Engineering Economic Analysis
Chapter 15  Selection of a MARR
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Sources of Capital
Money Generated from the Operations of the Firm
Profit
Depreciation
External Sources of Money
Loans
Mortgage Bonds
Choice of Source of Funds
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Preference of Capital
Companies prefer Internal to External financing
and debt to equity when external financing.
You need to raise $1M. Debt or Equity or does it matter?
Doesn't matter for fair valued assets.
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Equity Financing
Equity financing uses retained earnings raised from issuance
of stock to finance capital investments.
A company needs $10M and decides to sell its common stock. Current
price is $30/share, but investment bankers feel the price of $28/share is
better because of decreasing demand. Flotation costs (banker's fee,
etching fee, lawyers’ fee) is 6% of selling price; thus $26.32 How many
shares to sell to raise $10M?
Let X be the number of shares sold.
Flotation cost is 0.06 * 28 * X = 1.68X
Sales proceeds – flotation cost = Net proceeds
28X – 1.68X = $10M => X = 379,940 shares
Flotation cost for issuing common stock is
1.68 * 379,940 = $638,300.
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Debt Financing
Debt financing uses money raised through loans by an issuance
of bonds to finance a capital investment.
Task is to raise $10M by debt financing.
Bond financing ~ floatation cost is 1.8% of the $10M issue with face value
of $1000 sold at discount $985. Bond pays annual interest of 12%.
Term loan ~ $10M bank loan secured at 11%/year for 5 years.
How many $1000 par value bonds to raise $10M? 10,338.38
What is annual payments on bond and what is annual payment on loan?
$1,240,605.60
To net $10M; $10M/(1 – 0.018) = $10,183,300 paying $183,300 in
floatation costs. But bond sold at 1.5% discount, for bond financing
Total number of bonds sold $10,183,300/$985 = 10,338.38 bonds
Annual interest is $10,338,380 * 0.12 = $1,240,605.60 paid each year.
Term loan ~ $10M(A/P, 11%, 5) = $2,705,703.10 annual payment.
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MARR Factors
Project risk ~ higher perceived risk, higher MARR
Investment opportunity ~ MARR may be lowered to encourage
investment. Flexibility is important.
Tax structure ~ higher corporate taxes => higher MARR
Limited capital ~ tends to increase MARR. Opportunity cost
Market rates at other corporations ~ Keep in step.
Before-tax MARR = (1 – tax rate) * after-tax MARR
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Cost of Borrowed Money
Interest Rate
Prime
Financial strength of borrower
Duration
Cost of Capital
Common stock RoR
Mortgage bonds
Bank loans
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Weighted Average Cost of Capital
WACC= (equity fraction)(cost of equity capital)
+ (debt fraction)(cost of debt capital)
where equity capital can be preferred stock, common stock,
or retained earnings.
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Example 15-1
ROR
9%
7
11
Annual
$1.8M
1.4
6.6
$9.8 M
$20 million Bank loan
20
Mortgage bonds
60
Common stock
$100 million raised
After Tax analysis: Assume tax rate at 40%
Bank loan 
0.09(1 – 0.4) = 5.4%
Mortgage bonds 
0.07(1 – 0.4) = 4.2%
Dividends and retained earnings are not tax deductible.
$20M(5.4%) + 20M(4.2%) + 60M(11%) = $8.52M
Cost of capital = 8.52M/100M = 8.52%
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Table 15-1 Budget $1.2M
RoR's
Project
Cost ($K)
Estimated RoR %
45
1
150
30
2
50
45
3
50
38
4
100
40
35
5
200
35
30
6
100
28
7
200
18
25
8
250
25
20
9
300
20
18
10
300
10
15
11
400
15
10
12
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38
Opportunity
Cost
28
8
10
Selecting a MARR
Cost of Borrowed Money
Cost of Capital
Opportunity Cost
MARR should be the largest rate of the above costs.
Now we need to hedge for uncertainty in the estimates.
Probability => Risk
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Problem 15-2
A
B
C
First cost
$100
$50
$25
UAB
16.27
9.96
5.96
IRR
10%
15%
20%
Express the three mutually exclusive alternatives with10-year lives over
an unspecified MARR.
B-C  (UIRR 25 4 10)  9.61%
A-B  (UIRR 50 6.31 10)  4.47%
A-C  (UIRR 75 10.31 10)  6.25%
0 < MARR < 4.47
Choose A
4.47 < MARR < 9.61
Choose B
9.61 < MARR < 20
Choose C
MARR > 20%
Choose Do Nothing
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Example 15-3
n
A
B
0
-80
-80
1-10 11-20
10
20
13.86 10
14.05%
0
0
15.48%
10%
28.83
28.83
15%
-5
NPW
1.97 NPW
B–A
$6.97
At a MARR of 10% both are 28.83, both equally desirable, but
B is believed to have greater risk. Thus choose A.
At MARR 15%, A has negative return, but B is positive; thus
choose B.
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Problem 15-7
Budget = $70K
Project First Cost
1 $20K
2
30K
3
10K
4
5K
5
25K
6
15K
7
40K
Benefit
$11K
14K
6K
2.4K
13K
7K
21K
IRR (%)
(UIRR 20 11 3 0)  29.92
(UIRR 30 14 3 0)  18.91
(UIRR 10 6 3 0)  36.31
(UIRR 5 2.4 3 0)  20.71
(UIRR 25 13 3 0)  26.01
(UIRR 15 7 3 0)  18.91
(UIRR 40 21 3 0)  26.67
3 1 7 5 4 2 6
10 20 40 25 5 30 15
The opportunity cost of capital is (first reject project 5) at 26.1%
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Problem 15-8 with $500K Budget
Project
First Cost
UAB
Life IRR
1
2
$200K
$50K
15
(UIRR 200 50 15)  24.00%
2
5
300K
70K
10
(UIRR 300 70 10)  19.36
3
1
100K
40K
5
4
3
50K
12.5K 10
(UIRR 50 12.5 10)  21.41
5
7
250K
75K
5
(UIRR 250 75 5) 
6
4
150K
32K
20
(UIRR 150 32 20)  20.85
7
6
400K
125K
5
(UIRR 400 125 5)  16.99
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(UIRR 100 40 5) 
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28.65
15.24
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Problem 15-9
Project
First Cost
UAB
Life
IRR
E
40,000
11,933
5
15.00%
H
60,000
12692
8
13.44%
C
30,000
9878
4
12.00%
G
35,000
6794
8
10.97%
I
75,000
14058
8
10.00%
B
20,000
6173
4
9.00%
D
25,000
6261
5
8.00%
A
15,000
4429
4
7.01%
F
50,000
11,550
5
5.00%
Budget =
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E2 = RATE(life, UAB, -first cost)
MARR
260,000 for first 6 projects.
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Problem 16-11
Parabolic Benefit/Cost equation:
PWB2 – 22PWC + 44 = 0; find PWC for optimal size
project.
Let y = PWB and x = PWC.
Then y2 - 22x + 44 = 0; Solve for slope and set slope to 1.
2yy' - 22 = 0;
y' = 11/y = 1 => y = 11 and x = 7.5
112 -22x +44 = 0 => x = 7.5 = PWC
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Problem 16-26
MARR = 12%
A
B
C
$9500
$18,500
$22,000
Annual savings
3200
5000
9800
Annual costs
1000
2750
6400
Salvage value
6000
4200
14000
15
15
15
First Cost
Life
Conventional B/C and incremental analysis C-A
PW numerator
PW denominator
B/C ratio
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B
C
$21,794.77
$34,054.32
$66,746.47
152,14.69
36,462.55
63,031.79
0.93
1.06
1.43
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Determining the MARR
Suppose cost of capital is 10% (borrowing rate) and lending rate is 6%
(opportunity cost) with budget at) $40K b) $60K and c) $0K,
determine MARR using ranked projects by their IRR.
a) With $40K budget, invest in
Project First
UAB
IRR (%)
Cost
1,2,3,4. MARR = 8%.
b) With $60K, invest in projects
1
10K
$12K
20
1,2,3,4,5. Lend $10K at 6%.
