Specter Co. has identified an investment project with the following cash flows. The project requires an upfront investment of $\$1,500$ . What is the net present value of these cash flows if the discount rate is $18\%$ ? Year Cash Flow $1$ $\$795$ $2$ $945$ $3$ $1,325$ $4$ $1,860$

Full solution

Q. Specter Co. has identified an investment project with the following cash flows. The project requires an upfront investment of

\$1,500

. What is the net present value of these cash flows if the discount rate is

18\%

? Year Cash Flow

1

\$795

2

945

3

1,325

4

1,860

Calculate PV Year $1$ : Calculate the present value (PV) of the cash flow for Year $1$ . $\newline$ PV = Cash Flow / $(1 + r)^n$ $\newline$ PV for Year $1$ = $\$795 / (1 + 0.18)^1$ $\newline$ PV for Year $1$ = $\$795 / 1.18$ $\newline$ PV for Year $1$ = $\$673.73$
Calculate PV Year $2$ : Calculate the PV of the cash flow for Year $2$ . $\newline$ PV for Year $2$ = $\$945 / (1 + 0.18)^2$ $\newline$ PV for Year $2$ = $\$945 / 1.3924$ $\newline$ PV for Year $2$ = $\$678.87$
Calculate PV Year $3$ : Calculate the PV of the cash flow for Year $3$ . $\newline$ PV for Year $3$ = $\$1,325 / (1 + 0.18)^3$ $\newline$ PV for Year $3$ = $\$1,325 / 1.6401$ $\newline$ PV for Year $3$ = $\$807.83$
Calculate PV Year $4$ : Calculate the PV of the cash flow for Year $4$ . $\newline$ PV for Year $4$ = $\$1,860 / (1 + 0.18)^4$ $\newline$ PV for Year $4$ = $\$1,860 / 2.0397$ $\newline$ PV for Year $4$ = $\$912.16$
Add PV of Cash Flows: Add up all the present values of the cash flows. $\newline$ Total PV = PV for Year $1$ + PV for Year $2$ + PV for Year $3$ + PV for Year $4$ $\newline$ Total PV = $\$673.73$ + $\$678.87$ + $\$807.83$ + $\$912.16$ $\newline$ Total PV = $\$3,072.59$
Subtract Initial Investment: Subtract the initial investment from the total present value to get the NPV. $\newline$ NPV = Total PV - Initial Investment $\newline$ NPV = $\$3,072.59$ - $\$1,500$ $\newline$ NPV = $\$1,572.59$