Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 10 percent, and that the maximum allowable payback and discounted payback statistics for the project are three and a half and four and a half years, respectively. Use the discounted payback decision to evaluate this project; should it be accepted or rejected?
$$\begin{array} { l c c c c c c c c c }
\text { Time } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \
\text { Cash Flow } & - \$ 5,000 & \$ 1,200 & \$ 1,400 & \$ 1,600 & \$ 1,600 & \$ 1,100 & \$ 2,000
\end{array}$$
A) Discounted payback = 4.25 years, accept the project
B) Discounted payback = 3.50 years, accept the project
C) Discounted payback 5 years, reject the project
D) Discounted payback = 4.67 years, reject the project

Question

Suppose your firm is considering investing in a project with the cash flows shown as follows, that the required rate of return on projects of this risk class is 10 percent, and that the maximum allowable payback and discounted payback statistics for the project are three and a half and four and a half years, respectively. Use the discounted payback decision to evaluate this project; should it be accepted or rejected?
$$\begin{array} { l c c c c c c c c c } 
\text { Time } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \
\text { Cash Flow } & - \$ 5,000 & \$ 1,200 & \$ 1,400 & \$ 1,600 & \$ 1,600 & \$  1,100 & \$ 2,000
\end{array}$$
A) Discounted payback = 4.25 years, accept the project
B) Discounted payback = 3.50 years, accept the project
C) Discounted payback > 5 years, reject the project
D) Discounted payback = 4.67 years, reject the project

Quizplus · Accepted Answer

To calculate the discounted payback period, we discount each cash flow back to its present value using the required rate of return (10%). The discounted cash flows are as follows:- Year 1: $1,200 / (1 + 0.10)^1 = $1,090.91- Year 2: $1,400 / (1 + 0.10)^2 = $1,157.02- Year 3: $1,600 / (1 + 0.10)^3 = $1,215.90- Year 4: $1,600 / (1 + 0.10)^4 = $1,105.15- Year 5: $1,100 / (1 + 0.10)^5 = $683.01- Year 6: $2,000 / (1 + 0.10)^6 = $1,124.62Summing these up until the initial investment is recovered:- Year 1-3: $1,090.91 + $1,157.02 + $1,215.90 = $3,463.83- By Year 4: $3,463.83 + $1,105.15 = $4,568.98The initial investment is $5,000, so by the end of Year 4, the project has not yet paid back the initial investment when considering the time value of money. The payback occurs sometime during Year 5, as the cumulative discounted cash flow exceeds the initial investment with the addition of Year 5's discounted cash flow. Given the maximum allowable discounted payback period is four and a half years, the project should be rejected based on this criterion.

Suppose Your Firm Is Considering Investing in a Project with the Cash