Question

the company requires a 9% return from its investments. compute net present values using factors from table appendix b to determine which projects, if any, should be accepted. note: negative net present values should be entered as a negative value. round your present value factor to round your answers to the nearest whole dollar.

project c1 net cash flows x present value of 1 at 9% = present value of net cash flows
year 1 $ 38,000 x =
year 2 134,000 x =
year 3 194,000 x =
totals $ 366,000
net present value

project c2 net cash flows x present value of 1 at 9% = present value of net cash flows
year 1 $ 122,000 x =
year 2 122,000 x =
year 3 122,000 x =
totals $ 366,000

Explanation:

Step1: Recall present - value formula

The present - value formula for a single cash - flow $CF_n$ in year $n$ with a discount rate $r$ is $PV = CF_n\times(P/F,r,n)$, where $(P/F,r,n)$ is the present - value factor of 1 at rate $r$ for $n$ years. The net present value (NPV) is the sum of the present values of all net cash flows.

Step2: Find present - value factors for Project C1

For $n = 1$, from the present - value of 1 table at $r=9\%$, $(P/F,9\%,1)=0.9174$. For $n = 2$, $(P/F,9\%,2)=0.8417$. For $n = 3$, $(P/F,9\%,3)=0.7722$.

Step3: Calculate present values for Project C1

For year 1: $PV_1=38000\times0.9174 = 34861.2$. For year 2: $PV_2=134000\times0.8417 = 112787.8$. For year 3: $PV_3=194000\times0.7722 = 149806.8$.

Step4: Calculate NPV for Project C1

$NPV_{C1}=34861.2 + 112787.8+149806.8=297455.8\approx297456$.

Step5: Find present - value factors for Project C2

Since the cash flows are the same each year, we can use the present - value of an ordinary annuity formula $PV = A\times(P/A,r,n)$, where $A = 122000$ and $(P/A,9\%,3)=\frac{1-(1 + 0.09)^{-3}}{0.09}=2.5313$.

Step6: Calculate NPV for Project C2

$NPV_{C2}=122000\times2.5313 = 308818.6\approx308819$.

Answer:

Project C1 NPV: $\$297456$
Project C2 NPV: $\$308819$
Both projects should be accepted as their NPVs are positive.