Langton Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the MIRR. If the decision is made by choosing the project with the higher IRR rather than the one with the higher MIRR, how much, if any, value will be forgone. In other words, what's the NPV of the chosen project versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. MIRR will have no effect on the value lost. $\begin{array} { c c c c c c }
&r = 700 \% \
\text { Year } & 0& 1 & 2 & 3 & 4 \
\text { CF }_{S} & - \$ 1,100 & \$ 550 & \$ 600 & \$ 100 & \$ 100 \
\text { CF}_{L} & - \$ 2,750 & \$ 725 & \$ 725 & \$ 800 & \$ 1,400
\end{array}$

Question

Langton Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. The CEO believes the IRR is the best selection criterion, while the CFO advocates the MIRR. If the decision is made by choosing the project with the higher IRR rather than the one with the higher MIRR, how much, if any, value will be forgone. In other words, what's the NPV of the chosen project versus the maximum possible NPV? Note that (1) "true value" is measured by NPV, and (2) under some conditions the choice of IRR vs. MIRR will have no effect on the value lost. $\begin{array} { c c c c c c } 
&r = 700 \% \
\text { Year } & 0& 1 & 2 & 3 & 4 \
 \text { CF }_{S} & - \$ 1,100 & \$ 550 & \$ 600 & \$ 100 & \$ 100 \
\text { CF}_{L} & - \$ 2,750 & \$ 725 & \$ 725 & \$ 800 & \$ 1,400
\end{array}$

Quizplus · Accepted Answer

First, recognize that NPV makes theoretically correct capital budgeting decisions, so the higher NPV tells us how much value could be added. We calculate the two projects' NPVs, IRRs, and MIRRs. We then see what NPV would result if the decision were based on the IRR and the MIRR. Under some conditions, MIRR will choose the project with the higher NPV while the IRR chooses the lower NPV project. Then, the difference between the NPVs is the loss incurred if the IRR criterion is used. Of course, it's possible that both the MIRR and the IRR could choose the wrong project; with this set of cash flows, that happens at 8.62133% < WACC < 10.53093%.
 $\begin{array}{lccccccc}
\text { WACC: } & 7.00 \% & & & & & \
\text { Year } & 0 & 1 & 2 & 3 & 4 & \text { TV } & \text { IRR/MIRR } \
 \text { CF }_{\text {S }} & -\$ 1,100 & \$ 550 & \$ 600 & \$ 100 & \$ 100 && 12.2416 \% \
\text { Compounded CF s: } & 673.77 & 686.94 & 107.00 & 100.00 & \$ 1,567.71 & 9.2618 \% \
 \text { CF }_{\text {L}}& -\$ 2,750 & \$ 725 & \$ 725 & \$ 800 & \$ 1,400 & &10.9810 \% \
\text { Compounded CFs: }  & 888.16 & 830.05 & 856.00 & 1,400.00 & \$ 3,974.21 & 9.6426 \%\
\Delta&-\$ 1.650 & \$ 175 & \$ 125 & \$ 700 & \$ 1.300
\end{array}$ 
 $\text { Crossover rate }=10.53093 \% \text { At interestrates }<\text { crossover rate, conflict exists between }$
 $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $ $ \quad $  $ \quad $  $ \quad $  $ \quad $ $\text { IRR and NPV }$
 
 $ \begin{array}{ll}
\operatorname{MIRR}_{S}= & 9.2618 \% R_{S}= &12.2416 \% \mathrm{dPV}_{\mathrm{S}}=& \$96.00\ \operatorname{MIRR}_{\mathrm{L}}= & 9.6426 \% \mathrm{IR}_{\mathrm{L}}=&10.9810 \% \mathrm{NPV}_{\mathrm{L}}= &\$281.90\
\text { MIRR Choice:} & \text { LIRR Choice:}& \text { SNPV Choice: } & L\
\text { NPV based on }& \text { NPV based on}&\text { NPV using } &\
\text { MIRR.} & \$ 281.90 \text { OIRR.}&\$ 9600 \mathrm{NPV} .&\$281.90
\end{array} $
 
Lost value using IRR versus MIRR: NPVL σ NPVS = $185.90

Langton Inc A) $18590 B) $197

Langton Inc A) $18590
B) $197