Question

5. You are evaluating the following independent projects. You have the following information on to base your decision: Project A Prolet 30,000 13,100 NINY CF1 CF2 CFS Cost of capital 12,250 14,300 12% 20,000 8,900 7,400 9,800 10% A. Calculate the NPV of each project. B. Calculate the IRR for each project. C. Calculate the Pl of each project. D. What is your recommendation? Why?

Answer 1

			Project "A"	Project "B"
	A	NPV	1,641	1569
	B	IRR	15.112%	14.34%
	C	PI	1.0547	1.07845
	D	As NPV and IRR is higher in Project "A" , so project "A" should be accepted
		but project "B" has higher PI , so according to PI project "B" will be accepted.
	Working:
	For analyzing a long term project with multiple cash flows, the formula for the net present value of a project is
	Σ" CF NPV = (1 +r), t=0
	Where,
	CFt​ = net cash inflow - outflows during a single period t
	r     = discount rate
	t    = number of time periods​
Project A
	Year (t)	Net Cash Flows (CFt)	Present Value of 1 at 12% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}
	0	-30,000	1	-30,000
	1	13,100	0.89286	11,696
	2	12,250	0.79719	9,766
	3	14,300	0.71178	10,178
			Net present Value:	1,641
	IRR is the rate which makes NPV as zero. Using trial and error method, we get IRR as 15.112%
			NPV @ 15%		NPV @ 16%		NPV @ 15.112%
	Year (t)	Net Cash Flows (CFt)	Present Value of 1 at 15% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}	Present Value of 1 at 16% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}	Present Value of 1 at 15.112% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}
	0	-30,000	1	-30,000	1	-30,000	1	-30,000
	1	13,100	0.8696	11,391	0.8621	11,293	0.8687	11,380
	2	12,250	0.7561	9,263	0.7432	9,104	0.7547	9,245
	3	14,300	0.6575	9,402	0.6407	9,161	0.6556	9,375
		NPV		57		-442		0
	Profitability Index = (NPV + initial investment) ÷ Initial investment.
	Profitability Index = (1,641 + 30,000) ÷ 30,000
	Profitability Index = 31,641 ÷ 30,000
	Profitability Index = 1.0547
Project B
	Year (t)	Net Cash Flows (CFt)	Present Value of 1 at 10% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}
	0	-20,000	1	-20,000
	1	8,900	0.90909	8,091
	2	7,400	0.82645	6,116
	3	9,800	0.75131	7,363
			Net present Value:	1,569
	IRR is the rate which makes NPV as zero. Using trial and error method, we get IRR as 14.34%
			NPV @ 14%		NPV @ 15%		NPV @ 14.34%
	Year (t)	Net Cash Flows (CFt)	Present Value of 1 at 14% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}	Present Value of 1 at 15% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}	Present Value of 1 at 14.34% {1 / (1 + r)^t}	Present value of Net Cash flows CFt* {1 / (1 + r)^t}
	0	-20,000	1	-20,000	1	-20,000	1	-20,000
	1	8,900	0.8772	7,807	0.8696	7,739	0.8746	7,784
	2	7,400	0.7695	5,694	0.7561	5,595	0.7649	5,660
	3	9,800	0.6750	6,615	0.6575	6,444	0.6690	6,556
		NPV		116		-222		0
	Profitability Index = (NPV + initial investment) ÷ Initial investment.
	Profitability Index = (1,569 + 20,000) ÷ 20,000
	Profitability Index = 21,569 ÷ 20,000
	Profitability Index = 1.07845