A firm is considering Projects S and L,whose cash flows are shown below.These projects are mutually exclusive,equally risky,and not repeatable.The CEO wants to use the IRR criterion,while the CFO favours the NPV method,and you were hired to advise the firm on the best procedure.If the CEO's preferred criterion is used,how much value will the firm lose as a result of this decision? $\begin{array}{ccccc}
\text { WACC: } & 13.00 \% \
&0 & 1 & 2 & 3 & 4 \
\hline \mathrm{CFS}_{\mathrm{S}} &-\$ 1,025 & \$ 375 & \$ 380 & \$ 385 & \$ 390 \
\mathrm{CF}_{\mathrm{L}} &-\$ 2,150 & \$ 750 & \$ 759 & \$ 768 & \$ 777
\end{array}$
A)$5.83
B)$6.14
C)$6.46
D)$6.79

Question

Quizplus · Accepted Answer

To determine the value the firm will lose by choosing based on the IRR instead of the NPV, we first calculate the NPV of both projects using the given WACC of 13% as the discount rate. The NPV formula is $\text{NPV} = \sum \frac{CF_t}{(1 + r)^t}$, where $CF_t$ is the cash flow at time $t$, and $r$ is the discount rate.For Project S:$$\text{NPV}_S = -1025 + \frac{375}{(1+0.13)^1} + \frac{380}{(1+0.13)^2} + \frac{385}{(1+0.13)^3} + \frac{390}{(1+0.13)^4}$$$$\text{NPV}_S = -1025 + 331.86 + 298.14 + 266.43 + 237.17 = \$108.60$$For Project L:$$\text{NPV}_L = -2150 + \frac{750}{(1+0.13)^1} + \frac{759}{(1+0.13)^2} + \frac{768}{(1+0.13)^3} + \frac{777}{(1+0.13)^4}$$$$\text{NPV}_L = -2150 + 663.72 + 596.28 + 532.63 + 472.76 = \$115.39$$The difference in NPV between Project L and Project S, which represents the value lost if the firm chooses based on the IRR instead of the NPV, is:$$\text{Value Lost} = \text{NPV}_L - \text{NPV}_S = 115.39 - 108.60 = \$6.79$$Therefore, the firm will lose $6.79 in value by choosing based on the IRR criterion instead of the NPV method.

A Firm Is Considering Projects S and L,whose Cash Flows