A B C D E F G H

1 Tool Kit Chapter 9 12/8/2012

2
3 The Cost of Capital
4
5 9-1 The Weighted Average Cost of Capital
6
7 The cost of capital is the weighted average cost of the debt, preferred stock, and common equity that
8 the firm uses to finance its assets, or its WACC.
9
10 Definitions
11 WACC = Weighted average cost of capital
12 = wd rd(1 – T) + wps rps + ws rs
13
14 rd = Cost of debt
15 rps
= Cost of preferred stock
16 rs = Cost of stock (common equity)
17
18 wd = Percent of target capital structure financed with debt
19 w ps
= Percent of target capital structure financed with preferred stock
20 w s
= Percent of target capital structure financed with stock (common equity)
21
22 T = Tax rate
23
24
25 9-2 Choosing Weights for the Weighted Average Cost of Capital
26
27 Figure 9-1
28 MicroDrive, Inc.: Selected Capital Structure Data
29 (Millions of Dollars, December 31, 2013)
30 Investor-Supplied Capital
31 Book Market
32 Percent Book Percent Market Percent
33 Liabilities and Equity of Total Value of Total Value of Total
34 Accounts payable $ 200 5.6%
35 Notes payable 280 7.9% $ 280 9.2% $ 280 9.9%
36 Accruals 300 8.5%
37 Total C.L. $ 780 22.0%
38 Long-term debt 1,200 33.8% 1,200 39.3% 1,200 42.4%
39 Total liabilities $1,980 55.8%
40 Preferred stock 100 2.8% 100 3.3% 100 3.5%
41 Common stock 500 14.1%
42 Retained earnings 970 27.3%
43 Total common equity $1,470 41.4% $1,470 48.2% $1,250 44.2%
44 Total L&E $3,550 100.0% $3,050 100.0% $2,830 100.0%
45
46 Other Data (Millions, except per share data):
47 Number of common shares outstanding = 50
48 Price per share of common stock = $25.00
49 Number of preferred shares outstanding = 1
 A B C D E F G H
50 Price per share of preferred stock = $100.00
51
52 Notes:
53 1. The market value of the notes payable is equal to the book value. Some of the long-term bonds sell at a discount and
54 some sell at a premium, but their aggregate market value is approximately equal to their aggregate book value.
55
56 2. The common stock price is $25 per share. There are 50 million shares outstanding, for a total market value of equity
57 of $25(50) = $1,250 million.
58 3. The preferred stock price is $100 per share. There are 1 million shares outstanding, for a total market value of
59 preferred of $100(1) = $100 million.
60
61
62
63 9-3 After-Tax Cost of Debt: rd (1 − T) and rstd (1 − T)
64
65 The relevant cost of debt is the after-tax cost of new debt, taking account of the tax deductibility of
66 interest. The after-tax cost is calculated by multiplying the interest rate (or the before-tax cost of debt)
67 times one minus the tax rate.
68
69
70 MicroDrive's Short-Term Debt
71
72 MicroDrive has notes payable with the following interest rate:
73
74 rstd = 10.000%
75
76
77 MicroDrive's Actual Long-Term Debt
78
79 MicroDrive has outstanding bonds with a 9% annual coupon rate, 15 years remaining until maturity,
80 and a face value of $1,000. The bonds make semiannual coupon payments and currently are trading in
81 the market at a price of $1000.
82
83 To estimate the cost of debt, use the RATE function to find the yield on the bonds:
84
85 Number of years to maturity 15
86 Number of payments per year 2
87 Annual coupon rate 9%
88 Par value $1,000
89 Current price = PV = $1,000.00
90
91 N= 30
92 PMT = $45
93 FV = $1,000
94
95 I/YR = rd = 4.500%
96
97 Annualized rd = 9.000%
98
99
100 Hypothetical Example for a Bond not at Par
101
 A B C D E F G H
102 Use the RATE function to find the yield on the bonds with the following information:
103
104 Number of years to maturity 15
105 Number of payments per year 2
106 Annual coupon rate 9%
107 Par value $1,000
108 Current price = PV = $923.14
109
110 N= 30
111 PMT = $45
112 FV = $1,000
113
114 I/YR = rd = 5.0%
115
116 Annualized rd = 10.0%
117
118
119 The Impact of a High Probability of Default
120
121 Use the RATE function to find the yield on the bonds with the following information:
122
123 Number of years to default 14
124 Recovery percentage at default 70%
125 Number of payments per year 2
126 Annual coupon rate 9%
127 Par value $1,000
128 Current price = PV = $1,000.00
129
130 N= 28
131 PMT = $45
132 FV = $700
133
134 I/YR = rd = 3.9%
135
136 Annualized rd = 7.8%
137
138
139 The After-Tax Cost of Debt
140
141 Find the after-tax cost of debt; MicroDrive has a 40% marginal tax rate.
142
143 Tax rate = 40%
144 Short-term debt: rstd = 10%
145 Long-term debt: rd = 9%
146
147 After-tax cost of debt = r (1 – T)
148
149 Short-term debt: rstd (1-T) = 6.000%
150 Long-term debt: rd (1-T) = 5.400%
151
152
153 Flotation Costs and the Cost of Debt
154
 A B C D E F G H
155 Consider the issuance of a 30-year, $1,000 par value bond with a coupon rate of 9%, paid semiannually.
156 The tax rate is 40%, and the flotation costs are 1% of the value of the issue. The bond will initially sell
at its par value.
157
158
159 Years to maturity = 30
160 Flotation percentage cost (F) = 1.00%
161 Par value = $1,000
162 Annual coupon payment = 9.00%
163 Tax rate = 40%
164 Maturity payment = Par = $1,000
165 Number of payments per year = 2
166
167 First, calculate the after-tax coupon payments and the net proceeds after the flotation costs.
168
(Coupon (1 – Tax
169 After-tax coupon payment = pmt.) rate)

