Question

question 7 (5 points)
listen
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 -$750 $500 $500 $500
1.53 years
1.29 years
1.56 years
1.72 years
1.61 years

Explanation:

Step1: Calculate discounted cash flows

For year 1: $DCF_1 = \frac{500}{(1 + 0.10)^1} = \frac{500}{1.10} \approx 454.55$
For year 2: $DCF_2 = \frac{500}{(1 + 0.10)^2} = \frac{500}{1.21} \approx 413.22$
For year 3: $DCF_3 = \frac{500}{(1 + 0.10)^3} = \frac{500}{1.331} \approx 375.66$

Step2: Calculate cumulative discounted cash flows

Year 0: $-750$
Year 1: $-750 + 454.55 = -295.45$
Year 2: $-295.45 + 413.22 = 117.77$

Step3: Calculate discounted payback period

Payback occurs between year 1 and 2.
Fraction of year 2: $\frac{295.45}{413.22} \approx 0.715$
Total payback: $1 + 0.715 \approx 1.715 \approx 1.72$ years

Answer:

1.72 years