Question

You are considering a project that costs $500 to invest in today, and will pay you $100 next year, $50 in two years, and $100 in three years. The cash inflow will grow at a constant rate of 3% per year after year 3, and you will receive cash inflows for 25 years (total including the first three CFs). Your discount rate is 14%. What is the NPV of the project? Also, what would the NPV be if the cash inflows continued forever? Show your work.

Answer 1

NPV = present value of cash inflows - initial investment

present value of cash inflows = Year 1 cash inflow/(1+discount rate) + Year 2 cash inflow/(1+discount rate)² + Year 3 cash inflow/(1+discount rate)³ .... + Year 25 cash inflow/(1+discount rate)²⁵

Years	Cash flows
0	-$500.00
1	$100.00
2	$50.00
3	$100.00
4	$103.00
5	$106.09
6	$109.27
7	$112.55
8	$115.93
9	$119.41
10	$122.99
11	$126.68
12	$130.48
13	$134.39
14	$138.42
15	$142.58
16	$146.85
17	$151.26
18	$155.80
19	$160.47

20	$165.28
21	$170.24
22	$175.35
23	$180.61
24	$186.03
25	$191.61
Discount rate	14%
NPV	$257.91

Calculations

if the cash inflows continued forever then we need to calculate terminal value for cash inflows for year 4 and beyond. terminal value is calculated at the end of year 3 using year 4 cash inflows. so, it will be discounted for 3 years only.

Years	Cash flows	Present value
0	-$500.00	-$500.00
1	$100.00	$87.72
2	$50.00	$38.47
3	$100.00	$67.50
Terminal value	$936.36	$632.02
Discount rate	14%
NPV		$325.71

Calculations