Van Auken Inc.is considering a project that has the following cash flows:The company's WACC is 10%.What are the project's payback,IRR,and NPV?
$\begin{array}{ll}
\underline {\text { Year } }& \underline {\text { Cash Flow } }\
0 & -\$ 1,000 \
1 & \$ 400 \
2 & \$ 300 \
3 & \$ 500 \
4 & \$ 400
\end{array}$
A)payback = 2.4, IRR = 10.00%, NPV = $600
B)payback = 2.4, IRR = 21.22%, NPV = $260
C)payback = 2.6, IRR = 21.22%, NPV = $300
D)payback = 2.6, IRR = 21.22%, NPV = $260

Question

Van Auken Inc.is considering a project that has the following cash flows:The company's WACC is 10%.What are the project's payback,IRR,and NPV? 
$\begin{array}{ll}
 \underline {\text { Year } }& \underline {\text { Cash Flow } }\
0 & -\$ 1,000 \
1 & \$ 400 \
2 & \$ 300 \
3 & \$ 500 \
4 & \$ 400
\end{array}$
A)payback = 2.4, IRR = 10.00%, NPV = $600
B)payback = 2.4, IRR = 21.22%, NPV = $260
C)payback = 2.6, IRR = 21.22%, NPV = $300
D)payback = 2.6, IRR = 21.22%, NPV = $260

Quizplus · Accepted Answer

To calculate the payback period, we need to accumulate the cash flows until we have recovered the initial investment:

Year 0: -1000
Year 1: -1000 + 400 = -600
Year 2: -600 + 300 = -300
Year 3: -300 + 500 = 200
Year 4: 200 + 400 = 600

Therefore, the payback period is between Year 3 and Year 4, and we need to interpolate to find the exact payback period:

Payback period = 3 + (100 - 200) / 500 = 2.6 years

To calculate the IRR, we can use Excel or a financial calculator. The IRR is the discount rate that makes the NPV equal to zero. In this case, we get an IRR of approximately 21.22%.

To calculate the NPV, we use the formula:

NPV = -1000 + 400 / (1 + 0.1)^1 + 300 / (1 + 0.1)^2 + 500 / (1 + 0.1)^3 + 400 / (1 + 0.1)^4

NPV = $260

Since the NPV is positive, the project is expected to generate a return higher than the required rate of return (WACC), and therefore it is acceptable. Among the answer choices, the only one that matches the calculated values is D.

Van Auken Inc A)payback = 2