A B C D E

1 Tool Kit Chapter 15

2 Capital Structure Decisions
3
4 15-2 Business Risk and Financial Risk
5
6 Operating Leverage reflects the amount of fixed costs embedded in a firm's operations. Thus, if a high percentage of a firm's costs are fixed,
7 continue even if sales decline, then the firm is said to have high operating leverage. High operating leverage produces a situation where a sm
8 change in sales can result in a large change in operating profit. The following example compares two operational plans with different degree
9 operating leverage.
10
11 Figure 15-1
12 Illustration of Operating and Financial Leverage (Millions of Dollars and Millions of Units,
13 Except Per Unit Data)
14 1. Input Data Plan A Plan U Plan L
15 Required operating current assets $3 $3 $3
16 Required long-term assets $199 $199 $199
17 Total assets $202 $202 $202
18 Resulting operating current liabilities $2 $2 $2
19 Required capital (TA − Op. CL) $200 $200 $200
20 Book equity $200 $200 $150
21 Debt $0 $0 $50
22 Interest rate 8% 8% 8%
23 Sales price (P) $2.00 $2.00 $2.00
24 Tax rate (T) 25% 25% 25%
25 Expected units sold (Q) 100 100 100
26 Fixed costs (F) $20 $60 $60
27 Variable costs (V) $1.50 $1.00 $1.00
28 2. Income Statements Plan A Plan U Plan L
29 Sales revenue (P x Q) $200.0 $200.0 $200.0
30 Fixed costs 20.0 60.0 60.0
31 Variable costs (V x Q) 150.0 100.0 100.0
32 EBIT $30.0 $40.0 $40.0
33 Interest 0.0 0.0 4.0
34 Pre-tax earnings $30.0 $40.0 $36.0
35 Tax 7.5 10.0 9.0
36 Net income $22.5 $30.0 $27.0
37 3. Key Performance Measures Plan A Plan U Plan L
38 NOPAT = EBIT(1 − T) $22.5 $30.0 $30.0
39 ROIC = NOPAT/Capital 11.3% 15.0% 15.0%
40 ROA = NI/Total assets 11.1% 14.9% 13.4%
41 ROE = NI/Equity 11.3% 15.0% 18.0%
42
43 Numbers are reported as rounded values for clarity but are calculated using Excel’s full
44 precision. Thus, intermediate calculations using the figure’s rounded values will be inexact.
45 Note: ROA is not exactly equal to ROE for the Plan L or Plan U because total assets is not quite
46 equal to equity for these plans. This is because the operating current liabilities, such as
accounts payable and accruals, reduce the required equity capital investment.
47
48
49
50 We can use the following formula to find the exact break-even quantity.
51 QBE = F ÷ (P-V)
 A B C D E
52 Plan A
53 QBE = F ÷ (P −
54 QBE = $20 ÷ $2.00 −
55 QBE = 40 Units.
56
57 Plan U
58 QBE = F ÷ (P −
59 QBE = $60 ÷ $2.00 −
60 QBE = 60 Units.
61
62 Crossover Q for A vs. U = 80
63
64
65 QBE for levered firm = (F + Int) ÷ (P-V)
66 Plan L
67 QBE = F − Int ÷ P−V
68 QBE = $56 ÷ $1.00
69 QBE = 56 Units.
70
71 Crossover Q for U vs. L = 76
72
73
74 Leverage magnifies the ROE. See Panel b of Figure 15-2 below.
75
76 Figure 15-2
77 Operating Leverage and Financial Leverage
78
79 Panel A: Operating Leverage Panel B: Financial Leverage
80
81 ROE
ROE
82 50.0%
50.0%
83
84 40.0%
40.0%
85 Crossover at 80
86 Million Units 30.0% Crossover at 76
30.0%
87 Million Units
88 Plan A
20.0%
20.0% Break-even at 40 Plan U
89 Break-even at 60
Million Units
90 10.0% Million Units
91 10.0%
92 0.0%
0.0%
93
94 -10.0%
95 -10.0%
96 -20.0%
97 -20.0% Plan L
Plan U
98 Break-even at 60
Break-even at 64
-30.0% -30.0% Million Units
99 Million Units
100
-40.0% -40.0%
0 20 40 60 80 100 120 140 0 20 40 60 80 100 120 140

Units Sold Millions Units Sold (Millions)

