Question

CAPITAL BUDGETING CRITERIA

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	-$12,000	$4,000	$4,000	$4,000	$4,000	$4,000
Project N	-$36,000	$11,200	$11,200	$11,200	$11,200	$11,200

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

2. Assuming the projects are independent, which one(s) would you recommend?
   -Only Project M would be accepted because NPV(M) > NPV(N). -Only Project N would be accepted because NPV(N) > NPV(M). -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.
3. 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. -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. -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.

4. 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 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. -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.

Please explain step by step and in simplest terms as possible. Thank You

Answer 1

Project M

NPV = -$12,000 + ($4,000)(3.517) = $866.20

Using Present value of an annuity of $1 table

IRR using a spreadsheet = 19.86%

Modified IRR (MIRR) calculations:

Future value of cash flows re-invested at the WACC of 13%:

Year 1 CF = $4,000(1.13)⁴ = $6,521.894

Year 2 CF = $4,000(1.13)³ = $5,771.58

Year 3 CF = $4,000(1.13)² = $5,107.60

Year 4 CF = $4,000(1.13)¹ = $4,520.00

Year 5 CF = $4,000

Terminal value = $25,921.074

PV of Project cost = $12,000

$12,000 = $25,921.074/ (1 + MIRR)⁵ Þ MIRR = 0.1665 (16.65%)

Payback period = $12,000 / $4,000 = 3.00 years

Discounted payback period calculations:

Year 1 discounted CF = $4,000 / 1.13 = $3,539.823

Year 2 discounted CF = $4,000 / (1.13)² = $3132.586

Year 3 discounted CF = $4,000 / (1.13)³ = $2772.20

Year 4 discounted CF = $4,000 / (1.13)⁴ = $2,453.27

Year 5 discounted CF = $4,000 / (1.13)⁵ = $2,171.039

Discounted payback period = 4 + ($102.57/$2,171.039) = 4.047 years

Project N

NPV = -$36,000 + ($11,200)(3.517) = $3,390.4

IRR using a spreadsheet = 16.80%

Modified IRR (MIRR) calculations:

Future value of cash flows re-invested at the WACC of 13%:

Year 1 CF = $11,200(1.13)⁴ = $18,261.3044

Year 2 CF = $11,200 (1.13)³ = $16,160.4464

Year 3 CF = $11,200 (1.13)² = $14,301.28

Year 4 CF = $11,200 (1.13)¹ = $12,656.00

Year 5 CF = $11,200

Terminal value = $72,579.0308

PV of Project cost = $36,000

$36,000 =$72,579.0308/ (1 + MIRR)⁵ Þ MIRR = 0.1505 (15.05%)

Payback period = $36,000 / $11,200 = 3.21 years

Discounted payback period calculations:

Year 1 discounted CF = $11,200 / 1.13= $9,911.50

Year 2 discounted CF = $11,200 / (1.13)² = $8,771.24

Year 3 discounted CF = $11,200 / (1.13)³ = $7,762.16

Year 4 discounted CF = $11,200 / (1.13)⁴ = $6,869.16

Year 5 discounted CF = $11,200 / (1.13)⁵ = $6,078.911

Discounted payback period = 4 + ($2,685.94/$6,078.911) = 4.441 years

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

If the projects are independent, both would be accepted since they both have positive NPVs.

c) If the projects are mutually exclusive, which would you recommend?

If the projects are mutually exclusive then only one can be accepted, and Project N would be recommended as it has a higher NPV, even though its IRR and MIRR are lower.

d) 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 most likely occurs due to the difference in the size of the projects, as Project N is three times larger than Project M.