The Bull Company, a lawn mower manufacturer, is considering the introduction of a new model. The initial outlay required is $22 million. Net cash flows over the 4-year life cycle and the corresponding certainty-equivalents of the new model are as follows: $$\begin{array} { l l l }
\text { Year } & \text { Net Cash Flow } & \text { Certainty-equival ent } \
1 & \$ 15 \text { million } & 0.90 \
2 & 13 \text { million } & 0.75 \
3 & 11 \text { million } & 0.55 \
4 & 9 \text { million } & 0.30
\end{array}$$ ? The firm's cost of capital is 14%, and the risk-free rate is 6%. Bull uses the certainty-equivalent approach in evaluating above-average risk investments such as this one. What is the project's certainty-equivalent NPV?

Question

The Bull Company, a lawn mower manufacturer, is considering the introduction of a new model. The initial outlay required is $22 million. Net cash flows over the 4-year life cycle and the corresponding certainty-equivalents of the new model are as follows: $$\begin{array} { l l l } 
\text { Year } & \text { Net Cash Flow } & \text { Certainty-equival ent } \
1 & \$ 15 \text { million } & 0.90 \
2 & 13 \text { million } & 0.75 \
3 & 11 \text { million } & 0.55 \
4 & 9 \text { million } & 0.30
\end{array}$$ ? The firm's cost of capital is 14%, and the risk-free rate is 6%. Bull uses the certainty-equivalent approach in evaluating above-average risk investments such as this one. What is the project's certainty-equivalent NPV?

Quizplus · Accepted Answer

The certainty-equivalent NPV (CENPV) is calculated by discounting the certainty-equivalent cash flows at the risk-free rate, rather than discounting expected cash flows at the risk-adjusted discount rate. The formula for CENPV is: $$CENPV = \sum_{t=0}^{n} \frac{CE_t}{(1+r_f)^t} - I_0$$ where $CE_t$ is the certainty-equivalent cash flow in year $t$, $r_f$ is the risk-free rate, and $I_0$ is the initial investment.Given data:- Initial investment ($I_0$) = $22 million- Risk-free rate ($r_f$) = 6% or 0.06Calculating the certainty-equivalent cash flows:- Year 1: $15 million * 0.90 = $13.5 million- Year 2: $13 million * 0.75 = $9.75 million- Year 3: $11 million * 0.55 = $6.05 million- Year 4: $9 million * 0.30 = $2.7 millionDiscounting these cash flows at the risk-free rate:- Year 1: $13.5 million / (1 + 0.06)^1 = $12.7358 million- Year 2: $9.75 million / (1 + 0.06)^2 = $8.6906 million- Year 3: $6.05 million / (1 + 0.06)^3 = $5.0738 million- Year 4: $2.7 million / (1 + 0.06)^4 = $2.1282 millionSumming the discounted cash flows and subtracting the initial investment:$$CENPV = 12.7358 + 8.6906 + 5.0738 + 2.1282 - 22 = \$6.6284 \text{ million}$$

The Bull Company, a Lawn Mower Manufacturer, Is Considering the Introduction