Question

Fernando Designs is considering a project that has the following cash flow and WACC data. What is the project's discounted payback?

WACC: 10.00%
Year 0 1 2 3
Cash flows ($650) $500 $500 $500

a. 1.75years
b. 1.83years
c. 1.81years
d. 1.47years
e. 1.56years

Answer 1

Answer:

d. 1.47 years

Step-by-step explanation:

From the answer choices, it can be determined that the discounted payback will occur between the first and second year of the project. The present value of the first year of operations is:

$PV_1 = \frac{500}{(1+0.10)^1}\\PV_1 = 454.55$

The Accumulated cash flow after the first year is:

$CF_1 = -650+454.55\\CF_1 = -\ 195.45$

The present value of the second year of operations is:

$PV_1 = \frac{500}{(1+0.10)^2}\\PV_1 = 413.23$

Assuming that revenue is spread out evenly within a year, the payback will occur at:

$t_2=\frac{195.46}{413.23} =0.47$

Therefore, the payback period is the first whole year plus 0.47 of the second year, d. 1.47 years.

Answer 2

The project's discounted payback is 1.47 years.

Discounted payback calculates the length of time it takes to recover the amount invested in a project from its cumulative cash flows.

• Discounted cash flow in year 1 = $500 / (1.1) = $454.55
• Discounted cash flow in year 2 = $500 / (1.1)² = $413.22
• Discounted cash flow in year 3 = $500 / (1.1)³ = $375.66

Amount recovered in year 1 = $-650 +  $454.55 = $-195.45

Discounted payback = 1 + (195.45 / 413.22) = 1.47 years

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