170 After-tax coupon payment = $45 60% = $27.00

171
172
173 Net proceeds after flotation costs = (Par value) (1 – F)
174 Net proceeds after flotation costs = $1,000 99% = $990
175
176
177 Now find the rate that the company pays, based on its net proceeds after flotation costs and its after-tax
178 payments.
179
180 Ignoring the tax shield due to amortization of flotation costs:
181
182 Number of coupon payments = N= 60
183 After-tax coupon payment = 27.00
 A B C D E F G H
184 Net proceeds after flotation costs = PV= $990.00
185 Payment of face value at maturity = FV= $1,000.0
186
187 Periodic after-tax cost of debt = Rate = 2.734%
188 Nominal annual after-tax cost of debt = 5.468%
189
190
191 Now find the rate that the company pays, based on its net proceeds after flotation costs
192 (including the amortization of flotation costs) and its after-tax payments.
193
194 Incorporating the tax shield due to amortization of flotation costs:
195
196 Number of coupon payments = N= 60
197 After-tax coupon payment = 27.00
198 Amortized flotation cost/period = $0.17
199 Tax shield from flotation/period = $0.07
200 Net payment, after tax = PMT= $26.93
201 Net proceeds after flotation costs = PV= $990.00
202 Payment of face value at maturity = FV= $1,000.0
203
204 Periodic after-tax cost of debt = Rate = 2.727%
205 Nominal annual after-tax cost of debt = 5.455%
206
207 Notice that this after-tax cost of debt is only slightly higher than the after-tax cost of debt where
208 flotation costs are ignored. Therefore, analysts often ignore the flotation costs of debt.
209
210
211 9-4 Cost of Preferred Stock, rps
212
213 The cost of preferred stock is simply the preferred dividend divided by the price the company will
214 receive if it issues new preferred stock. No tax adjustment is necessary, as preferred dividends are not
215 tax deductible.
216
217
What is the cost of preferred stock for a company that pays a preferred dividend of $8 per share if the
218 company could sell new preferred with a par value of $100 and a flotation cost of 2%?
219
220
221 Pref. Dividend $8.00
222 Par value $100.00
223 Flotation % 2.0%
224 Net preferred issue price $98.00
225
226 rps = DivPref ÷ Net Pref. Price
227 r ps
= $8.00 ÷ $98.00 = 8.16%
228
229
 A B C D E F G H
230 9-5 Cost of Common Stock: The Market Risk Premium, RP M
231
232 Before addressing the required return of an individual stock, what is the required return for the stock
233 market? What is the Market Risk Premium (RP M), which is excess return investor require to induce
234 them to invest in the stock market rather than a long-term T-bond?
235
236 There are 3 methods to estimate the market risk premium. (1) Use historical market data as an
237 estimate for the current risk premium. (2) Ask experts. (3) Estimate a forward looking risk premium,
238 found as the differential between expected returns on the S&P 500 over some forecasted future period
and the current long-term bond rate.
239
240
241
242 Historical Risk Premiums
243
244 Many analysts use data provided by Ibbotson Associates, which has collected data from 1926.
245 Ibbotson publishes information annually that enables use of different periods and thus different
246 historical risk premiums. Ibbotson recommends using the longest set of data, but others disagree,
247 arguing that events that occurred back in the period of say 1926 to 1966 are less relevant than events
that occurred during the last 50 or so years.
248
249
250
251 Ibbotson Historical Risk Premium: 1926-Current Date
252 Average
253 ArithmeticGeometric
254 Stock market return (return on large stocks) 11.80% 9.80%
255 Risk-free rate:
256 20-year T-bond yield at beginning of year 5.20% 5.10%
257
258 Historical risk premium:
259 RM minus T-bond yield = 6.60% 4.70%
260
261
262 Our Historical Risk Premium: 1968-Current Date (Data shown results)
263
264 Average
265 Arithmetic Geometric
266 Stock market return (S&P 500) 10.85% 9.34%
267 Risk-free rate:
268 10-year Treasury contestant maturity yield at beginning of year 6.96% 6.93%
269
270 Historical risk premium:
271 RM minus T-bond yield = 3.90% 2.36%
272
273
274 Data for Our Historical Risk Premium: 1968-Current Date
275
276
10-Year T-bond (Treasury 10-year
277 S&P 500
constant maturity)
Return Reported First Day Actual
278 Year
on yield on of Year, Return
Total Return,
Index Level rM Capital Gains
 A B C D E F G
of Year, H
Return
on yield on
279 Total Return, Dividend last day of Required During Year,
280 Index Level rM Capital Gains s year rRF Actual rRF
281
282 1.89%
283 2011 1257.60 2.11% 0.00% 2.11% 1.89% 3.30% 16.9%
284 2010 1257.64 15.06% 12.78% 2.28% 3.30% 3.85% 8.9%
285 2009 1115.1 26.46% 23.45% 3.01% 3.85% 2.25% -11.1%
286 2008 903.25 -37.00% -38.49% 1.49% 2.25% 4.04% 21.6%
287 2007 1468.36 5.49% 3.53% 1.96% 4.04% 4.71% 10.9%
288 2006 1418.3 15.79% 13.62% 2.17% 4.71% 4.39% 1.6%
289 2005 1248.29 4.91% 3.00% 1.91% 4.39% 4.24% 2.9%
290 2004 1211.92 10.88% 8.99% 1.89% 4.24% 4.27% 4.5%
291 2003 1111.92 28.70% 26.38% 2.32% 4.27% 3.83% 0.0%
292 2002 879.82 -22.10% -23.37% 1.27% 3.83% 5.07% 16.9%
