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Chapter 19 - Financing and Valuation
CHAPTER 19
Financing and Valuation
Answers to Problem Sets
1. Market values of debt and equity are:
D = .9 x 75 = $67.5 million
E = 42 x 2.5 = $105 million
D/V = $67.5/(67.5 + 105) = .39
WACC = .09(1 - .35).39 + .18(.61) = .1325, or 13.25%
Est. Time: 01 – 05
2.
Step 1: r = .09(.39) + .18(.61) = .145.
Step 2: rD = .086, rE = .145 + (.145 - .086)(15/85) = .155.
Step 3: WACC = .086(1 - .35).15 + .155(.85) = .14.
Est. Time: 01 – 05
3.
a.
False. The ratio of the debt to value is constant over the project’s
economic life, but the amount of debt need not be fixed.
b.
True
c.
True
Est. Time: 01 – 05
4.
The method values the equity of a company by discounting cash flows to
stockholders at the cost of equity. See Section 19-2 for more details. The method
assumes that the debt-to-equity ratio will remain constant.
Est. Time: 01 – 05
5.
a.
True
b.
False if interest tax shields are valued separately
c.
True
Est. Time: 01 – 05
6.
APV 5 base-case NPV ± PV financing side effects.
a.
APV = 0 - .15(500,000) = -75,000.
19-1
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Chapter 19 - Financing and Valuation
b.
APV = 0 + 76,000 = +76,000.
Est. Time: 01 – 05
7.
a.
12%; for an all-equity-financed, the opportunity cost of capital is the
expected rate of return on the company’s shares.
b.
rE = .12 + (.12 - .075)(30/70) = .139, WACC = .075(1 - .35)(.30) + .139(.70)
= .112, or 11.2%.
Est. Time: 01 – 05
8.
a.
Base-case NPV = -1,000 + 1200/1.20 = 0.
b.
PV tax shield = (.35 x .1 x .3(1000))/1.1 = 9.55.
APV = 0 + 9.55 = $9.55.
Est. Time: 01 – 05
9.
No. The more debt you use, the higher rate of return equity investors will
require. (Lenders may demand more also.) Thus there is a hidden cost of the
“cheap” debt: It makes equity more expensive.
Est. Time: 01 – 05
10.
Patagonia does not have 90% debt capacity. KCS is borrowing $45 million partly
on the strength of its existing assets. Also the decision to raise bank finance for
the purchase does not mean that KCS has changed its target debt ratio. An APV
valuation of Patagonia would probably assume a 50% debt ratio.
Est. Time: 01 – 05
11.
If the bank debt is treated as permanent financing, the capital structure
proportions are:
Bank debt (rD = 10 percent)
Long-term debt (rD = 9 percent)
Equity (rE = 18 percent, 90 x 10 million shares)
$280
9.4%
1800
60.4
900
30.2
$2,980
100.0%
WACC* = [0.10  (1 - 0.35)  0.094] + [0.09  (1 - 0.35)  0.604]
+ [0.18  0.302]
= 0.096 = 9.6%.
19-2
© 2014 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution
in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
Est. Time: 01 – 05
12.
Forecast after-tax incremental cash flows as explained in Section 6-1. Interest is
not included; the forecasts assume an all-equity financed firm.
Est. Time: 01 – 05
13.
Calculate APV by subtracting $4 million, the other costs of financing, from basecase NPV.
Est. Time: 01 – 05
14.
We make three adjustments to the balance sheet:
 Ignore deferred taxes; this is an accounting entry and represents neither a
liability nor a source of funds.
 “Net out” accounts payable against current assets.
 Use the market value of equity (7.46 million x $46).
