Question

Project P costs $15,000 and is expected to produce benefits (cash flows) of $4,500 per year for five years. Project Q costs $37,500 and is expected to produce cash flows of $11,100 per year for five years. Calculate each project’s (a) net present value (NPV), (b) internal rate of return (IRR), and (c) modified internal rate of return (MIRR). The firm’s required rate of return is 14 percent. If the projects are independent, which project (s) should be selected? If they are mutually exclusive projects, which project should be selected? Explain.

Answer 1

Calculation of NPV
Year	Project P	Project Q	PV factor @ 14%	Present values-P	Present values-Q
0	(15,000)	(37,500)	1.000	(15,000)	(37,500)
1	4,500	11,100	0.877	3,947	9,737
2	4,500	11,100	0.769	3,463	8,541
3	4,500	11,100	0.675	3,037	7,492
4	4,500	11,100	0.592	2,664	6,572
5	4,500	11,100	0.519	2,337	5,765
		Net Present Value		449	607
Project Independed	Select P & Q both as positive NPV
Project Mutual exclusive	Select Q as this project gives highest NPV

Calculation of IRR
Year	Project P	PV factor @ 14%	Present values	PV factor @ 16%	Present values
0	(15,000)	1.000	(15,000)	1.000	(15,000)
1	4,500	0.877	3,947	0.862	3,879
2	4,500	0.769	3,463	0.743	3,344
3	4,500	0.675	3,037	0.641	2,883
4	4,500	0.592	2,664	0.552	2,485
5	4,500	0.519	2,337	0.476	2,143
			449		(266)
	IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	IRR	=14%+2%*(449/(449+266))
		15.26%
Year	Project Q	PV factor @ 14%	Present values	PV factor @ 16%	Present values
0	(37,500)	1.000	(37,500)	1.000	(37,500)
1	11,100	0.877	9,737	0.862	9,569
2	11,100	0.769	8,541	0.743	8,249
3	11,100	0.675	7,492	0.641	7,111
4	11,100	0.592	6,572	0.552	6,130
5	11,100	0.519	5,765	0.476	5,285
			607		(1,155)
	IRR	=Lower rate + Difference in rates*(NPV at lower rate)/(Lower rate NPV-Higher rate NPV)
	IRR	=14%+2%*(607/(607+1155))
		14.69%
Project Independed	Select P & Q both giving IRR more than 14%
Project Mutual exclusive	Select P as this project gives highest IRR
Calculation of MIRR
Year	Project P	Future Value factor @ 14%	Present values
1	4,500	1.689	7,600
2	4,500	1.482	6,667
3	4,500	1.300	5,848
4	4,500	1.140	5,130
5	4,500	1.000	4,500
		FV of inflow	29,745
	MIRR	=[(FV of Inflow/Initial Outflow)^(1/n)]-1
	MIRR	=[(29745/15000)^(1/5)]-1
	MIRR	14.67%
Year	Project Q	Future Value factor @ 14%	Present values
1	11,100	1.689	18,747
2	11,100	1.482	16,445
3	11,100	1.300	14,426
4	11,100	1.140	12,654
5	11,100	1.000	11,100
		FV of inflow	73,372
	MIRR	=[(FV of Inflow/Initial Outflow)^(1/n)]-1
	MIRR	=[(73372/37500)^(1/5)]-1
	MIRR	14.37%
Project Independed	Select P & Q both giving MIRR more than 14%
Project Mutual exclusive	Select P as this project gives highest MIRR