Given the following cash flows and certainty equivalent factors for an investment project, determine the certainty equivalent net present value. The firm's cost of capital is 14% and the risk-free rate is 6%. $$\begin{array} { l l l }
& \text { Cash } & \text { Certainty-Equivalent } \
\text { Year } & \text { Flow } & \text { Factor } \
0 & - \$ 100,000 & 1.00 \
1 & \$ 60,000 & 0.90 \
2 & \$ 60,000 & 0.75 \
3 & \$ 60,000 & 0.55
\end{array}$$
A) $32,000
B) $18,692
C) $4,238
D) Cannot be determined

Question

Given the following cash flows and certainty equivalent factors for an investment project, determine the certainty equivalent net present value. The firm's cost of capital is 14% and the risk-free rate is 6%. $$\begin{array} { l l l } 
& \text { Cash } & \text { Certainty-Equivalent } \
\text { Year } & \text { Flow } & \text { Factor } \
0 & - \$ 100,000 & 1.00 \
1 & \$ 60,000 & 0.90 \
2 & \$ 60,000 & 0.75 \
3 & \$ 60,000 & 0.55
\end{array}$$
A) $32,000
B) $18,692
C) $4,238
D) Cannot be determined

Quizplus · Accepted Answer

To calculate the certainty equivalent net present value (NPV), we first adjust each cash flow by its certainty equivalent factor to reflect the risk, then discount these adjusted cash flows back to present value using the risk-free rate (since the risk has already been accounted for by adjusting the cash flows). The calculation is as follows:Year 0: $-\$100,000 \times 1.00 = -\$100,000$Year 1: $\$60,000 \times 0.90 = \$54,000$Year 2: $\$60,000 \times 0.75 = \$45,000$Year 3: $\$60,000 \times 0.55 = \$33,000$Now, discount these adjusted cash flows back to present value using the risk-free rate of 6%:Year 0: $-\$100,000 / (1+0.06)^0 = -\$100,000$Year 1: $\$54,000 / (1+0.06)^1 = \$50,943.40$Year 2: $\$45,000 / (1+0.06)^2 = \$40,066.04$Year 3: $\$33,000 / (1+0.06)^3 = \$27,682.76$Adding these values together gives the certainty equivalent NPV:$-\$100,000 + \$50,943.40 + \$40,066.04 + \$27,682.76 = \$18,692.20$

Given the Following Cash Flows and Certainty Equivalent Factors for an Investment