Question

Compute the IRR, NPV, PI, and payback period for the following two projects. Assume the required return is 12%.

Cashflow for each year

Project A : Year 0= -2500 Year 1=900 Yaer 2=800 Year 3=1600 Year 4=100 Yaer 5=50 Year 6= 300

Project B Year 0 =-2500 Year 1=50 Year2= 600 Year 3=150 Year 4=900 Year 5= 500 Year 6=2500

Answer 1

NPV:

NPV is calculated by discounting the cashflows

PV = C/(1+r)^n

C - Cashflow

r - Discount rate

n - years to the cashflow

Project A:

NPV = -2500 + 900/(1+0.12)^1 + 800/(1+0.12)^2 + 1600/(1+0.12)^3 + 100/(1+0.12)^4 + 50/(1+0.12)^5 + 300/(1+0.12)^6 = 324.09

Project B:

NPV = -2500 + 50/(1+0.12)^1 + 600/(1+0.12)^2 + 150/(1+0.12)^3 + 900/(1+0.12)^4 + 500/(1+0.12)^5 + 2500/(1+0.12)^6 = $251.98

IRR:

IRR is the rate at which NPV = 0

Project A:

NPV = -2500 + 900/(1+IRR)^1 + 800/(1+IRR)^2 + 1600/(1+IRR)^3 + 100/(1+IRR)^4 + 50/(1+IRR)^5 + 300/(1+IRR)^6 = 0

By trail and error, IRR = 17.91%

Project B:

NPV = -2500 + 50/(1+IRR)^1 + 600/(1+IRR)^2 + 150/(1+IRR)^3 + 900/(1+IRR)^4 + 500/(1+IRR)^5 + 2500/(1+IRR)^6 = 0

By trail and error, IRR = 14.38%

PI:

Profitability Index = (NPV + Initial Investment) / Initial investment

Project A = (324.09 + 2500)/2500 = 1.13

Project B = (251.98 + 2500)/2500 = 1.10

Payback period :

Payback period = A + B/C

Where,
A = Last period with a negative cumulative cash flow;
B = Absolute value of cash flow at the end of the period A;
C = cash flow during the period after A.

Project A:

Year	Cashflow (A)	Cummulative
0	-2500	-2500
1	900	-1600
2	800	-800
3	1600	800
4	100	900
5	50	950
6	300	1250

Payback period = 2 + 800/1600 = 2.5 years

Project B:

Year	Cashflow (A)	Cummulative
0	-2500	-2500
1	50	-2450
2	600	-1850
3	150	-1700
4	900	-800
5	500	-300
6	2500	2200

Payback period = 5 + 300/2500 = 5.12 years