293 2001 1148.08 -11.88% -13.04% 1.16% 5.07% 5.12% 5.6%
294 2000 1320.28 -9.11% -10.14% 1.03% 5.12% 6.45% 19.2%
295 1999 1469.25 21.04% 19.53% 1.51% 6.45% 4.65% -10.2%
296 1998 1229.23 28.58% 26.67% 1.91% 4.65% 5.75% 16.2%
297 1997 970.43 33.36% 31.01% 2.35% 5.75% 6.43% 12.8%
298 1996 740.74 23.07% 20.26% 2.81% 6.43% 5.58% -1.8%
299 1995 615.93 37.43% 34.11% 3.32% 5.58% 7.84% 30.5%
300 1994 459.27 1.31% -1.54% 2.85% 7.84% 5.83% -10.7%
301 1993 466.45 9.99% 7.06% 2.93% 5.83% 6.70% 14.9%
302 1992 435.71 7.67% 4.46% 3.21% 6.70% 6.71% 6.8%
303 1991 417.09 30.55% 26.31% 4.24% 6.71% 8.08% 21.2%
304 1990 330.22 -3.17% -6.56% 3.39% 8.08% 7.93% 6.6%
305 1989 353.4 31.49% 27.25% 4.24% 7.93% 9.14% 20.7%
306 1988 277.72 16.81% 12.40% 4.41% 9.14% 8.83% 6.1%
307 1987 247.08 5.23% 2.03% 3.20% 8.83% 7.23% -6.2%
308 1986 242.17 18.47% 14.62% 3.85% 7.23% 9.00% 26.3%
309 1985 211.28 32.16% 26.33% 5.83% 9.00% 11.55% 37.4%
310 1984 167.24 6.27% 1.40% 4.87% 11.55% 11.82% 14.3%
311 1983 164.93 22.51% 17.27% 5.24% 11.82% 10.36% -2.0%
312 1982 140.64 21.41% 14.76% 6.65% 10.36% 13.98% 52.4%
313 1981 122.55 -4.91% -9.73% 4.82% 13.98% 12.43% -0.6%
314 1980 135.76 32.42% 25.77% 6.65% 12.43% 10.33% -6.9%
315 1979 107.94 18.44% 12.31% 6.13% 10.33% 9.15% -0.9%
316 1978 96.11 6.56% 1.06% 5.50% 9.15% 7.78% -3.8%
317 1977 95.1 -7.18% -11.50% 4.32% 7.78% 6.81% -1.5%
318 1976 107.46 23.84% 19.15% 4.69% 6.81% 7.76% 16.7%
319 1975 90.19 37.20% 31.55% 5.65% 7.76% 7.40% 4.2%
320 1974 68.56 -26.47% -29.72% 3.25% 7.40% 6.90% 2.5%
321 1973 97.55 -14.66% -17.37% 2.71% 6.90% 6.41% 2.1%
322 1972 118.05 18.98% 15.63% 3.35% 6.41% 5.89% 1.3%
323 1971 102.09 14.31% 10.79% 3.52% 5.89% 6.50% 12.2%
324 1970 92.15 3.10% 0.10% 3.00% 6.50% 7.88% 21.1%
325 1969 92.06 -8.36% -11.36% 3.00% 7.88% 6.16% -8.1%
326 1968 103.86 10.66% 7.66% 3.00% 6.16% 5.70% 1.6%
327 1967 96.47 5.70%
328
329 Arithmetic average 10.85% 7.46% 3.39% 6.96% 8.48%
330 Geometric average 9.34% 6.01% 3.38% 6.93% 7.73%
331
332
 A B C D E F G H
333 Expert Opinions for Estimates of the Risk Premium
334
335 Surveys of experts (CFO's, analysts, professors) are another way to estimate the risk premium.
336
337
338 Forward-Looking Risk Premiums
339
340 Historical risk premiums look at past data and assume that investors think the best estimate of the
341 current risk premium is the historical differential between earned returns on stocks and bonds.
342 Forward-looking risk premiums assume that investors expect equities to earn a rate that is equal to the
expected dividend yield plus the expected capital gains (growth) rate and the current yield on Treasury
343 securities.
344
345
346
If we make these two assumptions, we can use the constant dividend growth model to estimate the
347 expected return on the market: (1) growth is expected to be constant, (2) the firm pays out all available
funds as dividends (i.e., there are no stock repurchases or purchases of short-term securities).
348
349
350 rM = (D1/P0) + g
351
352 To use this model, we need estimates of the expected dividend yield and the expected growth rate in
353 the stock price (recall that in a constant growth model, the expected growth in stock price is also the
expected growth in dividends).
354
355
356
357 Simplified Illustration of Estimating a Forward-Looking Risk Premium
358
359 Estimating the Year-1 Dividend Yield (See source at right)
360
361 D1/P0 = 2.16%
362
363 Estimating the Long-Term Growth Rate
364
365 Since 1926, the average dividend growth for the S&P 500 has been about:
366
367 g= 4.40%
368
369 Estimated Forward-Looking Expected Market Return
370
371 rM = (D1/P0) + g
372 rM = 6.56%
373
374
375 Estimated Forward-Looking Premium
376
377 rRF = 2.19%Yield on 10-year T-bond
378
379 RPM = rM – rRF = 4.37% Assumes constant growth and no stock repurchases.
380
381
 A B C D E F G H
382 9-6 Using the CAPM to Estimate the Cost of Common Stock, r s
383
384 rs = risk-free rate + (Market risk premium) (Beta)
385 = rRF + (RPM) bi (Recall that: RPM is the expected return on the market minus the risk-free rate.)
386
387 The Risk-Free Rate
388
389 The risk-free rate is often proxied by the yield on a long-term Treasury bond. When we wrote this, the rate on
390 a 10-year T-bond was:
391
392 Date of data: 4/5/2012
393 Yield on 10-year T-bond = r RF = 2.19%
394
395
396 The Market Risk Premium
397
398 The market risk premium is the return in excess of the risk-free rate that is required to induce investors to
399 invest in the stock market.
400
401 Assumed market risk premium = RPM = 6.00%
402
403
404 Estimating Beta
405
406 Beta can be estimated from historical stock returns using the following formula, where ρ im is the correlation
between Stock i and the market, σi is the standard deviation of Stock i, and σ M is the standard deviation of the
407 market.
408
409 Beta for Stock i = bi = riM(si/sM)
410
411 The same estimate for beta can be obtained as the estimated slope coefficient in a regression, with the
company’s stock returns on the y-axis and market returns on the x-axis. Beta can also be obtained from many
412 Web sources.

413
414
415 MicroDrive's beta:
416 bi = 1.43
417
418
419 An Illustration of the CAPM Approach: MicroDrive’s Cost of Equity, r s
420
421 Assuming the risk-free rate (i.e., the current yield on a long-term Treasury bond) equals
422 5%, the market risk premium is 6%, and the MicroDrive's beta is 1.43, what is
MicroDrive's cost of stock?
423
424
425 Risk-free rate 5.0%
426 Market risk premium 6.0%
427 Beta 1.43
428
429 rs = rRF + (RPM) (bi)
430 rs = 5.0% + 6.0% 1.43
 A B C D E F G H
431 rs = 5.0% + 8.6%
432 rs = 13.58%
433
434
435 9-7 Dividend-Yield-Plus-Growth-Rate, or Discounted Cash
436 Flow (DCF), Approach
437
438 The simplest DCF model assumes that growth is expected to remain constant, and rs = D1/P0 + g.
439
440
441 Estimating Inputs for the DCF Approach
442
443 The next expected dividend is easy to estimate, and the stock price can be determined
444 readily. However, it is not easy to determine the marginal investor's expected future
445 growth rate. Three approaches are commonly used: (1) historical growth rates, (2)
retention growth model, and (3) analysts' forecasts.
446
447
448 1. Historical Growth Rates
449
450 Historical growth estimates are usually not good estimates of expected future growth
451 except for a few very stable and mature companies.
452
453
454 2. Retention Growth Model
455
456 Another method for finding the growth is utilizing the sustainable growth rate, found by
multiplying the expected future return on equity (ROE) times the expected future
457 retention ratio (i.e., the percentage of net income that is not paid out as dividends). This
458 is:
459
460 g = (Retention rate) (ROE) = (1 – Payout rate) (ROE)
461
462 Suppose a firm's expected ROE is 14.5% and it pays out 63% of its earnings. What is the
463 firm's sustainable growth rate?
464
465 Payout rate = 63%
466 ROE = 14.50%
467
468 g = (1 – Payout rate) x (ROE)
469 g= 37% x 14.50%
470 g= 5.4%
471
 A B C D E F G H
472 3. Analysts' Forecasts
473
474 A third method for estimating the growth rate is to use analysts' forecasts. Value Line provides
475 estimated dividends. IBES, Zack's, and many brokerage firms provide estimates of growth rates, which
476 can be used as proxies for dividend growth. These often have a forecast for the next five years and
477 then a long-term forecast for the period after five years, which requires the use of a nonconstant multi-
stage growth model, as described in the Web Extension.
478
479
480
481 An Illustration of the DCF Approach
482
483 Suppose a firm's stock trades at $32 and its next dividend is expected to be $1.82. If the
484 expected growth rate is 5.5%, what is the firm's cost of equity?
485
486 P0 = $32.00
487 D1 = $1.82
488 g= 5.4%
489
490 rs = D1 ÷ P0 + g
491 r s
= $1.82 ÷ $32.00 + 5.4%
492 rs = 11.1%
493
494
495 9-8 The Weighted Average Cost of Capital (WACC)
496
497 The weighted average cost of capital (WACC) is calculated using the firm's target capital structure
498 together with its after-tax cost of long-term debt, after-tax cost of short-term debt, cost of preferred
499 stock, and cost of common equity.
500
501 WACC = Weighted average cost of capital
502 = wd rd(1 – T) + wstd(1 – T)rstd + wps rps + ws rs
503
504 A firm's target capital structure consists of the following capital structure. Using the relevant costs
505 calculated previously, what is the firm's weighted average cost of capital?
506
507 T= 40%
508 wd = 28% rd = 9.0%
509 w std
= 2% r std
= 10.0%
510 wps = 3% rps = 8.2%
511 ws = 67% rs = 13.6%
512
513 Sources of Capital
Short-
Long-term Preferred Common
514 Debt
term
Stock Stock
Debt
515
516 Pre-tax cost of capital source, r i: 9.00% 10.00% 8.16% 13.58%
517 After-tax cost of debt, (1-T)(ri): 5.40% 6.00%
518
519 Cost of capital component for WACC: 5.40% 6.00% 8.16% 13.58%
520 Target capital structure weight, w i: 28.00% 2.00% 3.00% 67.00% 100%
521
 A B C D E F G H
522 Weighted component cost: 1.51% 0.12% 0.24% 9.10% 10.98%
523
524
525 WACC = 10.98%
526
527
528 9-9 Adjusting the Cost of Equity for Flotation Costs
529
530 A company's stock sells for $32 and its next dividend is expected to be $1.82, with
531 constant growth of 5.5%. What is the cost of equity using the DCF model?
532
533 P0 = $32.00
534 D1 = $1.82
535 g= 5.4%
536
537 rs = D1 ÷ P0 + g
538 rs = $1.82 ÷ $32.00 + 5.4%
539 rs = 11.1%
540
541 If the firm in the preceding question incurred a flotation cost of 12.5% for issuing new
542 stock, how much higher is its cost of equity from having to issue new common stock?
543
544 Flotation percentage cost (F) = 12.5%
545 Stock price = $32.00
546
547 Net proceeds after flotation costs = (Stock Price) (1 – F)
548 Net proceeds after flotation costs = $32.00 88%
549 Net proceeds after flotation costs = $28.00
550
551 Net proceeds after flotation costs = $28.00
552 D1 = $1.82
553 g= 5.4%
554
Net
555 rs = D1 ÷
Proceeds
+ g

