Question

A firm with a 13% WACC is evaluating two projects for this year's capital budget. After-tax cash flows, including depreciation, are as follows:

0

1

2

3

4

5

Project M	-$21,000	$7,000	$7,000	$7,000	$7,000	$7,000
Project N	-$63,000	$19,600	$19,600	$19,600	$19,600	$19,600

1. Calculate NPV for each project. Round your answers to the nearest cent. Do not round your intermediate calculations.
   Project M ____ $
   Project N ____ $

   Calculate IRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M ____ %
   Project N ____ %

   Calculate MIRR for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M _____ %
   Project N     _____ %

   Calculate payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M ____ years
   Project N ____ years

   Calculate discounted payback for each project. Round your answers to two decimal places. Do not round your intermediate calculations.
   Project M ____ years
   Project N ____ years

A. Assuming the projects are independent, which one(s) would you recommend?

-Both projects would be accepted since both of their NPV's are positive

-Only Project M would be accepted because IRR(M) > IRR(N)

-Both projects would be rejected since both of their NPV's are negative

-Only Project M would be accepted because NPV(M) > NPV(N)

-Only Project N would be accepted because NPV(N) > NPV(M)

B. If the projects are mutually exclusive, which would you recommend?

-If the projects are mutually exclusive, the project with the shortest Payback Period is chosen. Accept Project M

-If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project N

-If the projects are mutually exclusive, the project with the highest positive NPV is chosen. Accept Project N

-If the projects are mutually exclusive, the project with the highest positive IRR is chosen. Accept Project M

-If the projects are mutually exclusive, the project with the highest positive MIRR is chosen. Accept Project M

C. Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?

-The conflict between NPV and IRR occurs due to the difference in the size of the projects.

-The conflict between NPV and IRR is due to the relatively high discount rate.

-The conflict between NPV and IRR is due to the fact that the cash flows are in the form of an annuity.

-The conflict between NPV and IRR is due to the difference in the timing of the cash flows.

-There is no conflict between NPV and IRR

Answer 1

1]	NPV:
	Project M = -21000+7000*(1.13^5-1)/(0.13*1.13^5) =	$        3,620.62
	Project N = -63000+19600*(1.13^5-1)/(0.13*1.13^5) =	$        5,937.73
2]	IRR:
	IRR is that discount rate for which NPV = 0. As the cash flows are in the form of an annuity, the
	IRR can be found out using annuity factor tables.
	Project M:
	21000 = 7000*PVIFA(irr,5)
	PVIFA(irr,5) = 21000/7000 = 3.0000
	The PVs of annuity of $1 for 19% and 20% for n = 5	19%	20%
	are:	3.0576	2.9906
	IRR will fall between 19% and 20%.
	By simple interpoltion, IRR = 19%+1%*(3.0576-3)/(3.0576-2.9906) =	19.86%
	Project N:
	PVIFA(irr,5) = 63000/19600 = 3.2143
	The factor for IRR falls between 16% and 17%.	16%	17%
		3.2743	3.1993
	IRR = 16%+1%*(3.2743-3.2143)/(3.2743-3.1993) =	16.80%
3]	MIRR:
	MIRR assumes that the intervening cash inflows are reinvested at the WACC of 13%.
	Once the reinvestment of cash inflows is done and their FV found at t5, there are
	only two cash flows. The initial investment at t0 and the compounded value of the
	cash inflows at t5. MIRR is the discount rate that equates those two cash flows.
	Project M:
	FV of cash inflows = 7000*(1.13^5-1)/0.13 =	$      45,361.89
	MIRR = (45361.89/21000)^(1/5)-1 =	16.65%
	Project N:
	FV of cash inflows = 19600*(1.13^5-1)/0.13 =	$    127,013.30
	MIRR = (127013.30/63000)^(1/5)-1 =	15.05%
4]	PAYBACK PERIOD:
	Project M = 21000/7000 =	3.00	Years
	Project N = 63000/19600 =	3.21	Years
5]	DISCOUNTED PAYBACK PERIOD:
	Project M:
	Year	Cash flow	PVIF at 13%	PVIFA at 13%	Cumulative PV
	0	$    (21,000.00)	1	$(21,000.00)	$   (21,000.00)
	1	$        7,000.00	0.88496	$     6,194.69	$   (14,805.31)
	2	$        7,000.00	0.78315	$     5,482.03	$     (9,323.28)
	3	$        7,000.00	0.69305	$     4,851.35	$     (4,471.93)
	4	$        7,000.00	0.61332	$     4,293.23	$         (178.70)
	5	$        7,000.00	0.54276	$     3,799.32	$        3,620.62
	Discount payback period = 4+178.70/3799.32 =	4.05	Years
	Project N:
	Year	Cash flow	PVIF at 13%	PVIFA at 13%	Cumulative PV
	0	$    (63,000.00)	1	$(63,000.00)	$   (63,000.00)
	1	$      19,600.00	0.88496	$   17,345.13	$   (45,654.87)
	2	$      19,600.00	0.78315	$   15,349.67	$   (30,305.19)
	3	$      19,600.00	0.69305	$   13,583.78	$   (16,721.41)
	4	$      19,600.00	0.61332	$   12,021.05	$     (4,700.36)
	5	$      19,600.00	0.54276	$   10,638.09	$        5,937.73
	Discount payback period = 4+4700.36/10638.09 =	4.44	Years
	OTHER ANSWERS:
A]	Assuming the projects are independent, which one(s) would you recommend?
	-Both projects would be accepted since both of their NPV's are positive
B]	If the projects are mutually exclusive, which would you recommend?
	If the projects are mutually exclusive, the project with the highest positive NPV is chosen. Accept Project N
C]	Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?
	The conflict between NPV and IRR occurs due to the difference in the size of the projects.