Current Design Co. is considering two mutually exclusive, equally risky, and not repeatable projects, S and L. Their cash flows are shown below. The CEO believes the IRR is the best selection criterion, while the CFO advocates the NPV. If the decision is made by choosing the project with the higher IRR rather than the one with the higher NPV, how much, if any, value will be forgone, i.e., what's the chosen NPV versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. NPV will have no effect on the value gained or lost. $\begin{array}{cccccr}
r& 7.50 \% & & & \
\text { Year } & 0 & 1 & 2 & 3 & 4 \
\mathrm{CF}_{\mathrm{S}} & -\$ 1,100 & \$ 550 & \$ 600 & \$ 100 & \$ 100 \
\mathrm{CF}_{\mathrm{L}} & -\$ 2,700 & \$ 650 & \$ 725 & \$ 800 & \$ 1,400
\end{array}$

Question

Quizplus · Accepted Answer

First, recognize that NPV makes theoretically correct capital budgeting decisions, so the highest NPV tells us how much value could be added. We calculate the two projects' NPVs, IRRs, and MIRRs, but the MIRR information is not needed for this problem. We then see what NPV would result if the decision were based on the IRR (and the MIRR). The difference between the NPVs is the loss incurred if the IRR criterion is used. Of course, it's possible that IRR could choose the correct project.
 
$\begin{array}{lccccc}
WACC&7.5000 \%\
\text { Year } & 0 & 1 & 2 & 3 & 4 & \quad TV\quad \quad \quad MIRR \
\hline \mathrm{CF}_{\mathrm{S}} & -\$ 1,100 & \$ 550 & \$ 600 & \$ 100 & \$ 100 \
\text { Compounded CFs: } & 683.26 & 693.38 & 107.50 & 100.00 & \$ 1,584.14 &9.5469\%\
\mathrm{CF}_{\mathrm{L}} & -\$ 2,700 & \$ 650 & \$ 725 & \$ 800 & \$ 1,400 \
\text { Compounded CFs: } & 807.49 & 837.83 & 860.00 & 1,400.00 & \$ 3,905.32 &9.6663\%\
\Delta & -\$ 1,600 & \$ 100 & \$ 125 & \$ 700 & \$ 1,300
\end{array}$ 
 $\text { Crossover rate }=10.16 \% \quad   \quad  \quad\text { At interest rates }<\text { crossover rate, conflict exists. }$ 
 $\begin{array}{llll}
\operatorname{MIRR}_{\mathrm{L}}= & 9.67 \% \mathrm{IR}_{\mathrm{L}}= & 10.71181 \% \mathrm{NPV}_{\mathrm{L}}= & \$ 224.3065 \
\operatorname{MIR}_{\mathrm{S}}= & 9.55 \% \mathrm{MR}_{\mathrm{S}}= & 12.24157 \% \mathrm{NPV}_{\mathrm{S}}= & \$ 86.2036\
\text { MIRR Choice: }&\text {LIRR Choice: }&\text { SNPV Choice:}&\text {L }\
\text {NPV using MIRR:  }&\text {\$ 224.31 NPV using IRR:  }&\text {\$ 86.20NPV using NPV: }&\text {(\$ 224.31 }\
\end{array}$ 
 
$\begin{array}{llll}
\text { Lost value using IRR versus MIRR:}&\$ 138.10 \
\text { Lost value using MIRR versus NPV:}& \$ 0.00\
\text { Lost value using IRR versus NPV: }&\$ 138.10
\end{array}$

Current Design Co A) $13810 B) $149

Current Design Co A) $13810
B) $149