Farmer Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the shorter payback, some value may be forgone. How much value will be lost in this instance? Note that under some conditions choosing projects on the basis of the shorter payback will not cause value to be lost. $\begin{array} { c c c c c r }
& r = 10.25 \% \
\text { Year } &0& 1 & 2 & 3 & 4 \
\text { CFS } & - \$ 950 & \$ 500 & \$ 800 & \$ 0 & \$ 800
\end{array}$

Question

Farmer Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the shorter payback, some value may be forgone. How much value will be lost in this instance? Note that under some conditions choosing projects on the basis of the shorter payback will not cause value to be lost. $\begin{array} { c c c c c r } 
& r = 10.25 \% \
\text { Year } &0& 1 & 2 & 3 & 4 \
\text { CFS } & - \$ 950 & \$ 500 & \$ 800 & \$ 0 & \$ 800
\end{array}$

Quizplus · Accepted Answer

$\begin{array}{lccccc}
\text { Wear } & 10.250 \% \
\text { Year }&0& 1 & 2 & 3 & 4 \
 \mathrm{CF}_{\mathrm{S}} & -\$ 950 & \$ 500 & \$ 800 & \$ 0 & \$ 0 \
\mathrm{CF} \mathrm{L} & -\$ 2,100 & \$ 400 & \$ 800 & \$ 800 & \$ 1,000 \
\text { Cumulative CF} & -\$ 950 & -\$ 450 & \$ 350 & \$ 350 & \$ 350 \
\text { Cumulative } \mathrm{CF}_{\mathrm{S}} & -\$ 2,100 & -\$ 1,700 & -\$ 900 & -\$ 100 & \$ 900 \
\Delta & -\$ 1,150 & -\$ 100 & \$ 0 & \$ 800 & \$ 1,000
\end{array}$ 
 $\text { Crossover rate }=11.093 \% \quad \text { At interest rates }<\text { crossover rate, conflict exists. }$ 
 $\begin{array}{lccc}
\text { Payback }_{\mathrm{S}}=1.56  & -& - &1.56&- \
 \text { Payback }_{\mathrm{L}}=3.10 & -&-&-&3.10
\end{array}$
 
 $\begin{array} { l l } 
\mathrm { NP } _ { \mathrm { L } } = & \$ 194.79 \
\mathrm { NP } _ { \mathrm { S } } = & \$ 161.68 \
\mathrm { Value } _ { \text {lost } } & \$ 33.11
\end{array}$ 
Note that the WACC is not constrained to be less than the crossover rate. So, there may not be a conflict between NPV and payback; hence following the IRR rule may not result in a loss of value, so the correct answer may be $0.00.

Farmer Co Is Considering Projects S and L, Whose Cash Flows