Now the right-hand side of the balance sheet (in thousands) is:
Short-term debt
Long-term debt
Shareholders’ equity
Total
$75,600
208,600
343,160
$627,360
The after-tax weighted-average cost of capital formula, with one element for each
source of funding, is:
WACC = [rD – ST  (1 – Tc) (D-ST/V)] + [rD – LT  (1 – Tc) (D − LT/V)] + [rE  (E/V)]
WACC = [0.06  (1 – 0.35)  (75,600/627,360)] + [0.08  (1 – 0.35) 
(208,600/627,360)]
+ [0.15  (343,160/627,360)]
= 0.004700 + 0.017290 + 0.082049 = 0.1040 = 10.40%
Est. Time: 06 – 10
19-3
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
15.
Assume that short-term debt is temporary. From Problem 14:
Long-term debt
Shareholder equity
Total
$208,600
343,160
$551,760
Therefore:
D/V = $208,600/$551,760 = 0.378
E/V = $343,160/$551,760 = 0.622
Step 1:
r = rD (D/V) + rE (E/V) = (0.08  0.378) + (0.15  0.622) = 0.1235
Step 2:
rE = r + (r – rD) (D/E) = 0.1235 + (0.1235 – 0.08)  0.403 = 0.1410
Step 3:
WACC = [rD  (1 – TC)  (D/V)] + [rE  (E/V)]
= (0.08  0.65  0.287) + (0.1410  0.713) = 0.1155 = 11.55%
Est. Time: 06 – 10
16.
Base case NPV = –$1,000 + ($600/1.12) + ($700/1.122) = $93.75 or $93,750.
Year
1
2
Debt
Outstanding at
Start of Year
300
150
Interest
24
12
Interest
Tax Shield
7.20
3.60
PV
(Tax Shield)
6.67
3.09
APV = $93.75 + $6.67 + $3.09 = 103.5 or $103,500.
Est. Time: 06 – 10
17.
a.
Base-case NPV = –$1,000,000 + ($95,000/0.10) = –$50,000.
PV(tax shields) = 0.35  $400,000 = $140,000.
APV = –$50,000 + $140,000 = $90,000.
b.
PV(tax shields, approximate) = (0.35  0.07  $400,000)/0.10 = $98,000.
APV = –$50,000 + $98,000 = $48,000.
The present value of the tax shield is higher when the debt is fixed and
therefore the tax shield is certain. When borrowing a constant proportion of
the market value of the project, the interest tax shields are as uncertain as
19-4
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
the value of the project, and therefore must be discounted at the project’s
opportunity cost of capital.
Est. Time: 06 – 10
18.
The immediate source of funds (i.e., both the proportion borrowed and the
expected return on the stocks sold) is irrelevant. The project would not be any
more valuable if the university sold stocks offering a lower return. If borrowing
is a zero-NPV activity for a tax-exempt university, then base-case NPV equals
APV, and the adjusted cost of capital r* equals the opportunity cost of capital
with all-equity financing. Here, base-case NPV is negative; the university
should not invest.
Est. Time: 01 – 05
19.
a.
Base-case NPV   $10 
10
$1.75
 1.12
t 1
t
  $0.11 or – $112,110.
APV = base-case NPV + PV(tax shield).
PV(tax shield) is computed from the following table:
1
Debt Outstanding
at Start of Year
$5,000
2
4,500
360
126
108.02
3
4,000
320
112
88.91
4
3,500
280
98
72.03
5
3,000
240
84
57.17
6
2,500
200
70
44.11
7
2,000
160
56
32.68
8
1,500
120
42
22.69
9
1,000
80
28
14.01
10
500
40
14
6.48
Year
$400
Interest
Tax Shield
$140
Present Value
of Tax Shield
$129.63
Interest
Total
575.74
APV = –$112,110 + $575,740 = $463,630.
19-5
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
b.
APV = base-case NPV + PV(tax shield) – equity issue costs
= –$112,110 + $575,740 – $400,000 = $63,630.
Est. Time: 06 – 10
20.
Spreadsheet exercise; answers will vary depending on how the student varies
each item.
Est. Time: 06 – 10
21.
Note the following:



The costs of debt and equity are not 8.5% and 19%, respectively. These
figures assume the issue costs are paid every year, not just at issue.
The fact that Bunsen can finance the entire cost of the project with debt is
irrelevant. The cost of capital does not depend on the immediate source of
funds; what matters is the project’s contribution to the firm’s overall
borrowing power.
The project is expected to support debt in perpetuity. The fact that the first
debt issue is for only 20 years is irrelevant.
Assume the project has the same business risk as the firm’s other assets.
Because it is a perpetuity, we can use the firm’s weighted-average cost of
capital. If we ignore issue costs:
WACC = [rD  (1 – TC)  (D/V)] + [rE  (E/V)]
WACC = [0.07  (1 – 0.35)  0.4] + [0.14  0.6] = 0.1022 = 10.22%
Using this discount rate:
NPV  $1,000,000 
$130,000
 $272,016
0.1022
The issue costs are:
Stock issue:
Bond issue:
0.050  $1,000,000 = $50,000
0.015  $1,000,000 = $15,000
Debt is clearly less expensive. Project NPV net of issue costs is reduced to:
($272,016 – $15,000) = $257,016. However, if debt is used, the firm’s debt ratio
will be above the target ratio, and more equity will have to be raised later. If debt
financing can be obtained using retaining earnings, then there are no other issue
costs to consider. If stock will be issued to regain the target debt ratio, an
additional issue cost is incurred.
A careful estimate of the issue costs attributable to this project would require a
comparison of Bunsen’s financial plan with as compared to without this project.
19-6
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
Est. Time: 11 – 15
22.
Disagree. The Goldensacks calculations are based on the assumption that the
cost of debt will remain constant and that the cost of equity capital will not
change even though the firm’s financial structure has changed. The former
assumption is appropriate while the latter is not.
Est. Time: 01 – 05
23.
Latest
Year
0
40,123.0
22,879.0
8,025.0
9,219.0
5,678.0
3,541.0
1,239.4
2,301.7
1
36,351.0
21,678.0
6,797.0
7,876.0
5,890.0
1,986.0
695.1
1,290.9
2
30,155.0
17,560.0
5,078.0
7,517.0
5,670.0
1,847.0
646.5
1,200.6
Forecast
3
28,345.0
16,459.0
4,678.0
7,208.0
5,908.0
1,300.0
455.0
845.0
4
29,982.0
15,631.0
4,987.0
9,364.0
6,107.0
3,257.0
1,140.0
2,117.1
5
30,450.0
14,987.0
5,134.0
10,329.0
5,908.0
4,421.0
1,547.4
2,873.7
1.
2.
3.
4.
5.
6.
7.
8.
Sales
Cost of Goods Sold
Other Costs
EBITDA (1 – 2 – 3)
Depreciation and Amortization
EBIT (pretax profit) (4 – 5)
Tax at 35%
Profit after Tax (6 – 7)
9.
10.
Change in Working Capital
Investment
(change in gross PP&E)
Free Cash Flow (8 + 5 – 9 – 10)
784.0
-54.0
-342.0
-245.0
127.0
235.0
6,547.0
648.7
7,345.0
-110.1
5,398.0
1,814.6
5,470.0
1,528.0
6,420.0
1,677.1
6,598.0
1,948.7
PV Free Cash Flow, Years 1–
4
PV Horizon Value
PV of Company
3,501.6
15,480.0
18,981.7
11.
Horizon Value in Year 4
24,358.1
The total value of the equity is: $18,981.7 – $5,000 = $13,981.7.
Value per share = $13,981.7/865 = $16.16.
Est. Time: 06 – 10
24.
a.
For a one-period project to have zero APV:
APV  C0 
(T  r  D)
C1
 C D
0
1  rA
1  rD
Rearranging gives:
 D
C1
 1  r  ( TC  rD ) 
 C0
  C0



 1  rA 


 1  rD 
For a one-period project, the left-hand side of this equation is the project
IRR. Also, (D/ -C0) is the project’s debt capacity. Therefore, the minimum
acceptable return is:
19-7
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
 1  rA
r *  rA  ( TC  rD  L )
 1  rD



 1.0984 
r *  0.0984  (0.35  0.06  0.20)
  .09405 .
