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	-$24,000	$8,000	$8,000	$8,000	$8,000	$8,000
Project N	-$72,000	$22,400	$22,400	$22,400	$22,400	$22,400

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

Assuming the projects are independent, which one(s) would you recommend?
A. Both projects would be accepted since both of their NPV's are positive.

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

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

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

E. Only Project N would be accepted because NPV(N) > NPV(M).Item 11

If the projects are mutually exclusive, which would you recommend?
A. If the projects are mutually exclusive, the project with the shortest Payback Period is chosen. Accept Project M.

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

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

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

E. If the projects are mutually exclusive, the project with the highest positive MIRR is chosen. Accept Project M.Item 12

Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?
A. The conflict between NPV and IRR occurs due to the difference in the size of the projects.

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

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

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

E. There is no conflict between NPV and IRR.Item

Answer 1

NPV of Project M = -24000 + 8000 * PVIFA (13%, 5) = -24000 + 8000 * 3.5172312615427

NPV of Project M = -24000 + 28137.85 = $4137.85

NPV of Project N = -72000 + 22400 * PVIFA (13%, 5) = -72000 + 22400 * 3.5172312615427

NPV of Project N = -72000 + 78785.98 = $6785.98

For calculating IRR for project M, let ‘i’ be the IRR

-24000 + 8000 * PVIFA (i,5) = 0

• PVIFA (i,5) = 24000/8000 = 3

Hence, by Present Value Interest Factor Table for Annuity, we find that 19%<i<20%

NPV of Project M @ 19% = -24000 + 8000 * 3.0576348898368 = $461.0791

NPV of Project M @ 20% = -24000 + 8000 * 2.9906121399177 = -$75.1029

Using interpolation

i = 19% + (20%-19%) * ((0-461.0791)/(-75.1029-461.0791) = 19.859%

IRR for Project M = 19.859%

For calculating IRR for project N, let ‘i’ be the IRR

-72000 + 22400 * PVIFA (i,5) = 0

PVIFA (i,5) = 72000/22400 = 3.214286

Hence, by Present Value Interest Factor Table for Annuity, we find that 16%<i<17%

NPV of Project N @ 16% = -72000 + 22400 * 3.2742936536612 = $1344.1778

NPV of Project N @ 17% = -72000 + 22400 * 3.1993461627292 = -$334.6460

Using interpolation

i = 16% + (17%-16%) * ((0-1344.1778)/(-334.6460-1344.1778) = 16.800%

IRR for Project N = 16.8%

MIRR of project can be calculated using formula:

MIRR = (Future Value of Positive Cashflow/PV of Initial Outlay)^(1/n) – 1

For calculating MIRR of project M

Future value of positive cashflow = 8000 * [(((1+13%)^5) – 1)/13%] = 51842.16

PV of initial outlay = 24000

Hence MIRR = (51842.16/24000)^(1/5) – 1 = 16.65%

For calculating MIRR of project N

Future value of positive cashflow = 22400 * [(((1+13%)^5) – 1)/13%] = 145158.06

PV of initial outlay = 72000

Hence MIRR = (145158.06/72000)^(1/5) – 1 = 15.05%

For calculating payback period & discounted payback period

	Cash Flow		Accumulated Cashflow
Time	Project M	Project N	Project M	Project N
0	-24000.000	-72000.000	-24000.000	-72000.000
1	8000.000	22400.000	-16000.000	-49600.000
2	8000.000	22400.000	-8000.000	-27200.000
3	8000.000	22400.000	0.000	-4800.000
4	8000.000	22400.000	8000.000	17600.000
5	8000.000	22400.000	16000.000	40000.000

Payback period of project M = 3 years

Payback period of project N = 3 years + (4800+22400) = 3.21 years

	Cash Flow		Discounted cash flow		Accumulated discounted cash flow
Time	Project M	Project N	Project M	Project N	Project M	Project N
0	-24000.000	-72000.000	-24000.000	-72000.000	-24000.000	-72000.000
1	8000.000	22400.000	7079.646	19823.009	-16920.354	-52176.991
2	8000.000	22400.000	6265.173	17542.486	-10655.181	-34634.505
3	8000.000	22400.000	5544.401	15524.324	-5110.779	-19110.182
4	8000.000	22400.000	4906.550	13738.340	-204.229	-5371.842
5	8000.000	22400.000	4342.079	12157.823	4137.850	6785.980

Discounted Payback Period for Project M = 4 years + (204.229/4342.079) = 4.04 years

Discounted Payback Period for Project M = 4 years + (5371.842/12157.823) = 4.44 years

Assuming the projects are independent, which one(s) would you recommend?
A. Both projects would be accepted since both of their NPV's are positive.

As both project are providing more return than the cost of capital. Hence, Both projects would be accepted since both of their NPV's are positive subject to availability of funds

Notice that the projects have the same cash flow timing pattern. Why is there a conflict between NPV and IRR?
A. The conflict between NPV and IRR occurs due to the difference in the size of the projects.