2
10K
$11.5K
15
MARR = 6%.
3
10K
$11K
10
c) Borrow for projects 1 & 2.
4
10K
$10.8K
8
MARR = 10%
5
10K
$10.7K
7
lending < MARR < borrowing
6
10K
$10.4K
4
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Example
Calculate the after-tax cost of debt for the following:
a) Interest rate is 12%; tax rate is 25% ¾ * 12 = 9%
b) Interest rate is 14%; tax rate is 34% 0.66 *14 = 9.24%
c) Interest rate is 15%; tax rate is 40% 0.6 * 15 = 9%
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Example
N
A
B
C
0
-$2000
-$3000
-$1000
1
1000
4000
1400
-$1000
2
1000
-100
1090
3
1000
IRR (%)
23.38
32.45
9
33.33
D
With budget at $3500 and lend out remaining funds at 10%, and goal is to
maximize future worth at n = 3.
FWA(10%) = $648, FWB(10%) = $847; FWC(10%) = $190.08;
FWD(10%) = -$11 A & C for $838 + 500(F/P, 10%, 3) = $1503.58
B  847 + 500(F/P, 10%, 3) = $1512.50
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Example
You need $10M in capital.
Capital stock sales
 $5M at 13.7%
Use of retained earnings  $2M at 8.9%
Debt financing with bonds  $3M at 7.5%.
Historical D-E mix of 40% from debt costing 7.5% and 60%
from equity costing 10%.
Calculate historical WACC and current WACC.
Historical: 0.6(10) + 0.4(7.5) = 9%
Current: (5/10)(13.7) + (2/10)(8.9) + (3/10)(7.5) = 10.88%.
After-tax analysis is appropriate.
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Example Debt Capital
You need $10M in debt capital by issuing 5,000 $1K
10-year bonds paying 8%/year with 50% tax rate. Bonds
are discounted 2% for quick sale. Ignore flotation costs.
Compute cost of debt capital before and after taxes.
980 = 80(P/A, i%, 10) + 1000(P/F, i%, 10)
(UIRR 980 80 10 1000)  8.3% Before tax
(UIRR 980 40 10 1000)  4.24% After-tax
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Debt Capital
You buy a $20K 10-year asset by putting $10K down and
borrowing $10K at 6%/year by paying the interest each
year and the $10K in year 10. Tax rate is 42%. Compute
after tax cost of debt capital.
Deduction for interest is $600 at tax rate 42% leaving ATCF
600(1 – 0.42) = $348
(UIRR 10000 348 10 10000)  3.48%.
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Inflation
1. A machine costing $2550 4 years ago now costs $3930
with general inflation at 7% per year. Calculate the true
percentage increase in the cost of the machine.
a) 14.95% b) 54.12% c) 35.11% d) 7% e) 17.58%
2. If you want a 7% inflation-free return on your investment with
f = 9% per year, your actual interest rate must be
a) 16% b) 20% c) 12% d) 15% e) 14%
3. I want $25K per year forever in R$ when I die for my family.
Insurer offers 7% per year while inflation is expected to be 4% per
year. First payment is 1 year after my death. How much
insurance do I need?
a) $866K b) $357K c) $625K d) $841K
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Cost of Capital
250M shares priced at $29.30
20M preferred stock priced at $40.50
150M selling at $101.75 per 100
500M loan at 4.5% interest.
Source
Amount
Price
Total
Weight
Common
stock
250M
29.30
$7,235E6
83.36%
Preferred
stock
20M
40.50
$810M
9.22%
Bond
150M
$1.0175 $152,625K
1.74%
Loan
$500M
$1.00
$500M
5.69%
$8.787.625
100%
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