Capital Budeting Methods

Capital Budeting Methods

(10–10) Capital Budgeting Methods

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

(10–17) 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

(10–19) 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

(10–22) 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
17,500
6,250
14,000
6,250
11,000
6,250
5,000
6,250
0

Operate for 5 Years
Operate for 4 Years
Operate for 3 Years
Operate for 2 Years
Operate for 1 Year
a

b

NPV
NPV
NPV
NPV
NPV

$0
$0
$0
$0
$0

Year
0
1
2
3
4
5

Annual
Operating
Cash Flow
?$22,500
6,250
6,250
6,250
6,250
6,250

Salvage Value
$ 22,500
17,500
14,000
11,000
5,000
0

a. Should the firm operate the truck until the end of its 5-year physical life? If not,
then what is its optimal economic life?
b. Would the introduction of salvage values, in addition to operating cash flows, ever
reduce the expected NPV and/or IRR of a project?