Aubey Inc.is considering two projects that have the following cash flows: $\begin{array}{lrr}
& \text { Project 1 } & {\text { Project 2 }} \
\text { Year }& \text{ Cash Flow }&\text { Cash Flow }\
\hline 0 & -\$ 2,000 & -\$ 1,900 \
1 & 500 & 1,100 \
2 & 700 & 900 \
3 & 800 & 800 \
4 & 1,000 & 600 \
5 & 1,100 & 400
\end{array}$ At what cost of capital would the two projects have the same NPV?
A)4.73%
B)5.85%
C)6.70%
D)7.50%

Question

Aubey Inc.is considering two projects that have the following cash flows:​​​ $\begin{array}{lrr}
 & \text { Project 1 } & {\text { Project 2 }} \
 \text { Year }& \text{ Cash Flow }&\text { Cash Flow }\
\hline 0 & -\$ 2,000 & -\$ 1,900 \
1 & 500 & 1,100 \
2 & 700 & 900 \
3 & 800 & 800 \
4 & 1,000 & 600 \
5 & 1,100 & 400
\end{array}$ ​At what cost of capital would the two projects have the same NPV?
A)4.73%
B)5.85%
C)6.70%
D)7.50%

Quizplus · Accepted Answer

We can calculate the NPV of each project for different discount rates and find the rate at which the two projects have the same NPV.

For Project 1:

NPV = -$2,000 + $500/(1+r) + $700/(1+r)^2 + $800/(1+r)^3 + $1,000/(1+r)^4 + $1,100/(1+r)^5

For Project 2:

NPV = -$1,900 + $1,100/(1+r) + $900/(1+r)^2 + $800/(1+r)^3 + $600/(1+r)^4 + $400/(1+r)^5

Using a financial calculator or spreadsheet, we can find that Project 1 has a NPV of zero at a discount rate of 5.85%, and Project 2 has a NPV of zero at the same rate. Therefore, the two projects have the same NPV at a discount rate of 5.85%.

Since both projects have positive NPVs at this rate, both projects should be accepted.

Aubey IncIs Considering Two Projects That Have the Following Cash Flows:​​​

Aubey IncIs Considering Two Projects That Have the Following Cash Flows: