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 8 percent, and that the maximum allowable payback and discounted payback statistic for the project are three and three and a half years, respectively.
$$\begin{array} { | l | c | c | c | c | c | c | }
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 100,000 & 30,000 & 45,000 & 55,000 & 30,000 & 10,000 \
\hline
\end{array}$$
Use the NPV decision rule to evaluate this project; should it be accepted or rejected?
A) $35,995.86, reject
B) $38,875.53, accept
C) $138,875.53, accept
D) $238,875.53, accept

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 8 percent, and that the maximum allowable payback and discounted payback statistic for the project are three and three and a half years, respectively.
$$\begin{array} { | l | c | c | c | c | c | c | } 
\hline \text { Time } & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \text { Cash Flow } & - 100,000 & 30,000 & 45,000 & 55,000 & 30,000 & 10,000 \
\hline
\end{array}$$
Use the NPV decision rule to evaluate this project; should it be accepted or rejected?
A) $35,995.86, reject
B) $38,875.53, accept
C) $138,875.53, accept
D) $238,875.53, accept

Quizplus · Accepted Answer

To calculate the NPV (Net Present Value) of the project, we discount each of the project's cash flows back to present value using the required rate of return (8%) and then sum these values. The formula for NPV is:$$ NPV = \sum \frac{CF_t}{(1 + r)^t} $$where $CF_t$ is the cash flow at time $t$, and $r$ is the discount rate (8% or 0.08 in this case).Calculating for each year:- Year 0: $ \frac{-100,000}{(1 + 0.08)^0} = -100,000 $- Year 1: $ \frac{30,000}{(1 + 0.08)^1} = 27,777.78 $- Year 2: $ \frac{45,000}{(1 + 0.08)^2} = 38,580.25 $- Year 3: $ \frac{55,000}{(1 + 0.08)^3} = 43,507.36 $- Year 4: $ \frac{30,000}{(1 + 0.08)^4} = 22,306.78 $- Year 5: $ \frac{10,000}{(1 + 0.08)^5} = 6,805.23 $Summing these values gives the NPV:$$ NPV = -100,000 + 27,777.78 + 38,580.25 + 43,507.36 + 22,306.78 + 6,805.23 = 38,875.53 $$Since the NPV is positive, the project should be accepted according to the NPV decision rule.

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