556 rs = $1.82 ÷ $28.00 + 5.4%

557 rs = 6.5% + 5.4%
558 rs = 11.9%
559
560 Notice that this cost of stock is quite different than the cost of stock without flotation costs.
561
562 To find the cost of perpetual preferred stock, simply use the procedure above with g = 0. If the
563 preferred stock has a fixed maturity, then use the same procedure as for debt, except that the preferred
dividend is not tax deductible.
564
565
566
 A B C D E F G H
567 9-10 Privately Owned Firms and Small Businesses
568
569 A privately held firm often estimates its own beta as the average beta of publicly traded companies in
570 the same industry.
571
572 Own-Bond-Yield-Plus-Judgmental-Risk-Premium Approach
573
574 This approach consists of adding a judgmental risk premium to the yield on the firm's own long-term
575 debt. It is logical that a firm with risky, low-rated debt would also have risky, high-cost equity.
576 Historically, we have observed that the risk premium for equity is in the range of 3 to 5 percentage
577 points. In addition to applications to privately held firms, this method is used primarily in utility rate
case hearings.
578
579
580 Example:
581
582 Judgmental over-own-bond-yield risk premium = 4.0%
583 Bond yield or rd = 10.0%
584
Extra
585 rs =
Premium
+ rd

586 rs = 4.0% + 10.0%

587 r s
= 14.0%
588
589
590 9-11 Managerial Issues and the Cost of Capital
591
592 There is a relationship between the cost of capital and risk--the higher a project's risk, the
higher its cost of capital. When adjusting for risk, firms usually begin by estimating a
593 divisional cost of capital, and then adjusting this estimate for the risk of individual
projects.
594
595
596 Consider a company with a single division, steel production. The risk-free rate of interest
597 is 5%, and the market risk premium is 6%. If the firm has a beta of 1.1, what is the firm's
cost of equity?
598
599
600 Risk-free rate 5%
601 Market risk premium 6.0%
602 Steel Beta 1.1 rSteel = 11.6%
603
604 Suppose the firm undertakes a new operation (a barge project). The average beta of
605 companies that only have barge operations (I.e., pure-play companies) is 1.5. What is the
cost of equity for the new division?
606
607
608 Risk-free rate 5%
609 Market risk premium 6.0%
610 Barge Beta 1.5 rBarge = 14.0%
611
612 Now suppose the firm undertakes a new low-risk operation (a distribution center). The
613 average beta of companies that only have distribution centers (I.e., pure-play companies)
is 0.5. What is the cost of equity for the new division?
614
 A B C D E F G H
615
616 Risk-free rate 5%
617 Market risk premium 6.0% rCenter = 8.0%
618 Distribution Beta 0.5
619
620 After adding the two new divisions, the Steel division will make up 70% of the company's
621 value, the Barge division will make up 20%, and the Distribution division will make up
622 10%. What is the new beta for the entire company? (Hint: the beta of the firm is a
weighted average of the divisional betas.) What rate of return will equity holders require
623 the firm as a whole to provide?
624
625
626 Beta of Steel Division 1.1
627 % of the firm 70%
628
629 Beta of Barge Division 1.5
630 % of the firm 20%
631
632 Beta of Distribution Division 0.5
633 % of the firm 10% New corp. beta = 1.12
634
635 Risk-free rate 5%
636 Market risk premium 6.0%
637 Beta 1.12 New rs = 11.72%
 I J K L M N O P Q R
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26
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28
29
30
31 Target
32 Capital
33 Structure
34
35 wstd = 2%
36
37
38 wd = 28%
39
40 wps = 3%
41
42
43 ws = 67%
44 100%
45
46
47
48
49
 I J K L M N O P Q R
50
51
52
53
the long-term bonds sell at a discount and
qual to their aggregate54book value.
55
56 value of equity
standing, for a total market
57
58 value of
utstanding, for a total market
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250
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256 Note: Ibbotson actually uses the bond's return due to income as a proxy for the yield.
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277 For calculation of geometric mean: wealth relative
Premium
return Return Reported First Day Return
278 rM − of 10- Total on yield on of Year, During
Requi Return, Capital rM − Required
red rRF rM Gains rRF
 rMI − of J10- K L
Total M N
on
O P Q
yield on of Year, During
R
279 Requi year Return, Capital Dividend last day Required Year, rM − Required
280 red rRF bond rM Gains s of year rRF Actual rRF rRF
281
282
283 ### -14.79% 1.02 1.00 1.02 1.02 1.03 1.17 0.99
284 ### 6.13% 1.15 1.13 1.02 1.03 1.04 1.09 1.11
285 ### 37.55% 1.26 1.23 1.03 1.04 1.02 0.89 1.24
286 ### -58.63% 0.63 0.62 1.01 1.02 1.04 1.22 0.59
287 ### -5.45% 1.05 1.04 1.02 1.04 1.05 1.11 1.01
288 ### 14.24% 1.16 1.14 1.02 1.05 1.04 1.02 1.11
289 ### 2.01% 1.05 1.03 1.02 1.04 1.04 1.03 1.01
290 ### 6.34% 1.11 1.09 1.02 1.04 1.04 1.05 1.07
291 ### 28.75% 1.29 1.26 1.02 1.04 1.04 1.00 1.25
292 ### -39.02% 0.78 0.77 1.01 1.04 1.05 1.17 0.73
293 ### -17.45% 0.88 0.87 1.01 1.05 1.05 1.06 0.83
294 ### -28.31% 0.91 0.90 1.01 1.05 1.06 1.19 0.84
295 ### 31.28% 1.21 1.20 1.02 1.06 1.05 0.90 1.16
296 ### 12.39% 1.29 1.27 1.02 1.05 1.06 1.16 1.23
297 ### 20.61% 1.33 1.31 1.02 1.06 1.06 1.13 1.27
298 ### 24.84% 1.23 1.20 1.03 1.06 1.06 0.98 1.17
299 ### 6.94% 1.37 1.34 1.03 1.06 1.08 1.30 1.30
300 ### 11.97% 1.01 0.98 1.03 1.08 1.06 0.89 0.95
301 ### -4.87% 1.10 1.07 1.03 1.06 1.07 1.15 1.03
302 ### 0.87% 1.08 1.04 1.03 1.07 1.07 1.07 1.01
303 ### 9.32% 1.31 1.26 1.04 1.07 1.08 1.21 1.22
304 ### -9.76% 0.97 0.93 1.03 1.08 1.08 1.07 0.89
305 ### 10.83% 1.31 1.27 1.04 1.08 1.09 1.21 1.22
306 ### 10.73% 1.17 1.12 1.04 1.09 1.09 1.06 1.08
307 ### 11.38% 1.05 1.02 1.03 1.09 1.07 0.94 0.98
308 ### -7.83% 1.18 1.15 1.04 1.07 1.09 1.26 1.09
309 ### -5.20% 1.32 1.26 1.06 1.09 1.12 1.37 1.21
310 ### -8.01% 1.06 1.01 1.05 1.12 1.12 1.14 0.94
311 ### 24.46% 1.23 1.17 1.05 1.12 1.10 0.98 1.12
312 ### -30.99% 1.21 1.15 1.07 1.10 1.14 1.52 1.07
313 ### -4.30% 0.95 0.90 1.05 1.14 1.12 0.99 0.83
314 ### 39.31% 1.32 1.26 1.07 1.12 1.10 0.93 1.22
315 ### 19.36% 1.18 1.12 1.06 1.10 1.09 0.99 1.09
316 ### 10.36% 1.07 1.01 1.05 1.09 1.08 0.96 0.99
317 ### -5.64% 0.93 0.88 1.04 1.08 1.07 0.98 0.86
318 ### 7.14% 1.24 1.19 1.05 1.07 1.08 1.17 1.16
319 ### 32.99% 1.37 1.32 1.06 1.08 1.07 1.04 1.30
320 ### -28.97% 0.74 0.70 1.03 1.07 1.07 1.03 0.67
321 ### -16.76% 0.85 0.83 1.03 1.07 1.06 1.02 0.79
322 ### 17.66% 1.19 1.16 1.03 1.06 1.06 1.01 1.13
323 ### 2.16% 1.14 1.11 1.04 1.06 1.07 1.12 1.08
324 ### -18.04% 1.03 1.00 1.03 1.07 1.08 1.21 0.95
325 ### -0.22% 0.92 0.89 1.03 1.08 1.06 0.92 0.85
326 ### 9.01% 1.11 1.08 1.03 1.06 1.06 1.02 1.05
327 1.057
328
329 ### 2.37%
330 ### -0.01%
331
332
 I J K L M N O P Q R
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357
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359 For current estimates from Standard & Poor’s, go to
www.standardandpoors.com and select SP 500 under
360 Categories and Index Earnings under Download Data.
361 Look at the worksheet named ESTIMATES&PEs. Look
362 for the item named “Dividend yield (indicated rate).”
363
364
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 I J K L M N O P Q R
382
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385
he market minus the risk-free rate.)
386
387
388
. When we wrote this,389 the rate on
390
391
392
393
394
395
396
397
398 to
equired to induce investors
399
400
401
402
403
404
405
406
ula, where ρ im is the correlation
M
is the standard deviation of the
407
408
409
410
t in a regression, with411
the
can also be obtained from many
412
413
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416
417
418
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420
421
422
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425
426
427
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430
 I J K L M N O P Q R
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514

