Gamma Company is considering an investment proposal that would require an initial outlay of $816,000,and would yield yearly cash flows of $220,000 for 9 years.The company uses a discount rate of 10%.What is the NPV of the investment?
Present value of annuity of $1:
$$\begin{array} { | l | r | r | r | }
\hline & { 8 \% } & { 9 \% } & { 10 \% } \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 1.783 & 1.759 & 1.736 \
\hline 3 & 2.577 & 2.531 & 2.487 \
\hline 4 & 3.312 & 3.24 & 3.17 \
\hline 5 & 3.993 & 3.89 & 3.791 \
\hline 6 & 4.623 & 4.486 & 4.355 \
\hline 7 & 5.206 & 5.033 & 4.868 \
\hline 8 & 5.747 & 5.535 & 5.335 \
\hline 9 & 6.247 & 5.995 & 5.759 \
\hline
\end{array}$$

Question

Gamma Company is considering an investment proposal that would require an initial outlay of $816,000,and would yield yearly cash flows of $220,000 for 9 years.The company uses a discount rate of 10%.What is the NPV of the investment?
Present value of annuity of $1:
$$\begin{array} { | l | r | r | r | } 
\hline &  { 8 \% } & { 9 \% } &  { 10 \% } \
\hline 1 & 0.926 & 0.917 & 0.909 \
\hline 2 & 1.783 & 1.759 & 1.736 \
\hline 3 & 2.577 & 2.531 & 2.487 \
\hline 4 & 3.312 & 3.24 & 3.17 \
\hline 5 & 3.993 & 3.89 & 3.791 \
\hline 6 & 4.623 & 4.486 & 4.355 \
\hline 7 & 5.206 & 5.033 & 4.868 \
\hline 8 & 5.747 & 5.535 & 5.335 \
\hline 9 & 6.247 & 5.995 & 5.759 \
\hline
\end{array}$$

Quizplus · Accepted Answer

To find the NPV, we need to calculate the present value of all the cash flows, discounted at the company's discount rate of 10%.

Using the formula for the present value of an annuity, we can calculate the present value of the yearly cash flows as follows:

PV = A[(1 - (1+r)^-n)/r]

Where:
PV = Present value
A = Yearly cash flow
r = Discount rate
n = Number of years

PV = $220,000[(1 - (1+0.10)^-9)/0.10] = $1,580,477.92

Next, we need to calculate the present value of the initial investment of $816,000:

PV = $816,000/(1+0.10)^0 = $816,000

Finally, we can calculate the net present value (NPV) by subtracting the present value of the initial investment from the present value of the cash flows:

NPV = $1,580,477.92 - $816,000 = $764,477.92

Therefore, the NPV of the investment is $450,980 (rounded to the nearest dollar), which is positive, indicating that the investment is expected to generate a profit and should be undertaken by the company.

Gamma Company Is Considering an Investment Proposal That Would Require