The following data pertain to an investment proposal:
$\begin{array}{|l|r|}
\hline \text { Cost of the investment } & \$ 20,000 \
\hline \text { Annual cost savings } & \$ 5,000 \
\hline \text { Estimated Salvage Value } & \$ 1,000 \
\hline \text { Life of the Project } & 8 \text { years } \
\hline
\end{array}$
$$\begin{array} { | l | l |}
\hline \text { Discourt Rate } & 16 \%\\hline
\end{array}$$
What is the net present value of the proposed investment? (Ignore income taxes in this problem.)(Do not round your intermediate calculations and round the final answer to the nearest whole dollar.)
A) $1,720.
B) $2,023.
C) $2,154.
D) $6,064.

Question

The following data pertain to an investment proposal:
$\begin{array}{|l|r|}
\hline \text { Cost of the investment } & \$ 20,000 \
\hline \text { Annual cost savings } & \$ 5,000 \
\hline \text { Estimated Salvage Value } & \$ 1,000 \
\hline \text { Life of the Project } & 8 \text { years } \
\hline
\end{array}$
$$\begin{array} { | l | l |} 
\hline \text { Discourt Rate } & 16 \%\\hline
\end{array}$$
What is the net present value of the proposed investment? (Ignore income taxes in this problem.)(Do not round your intermediate calculations and round the final answer to the nearest whole dollar.)
A) $1,720.
B) $2,023.
C) $2,154.
D) $6,064.

Quizplus · Accepted Answer

To calculate the Net Present Value (NPV) of the proposed investment, we use the formula for NPV which involves discounting the future cash flows (annual cost savings and salvage value) back to their present value and then subtracting the initial investment. The formula for NPV is:$$ NPV = \sum \frac{R_t}{(1 + i)^t} - C_0 $$Where:- $R_t$ = net cash inflow during the period t- $i$ = discount rate (16% or 0.16 in this case)- $t$ = time period (years)- $C_0$ = initial investment (\$20,000)The annual cost savings of \$5,000 is an annuity over 8 years. We can calculate the present value of this annuity using the present value of annuity formula:$$ PV_{annuity} = R \times \left[\frac{1 - (1 + i)^{-n}}{i}\right] $$Where:- $R$ = annual cost savings (\$5,000)- $i$ = discount rate (0.16)- $n$ = life of the project (8 years)$$ PV_{annuity} = 5000 \times \left[\frac{1 - (1 + 0.16)^{-8}}{0.16}\right] $$$$ PV_{annuity} = 5000 \times \left[\frac{1 - (1.16)^{-8}}{0.16}\right] $$$$ PV_{annuity} = 5000 \times \left[\frac{1 - 0.31524}{0.16}\right] $$$$ PV_{annuity} = 5000 \times 4.29289 $$$$ PV_{annuity} = 21464.45 $$The salvage value of \$1,000 at the end of 8 years also needs to be discounted back to its present value:$$ PV_{salvage} = \frac{1000}{(1 + 0.16)^8} $$$$ PV_{salvage} = \frac{1000}{(1.16)^8} $$$$ PV_{salvage} = \frac{1000}{2.14359} $$$$ PV_{salvage} = 466.507 $$Adding the present value of the annuity and the salvage value, and then subtracting the initial investment:$$ NPV = 21464.45 + 466.507 - 20000 $$$$ NPV = 21930.957 - 20000 $$$$ NPV = 1930.957 $$Rounding to the nearest whole dollar, the NPV is approximately \$1,931, which is not an option provided. However, the closest provided option to the calculated NPV is:B) $2,023.It seems there was a mistake in the calculation or interpretation of the options. Given the options and the methodology, the correct approach would involve recalculating or correctly interpreting the given options based on standard NPV calculation methods. The explanation provided was intended to demonstrate the calculation process, but the final answer does not match the options due to a possible miscalculation or misunderstanding in the final step. The correct answer based on the options provided should be recalculated or reevaluated.

The Following Data Pertain to an Investment Proposal Discourt Rate 16%\begin{array} { | l | l |} \hline \text { Discourt Rate } & 16 \%\\\hline\end{array} Discourt Rate ​16%​​

The Following Data Pertain to an Investment Proposal $\begin{array} { | l | l |} \hline \text { Discourt Rate } & 16 \%\\\hline\end{array}$