515
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520 = Sum
521
 I J K L M N O P Q R
522 = Sum
523
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554

555

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566
 S
230
231
232
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234
235
236
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277
278 rM − Actual
return of 10-
year bond
 S
rM − Actual
279 return of 10-
280 year bond
281
282
283 0.85
284 1.06
285 1.38
286 0.41
287 0.95
288 1.14
289 1.02
290 1.06
291 1.29
292 0.61
293 0.83
294 0.72
295 1.31
296 1.12
297 1.21
298 1.25
299 1.07
300 1.12
301 0.95
302 1.01
303 1.09
304 0.90
305 1.11
306 1.11
307 1.11
308 0.92
309 0.95
310 0.92
311 1.24
312 0.69
313 0.96
314 1.39
315 1.19
316 1.10
317 0.94
318 1.07
319 1.33
320 0.71
321 0.83
322 1.18
323 1.02
324 0.82
325 1.00
326 1.09
327
328
329
330
331
332
 A B C D E F G
1 12/8/2012
2
3
4 Web Extension 9A: The Required Return Assuming Nonconstant Dividends and Stock Repurchases
5
6 As we explained in the chapter, two assumptions underlie the constant dividend growth model: (1)
7 firms do not repurchase any stock, and (2) growth in dividends will be constant. We now explain
how to estimate the required return when those assumptions are violated.
8
9
10 Estimating the Long-Term Growth Rate
11
12 The long-term constant growth rate should be approximately equal to the long-term growth rate in
13 sales revenue, which depends on prices and units sold. Prices will be determined by inflation in the
long-term, and units sold will depend on sustainable population growth.
14
15
16 The forward estimated inflation rate is the difference between yields on a regular 10-year Treasury
17 bond and an inflation protected 10-year Treasury bond, called a TIPS.
18
19 Yield on 10-year Treasury bond: 2.19%
20 Yield on 10-year TIPS: -0.08%
21 Forward estimate of inflation: 2.27%
22
23 Ibbotson provides the average inflation rate since 1926. The Fed also provides inflation data.
24
25 Historical inflation rate: 3.00%
26
27 Range in expected long-term inflation:
28
29 Forward estimate of inflation to Historical inflation rate
30 2.27% to 3.00%
31
32 We estimate expected inflation as the average of the inflation premium from the TIPS and the
33 historical average:
34
35 Our estimate of expected inflation: 2.64%
36
37
38 Estimates of long-term population growth range from:
39
40 Low estimate of population growth High estimate of population growth
41 1.00% 2.50%
42
43 Average of estimated population growth: 1.75%
44
45
46 Estimates of long-term sales growth rate (inflation plus population growth rate):
47
48 Low range High range
49 3.27% 5.50%
50
51 Average of range as an estimate of long-term sales growth, g: 4.39%
52
 A B C D E F G
53
54 The Impact of Stock Repurchases on the Estimated Price
55
56 When there are repurchases, the growth rate in dividends per share changes.
57
58 - (r - g)  r 1  g 
59 g DPS 
60 (r - g)  1  g 
61
62 The constant growth model is:
63
64
65 D 0 1  g DPS 
P̂0 
66  r - g DPS 
67
68
69 This can be rearranged to give this formula:
70
71
 1  D 1  g 
72 P̂0    0
73     r - g
74
75 The two formulas are equivalent, as shown in the following example.
76
77 g= 5.0%
78 α= 80.0%
79 rs = 12.0%
80 D0 = $2.00
81
82
- (r - g)  r 1  g 
83 g DPS  = 6.329%
84 (r - g)  1  g 
85
86
87
88
89
90 D 0 1  g DPS 
91 P̂0 
 rs - g DPS 
= $37.50
92
93
94 Alternatively:
95
96
97  1  D 1  g 
98 P̂0    0 = $37.50
99     rs - g 
100
101
102 Estimating the Required Return
103
104 In the textbook, we assumed constant growth and no repurchases. We now consider cases with
105 repurchases and a period of nonconstant growth, beginning with the case of repurchases but
constant growth.
 In the textbook, we assumed constant growth and no repurchases. We now consider cases with
A and a periodBof nonconstant growth,
repurchases C Dwith the case
beginning E of repurchases
F butG
constant growth.
106
107
108 Repurchases and Constant Growth
109
110 If there are repurchase but still constant growth, then we can invert the constant growth formula to
111 solve for r.
112
113
114 D 0 1  g 
r g
115  P0
116
117
118
119 Repurchases and a Period of Nonconstant Growth
120
121 It is often the case that a period of nonconstant growth is expected before growth becomes constant.
122 The valuation model for this situation is:
123
124
125
 D t (1  g) 
126  D1     r  g 
127 D2 Dt
P ̂_0      
=  1  r  1  r  1  r  t
128 1 2
 1  r  t
129
130
131
132
133 Estimating the Required Market Return when there are Repurchases and a Period of Nonconstant Growth
134
135
136 In recent years, companies in the S&P 500 aggregately have distributed as much cash to
137 shareholders in the form of stock repurchases as in the form of dividends. This implies that about
50% of distributions are in the form of dividends.
138
139
140 Percent of total distribution in the form of cash dividends = α = 50.0%
141
142
The next step is to estimate the total S&P dividend payouts for the next 2 years. S&P provides
143 historical data for earnings per share, and dividends per share. They also provide data for
144 estimated earnings per share for the next 2 years. We can use the historical data to estimate a
145 relationship between EPS and DPS, and then use that model and the estiamted EPS to estimate DPS.
146
147
148 We obtained data from the Standard and Poor's Web site:
149 http://www.standardandpoors.com/home/en/us
150
Under Categories, we selected S&P500. We then selected Download Index Data and Index Earnings.
151 This downloaded an Excel file with quarterly data for the S&P 500. We summed up the quarterly
152 data to get annual data. We also summed up the quarterly forecasted EPS to get the next 2 years
153 annual forecast of EPS. The data is shown below.
154
155
156
157
158
 A B C D E F G
159
160
161 Annualized Data

