Solution manual engineering economic analysis 9th edition ch15

Chapter 15: Selection of a Minimum Attractive Rate of Return
15-1
The interest rates on these securities vary greatly over time, making it impossible to predict
rates. Three factors that distinguish the securities:
Bond Duration
20 years
20 years

Municipal Bond
Corporate Bond

Bond Safety
Safe
Less Safe

The importance of the non-taxable income feature usually makes the municipal bond the
one with the lowest interest rate. The corporate bond generally will have the highest interest
rate.
15-2
As this is a situation of “neither input nor output fixed,” incremental analysis is required.
∆ Cost
∆ Benefit
∆ Rate of Return

C- D
$25
$4
9.6%

B- C
$50

$6.31
4.5%

B- D
$75
$10.31
6.2%

D- A
$25
$5.96
20%

Using the incremental rates of return one may determine the preferred alternative at any
interest rate.
For interest rates between:
0%

4.5%
B

9.6%
C

20%
D

∞
A

The problem here concerns Alternative C. C is preferred for 4.5% < Interest Rate < 9.6%.

15-3
Lease: Pay $267 per month for 24 months.
Purchase:
A = $9,400 (A/P, 1%, 24)
= $9,400 (0.0471) = $442.74
Salvage (resale) value = $4,700
(a) Purchase Rather than Lease
∆Monthly payment = $442.71 - $267
= $175.74
∆Salvage value = $4,700 - $0 = $4,700
∆ Rate of Return


PW of Cost = PW of Benefit
$175.74 (P/A, i%, 24) = $4,700
(P/A, i%, 24) = $4,700/$175.74 = 26.74
i = 0.93% per month
Thus, the additional monthly payment of $175.74 would yield an 11.2% rate of return.
Leasing is therefore preferred at all interest rates above 11.2%.
(b) Items that might make leasing more desirable:
1. One does not have, or does not want to spend, the additional $175.74 per month.
2. One can make more than 11.2% rate of return in other investment.
3. One does not have to be concerned about the resale value of the car at the end of
two years.
15-4
Investment opportunities may include:
1.
Deposit of the money in a Bank.

2.
Purchase of common stock, US Treasury bonds, or corporate
bonds.
3.
Investment in a new business, or an existing business.
4.
(and so on.)
Assuming the student has a single investment in which more than $2,000 could be invested,
the MARR equals the projected rate of return for the investment.

15-5
Venture capital syndicates typically invest money in situations with a substantial amount of
risk. The process of identifying and selecting investments is a time-consuming (and hence
costly) process. The group would therefore only make a venture capital investment where
(they think) the rate of return will be high- probably 25% or more.

15-6
The IRR for each project is calculated using the Excel function = RATE (life, annual benefit,
-first cost, salvage value), and then the table is sorted with IRR as the key. Projects A and B
are the top two projects, which fully utilize the $100,000 capital budget. The opportunity cost
of capital is 12.0% if based on the first project rejected.
Project

IRR

First Cost

A
B
D

C

13.15%
12.41%
11.99%
10.66%

$50,000
$50,000
$50,000
$50,000

Annual
Benefits
$13,500
$9,000
$9,575
$13,250

Life
5 yrs
10 yrs
8 yrs
5 yrs

Salvage
Value
$5,000
$0
$6,000

$1,000


15-7
The IRR for each project is calculated using the Excel function = RATE (3, annual benefit,
-first cost) since N = 3 for all projects. Then the table is sorted with IRR as the key. Do
projects 3, 1 and 7 with a budget of $70,000. The opportunity cost of capital is 26.0% if
based on the first project rejected.
Project

IRR

3
1
7
5
4
2
6

36.31%
29.92%
26.67%
26.01%
20.71%
18.91%
18.91%

Cumulative
First Cost

$10,000
$30,000
$70,000
$95,000
$100,000
$130,000
$145,000

First Cost
$10,000
$20,000
$40,000
$25,000
$5,000
$30,000
$15,000

Annual
Benefit
$6,000
$11,000
$21,000
$13,000
$2,400
$14,000
$7,000

15-8
The IRR for each project is calculated using the Excel function = RATE (life, annual benefit, -first
cost, salvage value), and then the table is sorted with IRR as the key. With a budget of

$500,000, the opportunity cost of capital is 19.36% if based on the first project rejected.
Projects 3, 1, 4, and 6 should be done.
Project

IRR

3
1
4
6
2
7
5

28.65%
24.01%
21.41%
20.85%
19.36%
16.99%
15.24%

Cumulative
First Cost
$100,000
$300,000
$350,000
$500,000
$800,000
$1,200,000

$1,450,000

First Cost
$100,000
$200,000
$50,000
$150,000
$300,000
$400,000
$250,000

Annual
Benefit
$40,000
$50,000
$12,500
$32,000
$70,000
$125,000
$75,000

Life (years)
5
15
10
20
10
5
5

15-9
The IRR for each project is calculated using the Excel function = Rate (life, annual benefit,
-first cost), and then the table is sorted with IRR as the key. The top 6 projects required
$260K in capital funding, and the opportunity cost of capital based on the first rejected
project is 8.0%.
Project

IRR

E
H
C
G
I
B

15.00%
13.44%
12.00%
10.97%
10.00%
9.00%

Cumulative
First Cost
$40,000
$100,000
$130,000
$165,000
$240,000

$260,000

First Cost
$40,000
$60,000
$30,000
$35,000
$75,000
$20,000

Annual
Benefit
$11,933
$12,692
$9,878
$6,794
$14,058
$6,173

Life (years)
5
8
4
8
8
4


D
A

F

8.00%
7.01%
5.00$

$285,000
$300,000
$350,000

$25,000
$15,000
$50,000

$6,261
$4,429
$11,550

5
4
5

15-10
The IRR for each project is calculated using the Excel function = RATE (life, annual benefit,
-first cost, salvage value), and then the table is sorted with IRR as the key. With a budget of
$100,000, the top 5 projects should be done (6, 5, 4, 1, and 7). The opportunity cost of
capital based on the first rejected project is 16.41%.
Project

IRR

First Cost

6
5
4
1
7
3
2

26.16%
22.50%
21.25%
19.43%
19.26%
16.41%
16.00%

$20,000
$20,000
$20,000
$20,000
$20,000
$20,000
$20,000

Annual
Benefits
$5,800

$4,500
$4,500
$4,000
$4,000
$3,300
$3,200

Life (years)
10
25
15
20
15
30
20

Salvage
Value
$0
-$20,000
$0
$0
$10,000
$10,000
$20,000