Question

Answer the following situation

Initial investment $1000

Annual cash flow of $300

Program life for 8 years

Hurdle rate of 5%

Find IRR, NPV, Payback

Answer 1

(a) NPV

Let cash flow for Year n be denoted by CFn

Given

CF0 = -1000
CF1 = 300
CF2 = 300
.......
CF8 = 300

Interest Rate = r = 5% or 0.05

Hence, NPV = Σ CFn/(1+r)ⁿ = -1000 + 300/(1+r) + 300/(1+r)² + ..... + 300/(1+r)⁸ = -1000 + 300[1- (1+r)^-8]/r

Hence, NPV = -1000 + 300[1- (1+0.05)^-8]/0.05 = $938.96

(b) IRR is the rate of return at which NPV is zero

Let IRR = i

=> -1000 + 300[1- (1+r)^-8]/r = 0

=> [1- (1+r)^-8]/r = 1000/300

Using Excel, we get i = 24.95%

(c) Let us calculate the cumulative cash flows for each period

Payback period is period when cumulative cash flow turns positive i.e. starts realizing profits

Year	Cash Flow	Cumulative CF
0	-1000	-1000
1	300	-700
2	300	-400
3	300	-100
4	300	200
5	300	500
6	300	800
7	300	1100
8	300	1400

Cash Flow becomes positive after period 3 i.e. in period 4

Hence, Payback Period = 3 + 100/300 = 3.33 Years