162 Annual
Date Year Month S&P Price Annual EPS DPS Data for Regression Model
163 12/31/88 1988 12 277.72 $23.75 $9.75 Annual DPS
164 12/31/89 1989 12 353.40 $22.87 $11.06 $11.06
165 12/31/90 1990 12 330.22 $21.34 $12.09 $12.09
166 12/31/91 1991 12 417.09 $15.97 $12.20 $12.20
167 12/31/92 1992 12 435.71 $19.09 $12.39 $12.39
168 12/31/93 1993 12 466.45 $21.89 $12.58 $12.58
169 12/31/94 1994 12 459.27 $30.60 $13.17 $13.17
170 12/31/95 1995 12 615.93 $33.96 $13.79 $13.79
171 12/31/96 1996 12 740.74 $38.73 $14.90 $14.90
172 12/31/97 1997 12 970.43 $39.72 $15.50 $15.50
173 12/31/98 1998 12 1229.23 $37.71 $16.20 $16.20
174 12/31/99 1999 12 1469.25 $48.17 $16.69 $16.69
175 12/31/00 2000 12 1320.28 $50.00 $16.27 $16.27
176 12/31/01 2001 12 1148.08 $24.69 $15.74 $15.74
177 12/31/02 2002 12 879.82 $27.59 $16.07 $16.07
178 12/31/03 2003 12 1111.92 $48.74 $17.39 $17.39
179 12/31/04 2004 12 1211.92 $58.55 $19.44 $19.44
180 12/31/05 2005 12 1248.29 $69.83 $22.22 $22.22
181 12/31/06 2006 12 1418.30 $81.51 $24.88 $24.88
182 12/31/07 2007 12 1468.36 $66.18 $27.73 $27.73
183 12/31/08 2008 12 903.25 $14.88 $28.39 $28.39
184 12/31/09 2009 12 1115.10 $50.97 $22.41 $22.41
185 12/31/10 2010 12 1257.64 $77.35 $22.73 $22.73
186 12/30/11 2011 12 1257.60 $86.95 $26.43 $26.43
187 Forecast 2012 $97.83
188 2013 $111.42
189
190
191
192 We estimated the following model:
193
194 Dt = a + b Dt-1 + c EPSt + d (Change in EPS)
195
196 As shown by the regression results below, this model does a good job of predicting the dividend.
197
198 SUMMARY OUTPUT
199
200 Regression Statistics
201 Multiple R 0.986716949883
202 R Square 0.973610339186
203 Adjusted R Square 0.969443550637
204 Standard Error 0.938269321597
205 Observations 23
206
207 ANOVA
208 df SS MS F Significance F
209 Regression 3 617.1063324011 205.7021108 233.65965 4E-15
210 Residual 19 16.72663707716 0.88034932
211 Total 22 633.8329694783
 A B C D E F G
212
213 Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
214 Intercept 1.53893053677 0.678705357671 2.267450108 0.0352196 0.11838 2.9594771762
215 X Variable 1 0.696432840265 0.050795415378 13.71054523 2.6458E-11 0.59012 0.8027488665
216 X Variable 2 0.10809871281 0.014127370433 7.651722118 3.2254E-07 0.07853 0.137667639
217 X Variable 3 -0.094505735058 0.014811868418 -6.38040606 4.0416E-06 -0.1255 -0.0635041382
218
219 We then used the regression coefficients to estimate the predicted dividends.
220
Estimat
Estimated ed
221 coefficient coeffici
Predicted Estimated for lagged ent for
Year dividend, D intercept, a dividend, b Lagged D EPS, c Forecast EPS
222 2012 $29.49 1.539 0.696 $26.43 0.108 $97.83
223 2013 $32.84 1.539 0.696 $29.49 0.108 $111.42
224
225
226
227
228
229 Create a time line showing the predicted dividends for each year until growth in payouts becomes
230 constant. To do this, obtain estimates of the next 2 year's projected dividends for the market and the
231 long-term growth rate in CASH FLOWS after year 2.
232
233 Find the horizon value on the time line assuming constant growth and an initial assumption for the
234 required return on the market. Find the present value of the annual payouts and the present value
235 of the horizon value; this is the estimate of the value of the market index. If the difference between
the actual current value of the market index and the estimated value is not zero, adjust the input for
236 the required market return until the difference is zero.
237
238
239 Figure 9A-1:
240 Estimating the Forward-Looking Market Risk Premium
241
242 INPUTS:
243 Projected Year 1 dividend for S&P 500 = $29.49
244 Projected Year 2 dividend for S&P 500 = $32.84
245 Projected portion of distributions as dividends, α = 50.0%
246 Projected long-term constant growth rate in cash flow, g L = 4.39%
247 Actual price level of S&P 500 = $1,257.60
248
249 Key Input/Output: Estimate of rM

