Carolina Company is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and are not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the IRR will cause $0.00 value to be lost. $\begin{array} { c c c c c c }
r : 7.75 \% & & & & \
\text { Year } & { 0} & 1 & 2 & 3 & 4 \
\mathrm{CF}_{\mathrm{S}}& - \$ 1,050 & \$ 675 & \$ 650 & & \
\mathrm { CF } _ { \mathrm { L } } & - \$ 1,050 & \$ 360 & \$ 360 & \$ 360 & 360
\end{array}$

Question

Carolina Company is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and are not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the IRR will cause $0.00 value to be lost. $\begin{array} { c c c c c c } 
r : 7.75 \% & & & &  \
\text { Year } & { 0} & 1 & 2 & 3 & 4 \
\mathrm{CF}_{\mathrm{S}}& - \$ 1,050 & \$ 675 & \$ 650 & & \
\mathrm { CF } _ { \mathrm { L } } & - \$ 1,050 & \$ 360 & \$ 360 & \$ 360 & 360
\end{array}$

Quizplus · Accepted Answer

$\begin{array}{ccccc}
WACC:&7.75 \% \
Year&0& 1 & 2 & 3 & 4 \
\hline- \mathrm{CF}_{\mathrm{S}} &\$ 1,050 & \$ 675 & \$ 650 & & \
 \mathrm{CF}_{\mathrm{L}}&-\$ 1,050 & \$ 360 & \$ 360 & \$ 360 & \$ 360 \
 \Delta &\$ 0 & -\$ 315 & -\$ 290 & \$ 360 & \$ 360
\end{array}$ 
 $\text { Crossover rate }=8.994 \% \quad \text { At interest rates }<\text { crossover rate, conflict exists. }$ 
 $\begin{array} { l l } 
\mathrm { IRR } _ { \mathrm { L } } & 13.95 \% \
\mathrm { IRR } _ { \mathbf { S } } & 17.13 \% \
\mathrm { NPV } _ { \mathrm { L } } & \$ 149.03 \
\mathrm { NPV } _ { \mathbf { S } } & \$ 136.31  \
&{ \$ 12.72 } = \text { Value lost if use the } \mathrm { IRR } \text { criterior }
\end{array}$ 
Note that the WACC is not constrained to be less than the crossover rate. So, there may not be a conflict between NPV and IRR; hence, following the IRR rule may not result in a loss of value. In that case, the correct answer is $0.00.

Carolina Company Is Considering Projects S and L, Whose Cash