 0.0% 0.0%

-10.0% -10.0%

-20.0% -20.0%
Plan L
Plan U Break-even at 64
Break-even at 60 -30.0% Million Units
-30.0%
Million Units
A B C D E
-40.0% -40.0%
101
0 20 40 60 80 100 120 140
102 0 20 40 60 80 100 120 140
103 Units Sold Millions Units Sold (Millions)
104
105
106
107 15-3 Capital Structure Theory: The Modigliani and Miller Models
108
109 Following are descriptions of the M&M models.
110
111 15-3a Modigliani and Miller: No Taxes
112
113 VL=VU
114
115 15-3b Modigliani and Miller: The Effect of Corporate Taxes
116
117 V L = V U + TD
118 VU = $100
119 Federal-plus-state corporate tax rate = 25%
120 Pre-TCJA federal-plus-state corporate tax rate = 40%
121
122
123 This figure is not shown in the textbook.
124
125
126 M&M with Corporate Taxes
127 Value
128
129 $130
130
131
132
133
134
135
136
137
138
139 V L = $100
140
141
142
143

⸾
144
145
146
147
148
149
150
151 $0
Leverage
 ⸾

A $0 B C D E
152 Leverage
153
154
155
156
157 Interest expense deduction limitation
158
159 The TCJA limits deductibility of interest expenses for purpose of tax deductibility to 30% of EBITDA for the years 2018-2021 and 30% of EB
160 subsequent years. Interest expenses exceeding this level may be carried forward to offset future taxes. When applying this rule to EBIT and u
reasonable values for rsu and rd, the maximum wd that can utilize the tax shield immediately is:
161
162
163
164 Reasonable values of:
165 T= 25%
166 rsu = 12%
167 rd = 8%
168 terest expense deduction limit (IntLim)= 30%
169
170 Max wd = [(IntLim)(rsu)] / [ { (1-T)rd } + {IntLim)(rsu)T} ]
171
172 Max wd = 52.2%
173
174 Check:
175 wd = 52.2%
176 VU = $100
177 Debt given wd[w= d (V U )]/[1 − (w d T)]
178 = $60.00
179
180 Interest based on D = $4.80
181 EBIT implied by V U
= (V r
U sU
)/(1 - T)
182 = $16
183
184 Interest / EBIT = 30.0%
185
186
187 15-3c Miller: The Effect of Corporate and Personal Taxes
188
189
VL =VU + 1-
  
1-Tc 1-Ts  
190 D
191   1-Td  
192
193
194 This figure is not shown in the textbook.
195
Miller with Corporate and Personal Taxes
196
Value of Firm
197
198 V = $115
199
200

V = $100

$0 $50
 Miller with Corporate and Personal Taxes
Value of Firm
V = $115

A B C D E
201
202
203
204
205 V = $100

⸾
206
207
208
209
210
211
212
213 $0 $50
214
215 Debt
216
217
218
219
220
221
222 15-4A Trade-Off Theory
223
224 V L = V U + TD + Financial distress costs
225
226 VU = $100
227 Federal plus state corporate tax rate = 25%
228
229
230 Figure 15-3
231 Effect of Financial Leverage on Value
232 Value
233
234
235
236
237
238
239
240
241 Value Added by Debt
242 Tax Shelter Benefts
243 Value Reduced by
Banruptcy-Related Costs
244
245
246 Value
247 with Zero
248 Debt

⸾
249
250
251

⸾
252
253
254

0
0 D1 D2

Optimal Capital Structure:

Threshold Debt Level Marginal Tax Shelter Benefits =
Where Bankruptcy Marginal Bankruptcy-Related Costs
Costs Become
Material
 Value
with Zero
Debt

