Billy Bob is considering building a water slide park that will require a net investment of $200,000 and yield the following net cash flows: $$\begin{array} { l l l }
\text { Year } & \text { Net Cash Flows } & \text { Cert. Equiv. Factor } \
1 & \$ 120,000 & 0.90 \
2 & \$ 90,000 & 0.80 \
3 & \$ 60,000 & 0.65 \
4 & \$ 30,000 & 0.50 \
5 & \$ 10,000 & 0.30
\end{array}$$ ? If the risk-free rate is 8 percent and the market risk premium is 6 percent, what is the certainty equivalent NPV for this project?
A) $12,805
B) $5,746
C) $3,703
D) $11,025

Question

Billy Bob is considering building a water slide park that will require a net investment of $200,000 and yield the following net cash flows: $$\begin{array} { l l l } 
\text { Year } & \text { Net Cash Flows } & \text { Cert. Equiv. Factor } \
1 & \$ 120,000 & 0.90 \
2 & \$ 90,000 & 0.80 \
3 & \$ 60,000 & 0.65 \
4 & \$ 30,000 & 0.50 \
5 & \$ 10,000 & 0.30
\end{array}$$ ? If the risk-free rate is 8 percent and the market risk premium is 6 percent, what is the certainty equivalent NPV for this project?
A) $12,805
B) $5,746
C) $3,703
D) $11,025

Quizplus · Accepted Answer

To calculate the certainty equivalent NPV (CENPV), we first need to find the present value (PV) of each year's net cash flow using the certainty equivalent factors provided. Then, we subtract the initial investment from the sum of these PVs.The formula for the present value of each year's cash flow is: $$PV = \text{Net Cash Flow} \times \text{Certainty Equivalent Factor} \div (1 + \text{Risk-Free Rate})^{\text{Year}}$$For Year 1: $$PV_1 = \$120,000 \times 0.90 \div (1 + 0.08)^1 = \$100,000 \times 0.9259 = \$92,590$$For Year 2: $$PV_2 = \$90,000 \times 0.80 \div (1 + 0.08)^2 = \$72,000 \times 0.8573 = \$61,725.6$$For Year 3: $$PV_3 = \$60,000 \times 0.65 \div (1 + 0.08)^3 = \$39,000 \times 0.7938 = \$30,958.2$$For Year 4: $$PV_4 = \$30,000 \times 0.50 \div (1 + 0.08)^4 = \$15,000 \times 0.7350 = \$11,025$$For Year 5: $$PV_5 = \$10,000 \times 0.30 \div (1 + 0.08)^5 = \$3,000 \times 0.6806 = \$2,041.8$$Summing these PVs: $$CENPV = \$92,590 + \$61,725.6 + \$30,958.2 + \$11,025 + \$2,041.8 - \$200,000 = \$5,746.6$$Therefore, the certainty equivalent NPV for this project is approximately $5,746.

Billy Bob Is Considering Building a Water Slide Park That