 1.06 
Est. Time: 06 – 10
b.
25.
Fixed debt levels, without rebalancing, are not necessarily better for
stockholders. Note that, when the debt is rebalanced, next year’s interest tax
shields are fixed and, thus, discounted at a lower rate. The following year’s
interest is not known with certainty for one year and, hence, is discounted for one
year at the higher risky rate and for one year at the lower rate. This is much
more realistic since it recognizes the uncertainty of future events.
Est. Time: 06 – 10
26.
The table below is a modification of Table 19.1 based on the assumption that
after Year 7:





Sales remain constant (that is, growth = 0%)
Costs remain at 76.0% of sales
Depreciation remains at 14.0% of net fixed assets
Net fixed assets remain constant at 93.8
Working capital remains at 13.0% of sales
TABLE 19.1 Free Cash Flow Projections and Company Value for Rio Corporation ($ millions)
Latest
Year
Forecast
0
1
2
3
4
5
6
7
8
1.
2.
3.
4.
5.
6.
7.
Sales
Cost of Goods Sold
EBITDA (1 - 2)
Depreciation
Profit before Tax (EBIT) (3 - 4)
Tax
Profit after Tax (5 - 6)
83.6
63.1
20.5
3.3
17.2
6.0
11.2
89.5
66.2
23.3
9.9
13.4
4.7
8.7
95.8
71.3
24.4
10.6
13.8
4.8
9.0
102.5
76.3
26.1
11.3
14.8
5.2
9.6
106.6
79.9
26.6
11.8
14.9
5.2
9.7
110.8
83.1
27.7
12.3
15.4
5.4
10.0
115.2
87.0
28.2
12.7
15.5
5.4
10.1
118.7
90.2
28.5
13.1
15.4
5.4
10.0
118.7
90.2
28.5
13.1
15.4
5.4
10.0
8.
9.
10.
Investment in Fixed Assets
Investment in Working Capital
Free Cash Flow (7 + 4 - 8 - 9)
11.0
1.0
2.5
14.6
0.5
3.5
15.5
0.8
3.2
16.6
0.9
3.4
15.0
0.5
5.9
15.6
0.6
6.1
16.2
0.6
6.0
15.9
0.4
6.8
13.1
0.0
10.0
PV Free Cash Flow, Years 1–7
PV Horizon Value
PV of Company
24.0
60.7
84.7
(Horizon Value in Year 7)
110.9
19-8
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
Assumptions:
Sales Growth (%)
Costs (% of sales)
Working Capital (% of sales)
Net Fixed Assets (% of sales)
Depreciation (% net fixed assets)
6.7
75.5
13.3
79.2
5.0
Tax Rate, %
Cost of Debt, % (rD)
Cost of Equity, % (rE)
Debt Ratio (D/V)
WACC, %
Long-Term Growth Forecast, %
35.0
6.0
12.4
0.4
9.0
0.0
Fixed Assets and Working Capital
Gross Fixed Assets
Less Accumulated Depreciation
Net Fixed Assets
Net Working Capital
95.0
29.0
66.0
11.1
7.0
74.0
13.0
79.0
14.0
7.0
74.5
13.0
79.0
14.0
7.0
74.5
13.0
79.0
14.0
4.0
75.0
13.0
79.0
14.0
4.0
75.0
13.0
79.0
14.0
4.0
75.5
13.0
79.0
14.0
3.0
76.0
13.0
79.0
14.0
109.6
38.9
70.7
11.6
125.1
49.5
75.6
12.4
141.8
60.8
80.9
13.3
156.8
72.6
84.2
13.9
172.4
84.9
87.5
14.4
188.6
97.6
91.0
15.0
204.5
110.7
93.8
15.4
Est. Time: 11 – 15
27.
