Compute the discounted payback statistic for Project X and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 10 percent and the maximum allowable discounted payback is three years.
$$\begin{array}{l}
\begin{array} {| l | l | l | l | l | l | l |}
\hline\text {Time: }&0&1&2&3&4&5\
\hline\text {Cash flow:}&-1,000&500&480&400&300&150\\hline
\end{array}
\end{array}$$
A) 2.49 years, accept
B) 2.98 years, accept
C) 3.49 years, reject
D) 4.98 years, reject

Question

Compute the discounted payback statistic for Project X and recommend whether the firm should accept or reject the project with the cash flows shown as follows if the appropriate cost of capital is 10 percent and the maximum allowable discounted payback is three years.
$$\begin{array}{l}
\begin{array} {| l | l | l | l | l |  l |  l |}
\hline\text {Time: }&0&1&2&3&4&5\
\hline\text {Cash flow:}&-1,000&500&480&400&300&150\\hline
\end{array}
\end{array}$$
A) 2.49 years, accept
B) 2.98 years, accept
C) 3.49 years, reject
D) 4.98 years, reject

Quizplus · Accepted Answer

To calculate the discounted payback period, we first need to discount each of the cash flows back to their present value using the formula $\frac{CF}{(1+r)^t}$, where $CF$ is the cash flow at time $t$, and $r$ is the discount rate (10% or 0.10 in this case). - At time 0, the cash flow is -1,000 (already in present value).- At time 1, the cash flow is $500 / (1 + 0.10)^1 = 454.55$.- At time 2, the cash flow is $480 / (1 + 0.10)^2 = 397.52$.- At time 3, the cash flow is $400 / (1 + 0.10)^3 = 300.66$.- At time 4, the cash flow is $300 / (1 + 0.10)^4 = 204.58$.- At time 5, the cash flow is $150 / (1 + 0.10)^5 = 93.17$.Now, we sum these discounted cash flows year by year until the initial investment is recovered:- End of Year 1: -1,000 + 454.55 = -545.45- End of Year 2: -545.45 + 397.52 = -147.93- End of Year 3: -147.93 + 300.66 = 152.73The initial investment is fully recovered between Year 2 and Year 3. To find the exact time, we interpolate between these two years. Since we recover the investment in less than 3 years, the project meets the maximum allowable discounted payback period of 3 years. Therefore, the project should be accepted.

Compute the Discounted Payback Statistic for Project X and Recommend