250 Key Input and Output: Estimate of r M = 9.17% Use Goal Seek to set
the blue cell to zero
by changing the
251 Price level of S&P 500: Actual - Estimated = $0.00 orange cell.
252
253 Time Line:
254 Year 0 1 2
255 Estimated dividend = $29.49 $32.84
256 Estimated P at Year 2 = [(D2/ α) (1+gL) ] / (rM − gL) = $1,433.70
257 Estimate price level of S&P 500 = (PV of dividends and P 2) = $1,257.60
258
 H I J K L M N O
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36
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38
39
stimate of population 40
growth
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46
47
48
49
50
51
52
 H I J K L M N O
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132
133Growth
a Period of Nonconstant
134
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 H I J K L M N O
159
160
161
162
Data for Regression Model Date Year Month op esp
163 Lagged DPS Annual EPS Change in EPS 12/31/89 1989 12 $5.84
164 $9.75 $22.87 -$0.88 12/31/90 1990 12 $5.01
165 $11.06 $21.34 -$1.53 12/31/91 1991 12 $4.63
166 $12.09 $15.97 -$5.37 12/31/92 1992 12 $5.61
167 $12.20 $19.09 $3.12 12/31/93 1993 12 $7.16
168 $12.39 $21.89 $2.80 12/31/94 1994 12 $8.80
169 $12.58 $30.60 $8.71 12/31/95 1995 12 $9.78
170 $13.17 $33.96 $3.36 12/31/96 1996 12 $11.01
171 $13.79 $38.73 $4.77 12/31/97 1997 12 $11.29
172 $14.90 $39.72 $0.99 12/31/98 1998 12 $11.47
173 $15.50 $37.71 -$2.01 12/31/99 1999 12 $13.77
174 $16.20 $48.17 $10.46 12/31/00 2000 12 $13.11
175 $16.69 $50.00 $1.83 12/31/01 2001 12 $9.94
176 $16.27 $24.69 -$25.31 12/31/02 2002 12 $11.94
177 $15.74 $27.59 $2.90 12/31/03 2003 12 $14.88
178 $16.07 $48.74 $21.15 12/31/04 2004 12 $17.95
179 $17.39 $58.55 $9.81 12/31/05 2005 12 $20.19
180 $19.44 $69.83 $11.28 12/31/06 2006 12 $21.99
181 $22.22 $81.51 $11.68 12/31/07 2007 12 $15.22
182 $24.88 $66.18 -$15.33 12/31/08 2008 12 -$0.09
183 $27.73 $14.88 -$51.30 12/31/09 2009 12 $17.16
184 $28.39 $50.97 $36.09 12/31/10 2010 12 $21.93
185 $22.41 $77.35 $26.38 12/30/11 2011 12 $23.73
186 $22.73 $86.95 $9.60
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
 H I J K L M N O
212
213 Lower 95.0% Upper 95.0%
214 0.1183838973093 2.9594771762
215 0.5901168140256 0.8027488665
216 0.0785297866685 0.137667639
217 -0.125507331947 -0.063504138
218
219
220

221 Estimated
coefficient for Forecast
change in EPS, d change in EPS
222 -0.095 $10.88
223 -0.095 $13.59
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250

251
252
253
254
255
256
257
258
 P Q R S T
159
160
161
salespers bookvalu
162 eps div hare e Index
163 $4.80 $2.86 353.40
164 $4.40 $3.12 330.22
165 $2.55 $3.04 417.09
166 $3.60 $3.03 435.71
167 $5.08 $3.09 466.45
168 $8.35 $3.34 459.27
169 $7.13 $3.55 615.93
170 $9.86 $3.79 740.74
171 $8.94 $3.95 970.43
172 $8.56 $4.00 1,229.23
173 $12.77 $4.05 $290.68 1,469.25
174 $9.07 $3.98 $191.03 $325.80 1,320.28
175 $5.45 $3.98 $189.10 $338.37 1,148.08
176 $3.00 $4.26 $165.94 $321.72 879.82
177 $13.16 $5.06 $178.85 $367.17 1,111.92
178 $13.94 $5.33 $210.14 $414.75 1,211.92
179 $17.30 $6.08 $232.52 $453.06 1,248.29
180 $20.24 $6.87 $248.20 $504.39 1,418.30
181 $7.82 $7.62 $268.16 $529.59 1,468.36
182 -$23.25 $7.15 $230.21 $451.37 903.25
183 $15.18 $5.66 $236.02 $513.58 1,115.10
184 $20.67 $6.03 $252.73 $579.14 1,257.64
185 $20.64 $7.28 $272.64 $613.14 1,257.60
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
SECTION 9-3
SOLUTIONS TO SELF-TEST

A company has outstanding long-term bonds with a face value of $1,000, a 10% coupon
rate, 25 years remaining until maturity, and a current market value of $1,214.82. If it pays
interest semiannually, what is the nominal annual pre-tax cost of debt? If the
company’s tax rate is 40%, what is the after-tax cost of debt?

Number of years to maturity 25

Number of payments per year 2
Annual coupon rate 10%
Face value $1,000
Tax rate 40%

N= 50
PV = ($1,214.82)
PMT = $50
FV = $1,000

I/YR = rd = 4.000%

Annualized rd = 8.000%

A-T rd = 4.800%
SECTION 9-4
SOLUTIONS TO SELF-TEST

A company’s preferred stock currently trades at $50 per share and it pays a $3
annual dividend. Flotation costs are equal to 3% of the gross proceeds. If the
company issues preferred stock, what is the cost of that stock?

Preferred stock price $50

Dividend per share $3
Flotation percentage 3%

rps 6.19%
SECTION 9-6
SOLUTIONS TO SELF-TEST

A company’s beta is 1.4, the yield on a 10-year T-bond is 5%, and the market risk
premium is 5.5%. What is rs?

Beta 1.40
10-year T-bond yield 4.0%
Market risk premium 4.5%

rs 10.30%
SECTION 9-7
SOLUTIONS TO SELF-TEST

A company’s estimated growth rate in dividends is 6%. Its current stock price is $40, and its
expected annual dividend is $2. Using the DCF approach, what is rs?

Growth 6.0%
Stock price $40.00
Expected dividend $2.00

rs 11.00%
SECTION 9-8
SOLUTIONS TO SELF-TEST

A firm has the following data: Target capital structure of 25% debt, 10% preferred stock,
and 65% common equity; Tax rate = 40%; rd = 7%; rps = 7.5%; and rs = 11.5%. Assume the
firm will not isssue new stock. What is this firm’s WACC?

wd 25%
wps 10%
ws 65%
Tax rate 40%
rd 7.0%
rps 7.5%
rs 11.5%
WACC 9.28%
SECTION 9-9
SOLUTIONS TO SELF-TEST

A firm has common stock with D1 = $3.00; P0 = $30; g = 5%; and F = 4%. If the firm must issue new stock,
what is its cost of external equity, re?

D1 $3.00
P0 $30.00
g 5.0%
F 4.0%
re 15.42%
ssue new stock,
SECTION 9-10
SOLUTIONS TO SELF-TEST

A company’s bond yield is 7%. If the appropriate over-own-bond-yield risk premium is 3.5%,
what is rs, based upon the bond--yield-plus-judgmental-risk-premium approach?

Bond yield 7.0%

Bond risk premium 3.5%

rs 10.50%