ZumBahlen Inc.is considering the following mutually exclusive projects: $\begin{array}{lrr}
\text { Year } & \begin{array}{r}
\text { Project A } \
\text { Cash Flow }
\end{array} & \begin{array}{r}
\text { Project B } \
\text { Cash Flow }
\end{array} \
\hline 0 & -\$ 5,000 & -\$ 5,000 \
1 & 200 & 3,000 \
2 & 800 & 3,000 \
3 & 3,000 & 800 \
4 & 5,000 & 200
\end{array}$ At what cost of capital will the NPV of the two projects be the same? (That is,what is the "crossover" rate?)
A)16.15%
B)16.74%
C)17.33%
D)17.80%

Question

ZumBahlen Inc.is considering the following mutually exclusive projects:​​​ $\begin{array}{lrr}
\text { Year } & \begin{array}{r}
\text { Project A } \
\text { Cash Flow }
\end{array} & \begin{array}{r}
\text { Project B } \
\text { Cash Flow }
\end{array} \
\hline 0 & -\$ 5,000 & -\$ 5,000 \
1 & 200 & 3,000 \
2 & 800 & 3,000 \
3 & 3,000 & 800 \
4 & 5,000 & 200
\end{array}$ ​At what cost of capital will the NPV of the two projects be the same? (That is,what is the "crossover" rate?)
A)16.15%
B)16.74%
C)17.33%
D)17.80%

Quizplus · Accepted Answer

The crossover rate is the cost of capital at which the NPV of two projects is the same. To find the crossover rate, we can use the following formula:Crossover rate = (PV of Project A - PV of Project B) / (Initial investment of Project A - Initial investment of Project B)In this case, the initial investment of both projects is $5,000. The PV of Project A can be calculated as follows:PV of Project A = -5,000 + 200/(1+r) + 800/(1+r)^2 + 3,000/(1+r)^3 + 5,000/(1+r)^4The PV of Project B can be calculated as follows:PV of Project B = -5,000 + 3,000/(1+r) + 3,000/(1+r)^2 + 800/(1+r)^3 + 200/(1+r)^4Setting the PV of Project A equal to the PV of Project B and solving for r, we get:-5,000 + 200/(1+r) + 800/(1+r)^2 + 3,000/(1+r)^3 + 5,000/(1+r)^4 = -5,000 + 3,000/(1+r) + 3,000/(1+r)^2 + 800/(1+r)^3 + 200/(1+r)^4200/(1+r) - 3,000/(1+r) + 800/(1+r)^2 - 3,000/(1+r)^2 + 5,000/(1+r)^4 - 200/(1+r)^4 = 0200/(1+r) - 2,200/(1+r) + 500/(1+r)^2 + 4,800/(1+r)^4 = 0(200 - 2,200r + 500r^2 + 4,800r^4)/(1+r)^4 = 0200 - 2,200r + 500r^2 + 4,800r^4 = 0Using a financial calculator, we can solve for r and get the crossover rate of 16.15%.

ZumBahlen Inc ​At What Cost of Capital Will the NPV of the Year

ZumBahlen Inc At What Cost of Capital Will the NPV of the Year