Projects S and L, whose cash flows are shown below, are mutually exclusive, equally risky, and not repeatable. Hooper Inc. is considering which of these two projects to undertake. If the decision is made by choosing the project with the higher IRR, how much value will be forgoneσ Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the project with the higher IRR will also have the higher NPV, so no value will be lost if the IRR method is used.
$\begin{array}{cccccr}
{r}{: 10.25 \%} & & & & \
\text { Year } & 0 & 1 & 2 & 3 & 4 \
\hline\mathrm{CF}_{\mathrm{S}} & -\$ 2,050 & \$ 750 & \$ 760 & \$ 770 & \$ 780 \
\mathrm{CF}_{\mathrm{L}} & -\$ 4,300 & \$ 1,500 & \$ 1,518 & \$ 1,536 & \$ 1,554
\end{array}$

Question

Projects S and L, whose cash flows are shown below, are mutually exclusive, equally risky, and not repeatable. Hooper Inc. is considering which of these two projects to undertake. If the decision is made by choosing the project with the higher IRR, how much value will be forgoneσ Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the project with the higher IRR will also have the higher NPV, so no value will be lost if the IRR method is used.
 $\begin{array}{cccccr}
{r}{: 10.25 \%} & & & & \
\text { Year } & 0 & 1 & 2 & 3 & 4 \
\hline\mathrm{CF}_{\mathrm{S}} & -\$ 2,050 & \$ 750 & \$ 760 & \$ 770 & \$ 780 \
\mathrm{CF}_{\mathrm{L}} & -\$ 4,300 & \$ 1,500 & \$ 1,518 & \$ 1,536 & \$ 1,554
\end{array}$

Quizplus · Accepted Answer

$\begin{array}{lccccc}
\text { YACC: } & 10.25 \% & & & & \
\text { Year } & 0 & 1 & 2 & 3 & 4 \
\hline\mathrm{CF}_{\mathrm{S}} & -\$ 2,050 & \$ 750 & \$ 760 & \$ 770 & \$ 780 \
\mathrm{CF}_{\mathrm{L}} & -\$ 4,300 & \$ 1,500 & \$ 1,518 & \$ 1,536 & \$ 1,554 \
\Delta & -\$ 2,250 & \$ 750 & \$ 758 & \$ 766 & \$ 774
\end{array}$ 
 $\text { Crossover rate }=13.275 \% \quad \text { At interest rates }<\text { crossover rate, conflict exists. }$ 
 $\begin{array} { l l } 
\mathrm { IRR } _ { \mathrm { L } } & 15.58 \% \
\mathrm { IRR } _ { \mathbf { S } } & 18.06 \% \
\
\mathrm { NPV } _ { \mathrm { L } } & \$ 507.40 \
\mathrm { NPV } _ { \mathbf { S } } & \$ 358.05 \
& \$ 149.36 = \text { Value lost if use the } \mathrm { IRR } \text { criterior }
\end{array}$ 
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.

Projects S and L, Whose Cash Flows Are Shown Below