Question

Payback, NPV, and MIRR

Your division is considering two investment projects, each of which requires an up-front expenditure of $23 million. You estimate that the cost of capital is 9% and that the investments will produce the following after-tax cash flows (in millions of dollars):

Year	Project A	Project B
1	5	20
2	10	10
3	15	8
4	20	6

What is the regular payback period for each of the projects? Round your answers to two decimal places.

Project A years

Project B years

What is the discounted payback period for each of the projects? Round your answers to two decimal places.

Project A years

Project B years

If the two projects are independent and the cost of capital is 9%, which project or projects should the firm undertake?
-Select-Project AProject BBoth projectsItem 5

If the two projects are mutually exclusive and the cost of capital is 5%, which project should the firm undertake?
-Select-Project AProject BItem 6

If the two projects are mutually exclusive and the cost of capital is 15%, which project should the firm undertake?
-Select-Project AProject BItem 7

What is the crossover rate? Round your answer to two decimal places.
%

If the cost of capital is 9%, what is the modified IRR (MIRR) of each project? Round your answers to two decimal places.

Project A %

Project B %

Answer 1

1)	PAYBACK PERIOD:
	PROJECT A:
	Year	Cash flow	Cumulative cash flow
	0	-23	-23
	1	5	-18
	2	10	-8
	3	15	7
	4	20	27
	Payback period = 2+8/15 = 2.53 years
	PROJECT B:
	Year	Cash flow	Cumulative cash flow
	0	-23	-23
	1	20	-3
	2	10	7
	3	8	15
	4	6	21
	Payback period = 1+3/10 = 1.30 years.
2)	DISCOUNTED PAYBACK:
	PROJECT A:
	Year	Cash flow	PVIF at 9%	PV at 9%	Cumulative PV
	0	-23	1.00000	-23.00	-23.00
	1	5	0.91743	4.59	-18.41
	2	10	0.84168	8.42	-10.00
	3	15	0.77218	11.58	1.59
	4	20	0.70843	14.17	15.76
	Discounted Payback period = 2+10/11.58 = 2.86 years
	PROJECT B:
	Year	Cash flow	PVIF at 9%	PV at 9%	Cumulative PV
	0	-23	1.00000	-23.00	-23.00
	1	20	0.91743	18.35	-4.65
	2	10	0.84168	8.42	3.77
	3	8	0.77218	6.18	9.94
	4	6	0.70843	4.25	14.19
	Payback period = 1+4.65/8.42 = 1.55
3)	NPV AT 9%.
	PROJECT A:
	Year	Cash flow	PVIF at 9%	PV at 9%
	0	-23	1.00000	-23.00
	1	5	0.91743	4.59
	2	10	0.84168	8.42
	3	15	0.77218	11.58
	4	20	0.70843	14.17
	NPV=			15.76
	PROJECT B:
	Year	Cash flow	PVIF at 9%	PV at 9%
	0	-23	1.00000	-23.00
	1	20	0.91743	18.35
	2	10	0.84168	8.42
	3	8	0.77218	6.18
	4	6	0.70843	4.25
	NPV			14.19
	If the COC is 9% and the projects are independent, both the projects
	are acceptable as the NPV is positive.
4)	NPV AT 5%:
	PROJECT A:
	Year	Cash flow	PVIF at 5%	PV at 5%
	0	-23	1.00000	-23.00
	1	5	0.95238	4.76
	2	10	0.90703	9.07
	3	15	0.86384	12.96
	4	20	0.82270	16.45
	NPV=			20.24
	PROJECT B:
	Year	Cash flow	PVIF at 5%	PV at 5%
	0	-23	1.00000	-23.00
	1	20	0.95238	19.05
	2	10	0.90703	9.07
	3	8	0.86384	6.91
	4	6	0.82270	4.94
	NPV			16.96
	If the projects are mutually exclusive, Project A with higher NPV is to be chosen.
5)	NPV with cost of capital of 15%:
	PROJECT A:
	Year	Cash flow	PVIF at 15%	PV at 15%
	0	-23	1.00000	-23.00
	1	5	0.86957	4.35
	2	10	0.75614	7.56
	3	15	0.65752	9.86
	4	20	0.57175	11.44
	NPV=			10.21
	PROJECT B:
	Year	Cash flow	PVIF at 15%	PV at 15%
	0	-23	1.00000	-23.00
	1	20	0.86957	17.39
	2	10	0.75614	7.56
	3	8	0.65752	5.26
	4	6	0.57175	3.43
	NPV			10.64
	If the projects are mutually exclusive, Project B with higher NPV is to be chosen.
6)	Cross over rate is the IRR of the incremental cash flows:
	Year	Incremental cash flows   (A-B)	PVIF at 15%	PV at 15%	PVIF at 14%	PV at 14%
	1	-15	0.86957	-13.04	0.87719	-11.44
	2	0	0.75614	0.00	0.76947	0.00
	3	7	0.65752	4.60	0.67497	3.11
	4	14	0.57175	8.00	0.59208	4.74
				-0.44		-3.60
	The cross over rate can be taken as 15%.
7)	MIRR:
	PROJECT A:
	Year	Cash flow	FVIF at 9%	FV at 9%
	1	5	1.29503	6.48
	2	10	1.18810	11.88
	3	15	1.09000	16.35
	4	20	1.00000	20.00
				54.71
	MRR = (54.71/23)^(1/4)-1=		24.19%
	PROJECT B:
	Year	Cash flow	FVIF at 9%	FV at 9%
	1	20	1.29503	25.90
	2	10	1.18810	11.88
	3	8	1.09000	8.72
	4	6	1.00000	6.00
				52.50
	MIRR = (52.50/23)^(1/4)-1=		22.92%