$3,333 for six years.

a. What is the discounted payback period if the discount rate is 0%? (Round answer to 2 decimal places.)

b. What is the discounted payback period if the discount rate is 5%? (Round answer to 2 decimal places.)

c. What is the discounted payback period if the discount rate is 18%? (Round answer to 2 decimal places.)

## Payback Period:

Payback period is the number of periods it takes a project to generate enough cash flows to cover the initial cost of the project. In the simple payback analysis, future cash flows are not discounted.

a. If the discount rate is zero, then the discounted payback period is the same as the simple payback period, which is:

• 13,000 / 3,333 = 3.9

b. If the discount rate is 5%, the discounted payback period is the number of years such that the present value of the cash flows is equal to the initial cost, i.e., the solution to the following equation:

• {eq}\dfrac{3,300*(1 - (1 + 5\%)^{-T})}{5\%} = 13,000\\ T = 4.46{/eq}

That is, the discounted payback period is 4.44 years.

c. If the discount rate is 18%, the discounted payback period is the solution to the following equation:

• {eq}\dfrac{3,300*(1 - (1 + 18\%)^{-T})}{18\%} = 13,000\\ T = 24.80{/eq}

That is, the discounted payback period is 24.80 years.