The following data pertain to an investment proposal: $\begin{array} { l r }
\text { Cost of the Investment } & \$ 20,000 \
\text { Annual Cost Savings } & \$ 5,000 \
\text { Estimated Salvage Value } & \$ 1,000 \
\text { Life of the Project } & 8 \text { years } \
\text { Discount Rate } & 16 \%
\end{array}$ What is the net present value of the proposed investment? (Ignore income taxes in this problem.)

Question

The following data pertain to an investment proposal: $\begin{array} { l r } 
\text { Cost of the Investment } & \$ 20,000 \
\text { Annual Cost Savings } & \$ 5,000 \
\text { Estimated Salvage Value } & \$ 1,000 \
\text { Life of the Project } & 8 \text { years } \
\text { Discount Rate } & 16 \%
\end{array}$ What is the net present value of the proposed investment? (Ignore income taxes in this problem.)

Quizplus · Accepted Answer

Net Present Value (NPV) can be calculated as follows:
NPV = -(Cost of Investment) + PV of Annual Cost Savings + PV of Salvage Value

PV of Annual Cost Savings can be found using the formula:
PV = CF / (1+r)^n
where CF = Annual Cost Savings, r = Discount Rate, n = Number of years
Hence PV of Annual Cost Savings = 5000/(1+0.16)^1 + 5000/(1+0.16)^2 + .... +5000/(1+0.16)^8
= 5000 * [1/(1.16)^1 + 1/(1.16)^2 + .... + 1/(1.16)^8]
= 5000 * 4.6009 = 23,004.50

PV of Salvage Value = 1000/(1+0.16)^8 = 322.07

Hence NPV = -20,000 + 23,004.50 + 322.07 = $2,326.57

Since NPV is positive, the investment proposal should be accepted. The best choice is  B ($2,025) as it is closest to our calculated NPV.

The Following Data Pertain to an Investment Proposal What Is the Net Present Value of the Proposed Investment