## Description

Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected to produce cash flows of $7,400 per year for 5 years. Calculate the two projects’ NPVs, IRRs, MIRRs, and PIs, assuming a cost of capital of 12%. Which project would be selected, assuming they are mutually exclusive, using each ranking method? Which should actually be selected?

Inputs

r

12%

Initial Cost

Time

Project S

Project L

0

-$10,000

-$25,000

Project S

NPV

IRR

MIRR

PI

$814.33

15.24%

13.77%

1.081

Cash Flows

1

$3,000

$7,400

2

$3,000

$7,400

3

$3,000

$7,400

4

$3,000

$7,400

Project L

$1,675.34

14.67%

13.46%

1.067

5

$3,000

$7,400

Initial Cost

Year

Proj S

0

1

2

3

4

5

-10000

2678.57142857

2391.58163265

2135.34074344

1906.55423521

1702.28056716

Proj L

-25000

6607.1429

5899.2347

5267.1738

4702.8338

4198.9587

Which Project is to be selected?

Using NPV, Project S wins with 814.33 vs 1,675.34

Using IRR, Project S also wins with 15.24% vs 14.67%

Using MIRR, Project S also wins with 13.77% vs 13.46%

Using PI, again, project S wins with 1.081 vs 1.067

Overall, although project L has an NPV higher than project S, in both IRR and MIRR, S is higher. PI is also smaller for project S, so I would choose S over L

(10â€“17) Unequal Lives

The Perez Company has the opportunity to invest in one of two mutually exclusive machines that will produce a product it will need for the foreseeable future. Machine A costs $10 million but realizes after -tax inflows of $4 million per year for 4 years.

After 4 years, the machine must be replaced. Machine B costs $15 million and realizes after-tax inflows of $3.5 million per year for 8 years, after which it must be replaced. Assume that machine prices are not expected to rise because inflation will be offset by cheaper components used in the machines. The cost of capital is 10%. By how much would the value of the company increase if it accepted the better machine?

What is the equivalent annual annuity for each machine ?

Unequal Lives

Inputs

r

10%

Initial Cost

Time

Machine A-1

Machine A-2

Sum CFs

0

NPVA-1

EFFA

Machine B

NPV

EFFB

Analysis

Cash Flows

1

2

3

4

NPVA-1,A-2

5

6

7

8

Multiple Rates of Return

COC

8%

Initial Cost

Time

Project

PV

NPV

IRR

Cash Flows

0

2

$4.40

$0

-$4

a. Plot the project’s NPV profile.

b. Should the project be accepted if r = 8%? If r = 14%? Explain your reasoning.

a

Data table for question

Cost of Capital NPV

IRR

-$4.40

c. Can you think of some other capital budgeting situations in which negative cash

flows during or at the end of the project’s life might lead to multiple IRRs?

0%

d. What is the project’s MIRR at r = 8%? At r = 14%? Does the MIRR method lead to

the same accept-reject decision as the NPV met

2%

4%

6%

8%

10%

12%

14%

16%

18%

20%

100%

200%

400%

b

1

(10â€“19) Multiple Rates of Return

The Ulmer Uranium Company is deciding whether or not it should open a strip mine

whose net cost is $4.4 million. Net cash inflows are expected to be $27.7 million, all

coming at the end of Year 1. The land must be returned to its natural state at a cost of

$25 million, payable at the end of Year 2.

see your table above and decide using NPV rule: accept positive NPV, reject negative net present values

c

d

MIRR

r

8%

14%

Economic Life

(10â€“22) Economic Life

The Scampini Supplies Company recently purchased a new delivery truck. The new

truck cost $22,500, and it is expected to generate net after-tax operating cash flows,

including depreciation, of $6,250 per year. The truck has a 5 -year expected life. The

expected salvage values after tax adjustments for the truck are given below. The

company’s cost of capital is 1

Inputs

r

10%

Year

0

1

2

3

4

5

Annual

Total PV

PV Cash PF Salvage

Operating Salvage Value

per year D

flows

Value

Cash Flow

+E

?$22,500

$ 22,500

6,250

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