The PV of HK$17.5 per year for 10 years at 8% is $HK117.4 million. NPV(basecase, all-equity) = + HK$17.4. You could also increase cash flows by 4% per
year and discount at the nominal rate of 1.08×1.04 – 1 = .123 or 12.3%.
a. The PV of interest tax shields is $HK4.70 million at 7.5%, as shown below.
APV = 17.4 + 4.7 = + $HK22.1. Notice that the interest payments are nominal
and can be discounted at the 7.5% cost of debt. Also the ratio of debt to APV,
including investment, is 50/122.1 = .4095 or 41%.
Year
1
2
3
4
5
6
7
8
9
10
Project value
(real)
start of year
Project
value
(nominal)
Principal
start of
year
117.43
109.32
100.57
91.11
80.90
69.87
57.96
45.10
31.21
16.20
117.43
113.69
108.77
102.49
94.64
85.01
73.34
59.35
42.71
23.06
50.00
48.41
46.32
43.64
40.30
36.20
31.23
25.27
18.19
9.82
Interest
3.75
3.63
3.47
3.27
3.02
2.71
2.34
1.90
1.36
0.74
Tax
shield
1.13
1.09
1.04
0.98
0.91
0.81
0.70
0.57
0.41
0.22
$5.79
19-9
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
0.0
76.0
13.0
79.0
14.0
217.6
123.9
93.8
15.4
Chapter 19 - Financing and Valuation
b. The following table sets debt service as a growing annuity, starting at $HK6.21
million and growing at the rate of inflation. The PV of debt service is $HK50, so
the debt is paid off at the end of year 10. The PV of interest tax shields increases
to $HK7.3. APV = 17.4 + 7.3 = $HK24.3.
Year
1
2
3
4
5
6
7
8
9
10
11
Principal
50.00
47.54
44.65
41.28
37.39
32.93
27.84
22.07
15.55
8.22
0.00
Debt
service
6.21
6.46
6.72
6.99
7.27
7.56
7.86
8.17
8.50
8.84
Principal
Interest payment
3.75
3.57
3.35
3.10
2.80
2.47
2.09
1.66
1.17
0.62
$50.00
c.
2.46
2.89
3.37
3.89
4.46
5.09
5.77
6.52
7.33
8.22
Tax
shield
1.50
1.43
1.34
1.24
1.12
0.99
0.84
0.66
0.47
0.25
$7.29
Assume a 41% market-value debt ratio and a D/E ratio of 41/59 = .695 or 69.5%.
The nominal cost of equity is rE = 12.3 + (12.3 – 7.5).695 = 15.6%. WACC =
7.5× (1 - .3)×.41 + 15.6×.59 = 11.4%. The cash flows are a 10-year annuity
growing at 4%. PV, using the growing annuity formula from Ch. 4, is $HK117.6.
This procedure assumes that debt remains at 41% of project value throughout
the project’s economic life.
d. Just subtract $HK4 million from project value.
Est. Time: 11 – 15
28.
Just calculate the NPVs of the loans and add the NPVs to the APVs of the
projects that the loans support. Discount after-tax debt service (at the belowmarket rates) at the after-tax market borrowing rate. See the Appendix to this
chapter.
Est. Time: 11 – 15
19-10
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in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 19 - Financing and Valuation
Appendix Problems
1.
The award is risk free because it is owed by the U.S. government. The after-tax
amount of the award is: 0.65 × $16 million = $10.40 million.
The after-tax discount rate is: 0.65 × 0.055 = 0.03575 = 3.575%.
The present value of the award is: $10.4 million/1.03575 = $10.04 million.
Est. Time: 06 – 10
2.
The after-tax cash flows are: 0.65 × $100,000 = $65,000 per year.
The after-tax discount rate is: 0.65 × 0.09 = 0.0585 = 5.85%.
The present value of the lease is equal to the present value of a five-year annuity
of $65,000 per year plus the immediate $65,000 payment:
$65,000 × [annuity factor, 5.85%, 5 years] + $65,000 =
($65,000 × 4.2296) + $65,000 = $339,924
Est. Time: 06 – 10
19-11
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