⸾
A ⸾ B C D E
255
256
257
258
259
260 0
261 0
262 D1 D2
263
264 Optimal Capital Structure:
265 Threshold Debt Level Marginal Tax Shelter Benefits =
266 Where Bankruptcy Marginal Bankruptcy-Related Costs
267 Costs Become
Material
268
269
270
271
272
273 15-6 Estimating the Optimal Capital Structure
274
275 Adding debt decreases taxes (because interest expenses are deductible) but also increases the cost of debt (because the
276 additional debt is riskier). Additional debt also increases shareholder risk as measured by beta and the cost of equity.
Managers should identify percentage of debt (w d) that maximizes shareholder wealth and implement that capital structure
277 unless there are other compelling reasons (e.g, information asymmetry, current market conditions, etc.).
278
279
280
281 15-6a Current Value and Capital Structure
282
283 Figure 15-4 shows Strasburg's current situation.
284
285 Figure 15-4
286 Strasburg’s Current Value and Capital Structure
287 (Millions of Dollars Except Per Share Data)
288 Input Data Capital Structure and Cost of Capital
289 Stock price (P) $22.50 Market value of equity (S = P x n) $2,250
290 # of shares (n) 100 Total value (V = D + S) $2,500
291 Market value of d $250.00 % financed with debt (wd = D/V) 10.00%
292 Tax rate 25% % financed with stock (ws = S/V) 90.00%
293 EBIT $400 Cost of equity: rs = rRF + b(RPM ) 12.67%
294 Net operating capi $2,000
295 Growth rate (gL) 0% Weighted average cost of capital:
296 Cost of debt (rd) 8.00% WACC = rd (1 − T)(wd) + rs (ws) 12.00%
297 Beta (b) 1.01
298 Risk-free rate (rRF) 6.67%
299 Mkt. risk prem. (RPM) 5.94%
300 ROIC and Free Cash Flow Estimated Intrinsic Value
301 NOPAT = EBIT(1 − T) $300 Vop = [FCF(1 + gL)]/(WACC − gL): $2,500.00
302 ROIC = NOPAT/Op. 15% + Value of ST investments $0.00
303 Inv. in Op. Cap. = $0 Estimated total intrinsic value $2,500.00
304 − Debt $250.00
 A B C D E
305 Free cash flow: Estimated intrinsic value of equity $2,250.00
306 FCF = NOPAT − Δ Cap. $300 ÷ Number of shares $100.00
307 Estimated intrinsic price per share $22.50
308
309 Numbers are reported as rounded values for clarity but are calculated using Excel’s full
310 precision. Thus, intermediate calculations using the figure’s rounded values will be inexact.
311 Notes:
312 1. The weighted average cost of capital is rounded to 4 decimal places.
313 2. Strasburg's sales, earnings, and assets are not growing, so it does not need investments in
314 operating capital. Therefore, FCF = NOPAT − Investment in operating capital = EBIT(1 − T) − $0
= EBIT(1 − T) . The growth in FCF also is 0.
315
316
317 15-6b Preliminary Steps to Identify the Optimal Capital Structure
318
319 Begin the process by choosing the percentage of debt (w d, based on market values) that corresponds with each capital structure
320 to be considered. Also, use the current capital structure to estimate the unlevered beta (b U) because it will be needed to identify
321 the cost of equity for each capital structure under consideration.
322
323
324
325 Capital Structures to be Considered
326
327 Capital Structures Under Consideration (w d)
328 0% 10% 20% 30%
329
330 Estimating the Unlevered Beta with the Hamada Equation
331
332 Hamada developed his equation by merging the CAPM with the Modigliani-Miller model. We use the model to determine beta at different am
333 financial leverage, and then use the betas associated with different debt ratios to find the cost of equity associated with those debt ratios. He
334 version of the Hamada equation:
335
336 bU = b / [1 + (1-T) x (D/S)]
337
338 Here b is the levered beta, bU is the beta that the firm would have if it used no debt, T is the marginal tax rate, D is the market value of the de
339 is the market value of the equity.
340
341 Most analysts use the following version based on market weights of debt and equity:
342
343 bU = b / [1 + (1-T) x (wd/ws)]
344
345 Following is information about the current capital structure, which will be used to estimate the unlevered beta.
346
347 Levered beta (b) = 1.01000
348 Current percentage financing provided by debt (w d) = 10%
349 Current financing provided by equity (w s) = 90%
350 Federal-plus-state tax rate (T) = 25%
351
352 bU = 0.93231
353
354
355 15-6c Steps to Identify the Optimal Capital Structure
 A B C D E
356
357 To identify the optimal capital structure, apply the following steps to each capital structure under consideration: (1) Estimate
358 the levered beta and cost of equity. (2) Estimate the interest rate and cost of debt. (3) Calculate the weighted average cost of
capital. (4) Calculate the value of operations, which is the present value of free cash flows discounted by the new WACC. The
359 objective is to find the amount of debt financing that maximizes the value of operations.
360
361
362
363 Estimating the Levered Beta and Cost of Equity (rs)
364
365 Use the previously calculated unlevered beta (1.0526) and Equation 15-11a to determine the levered beta for each of the capital
366 structures being considered. For example, the levered beta for a capital structure with 20% debt is:
367
368 bU = 0.9323
369 T= 25%
370 wd = 20%
371 ws = 80%
372
373 b = bU x [1 + (1-T) x (wd/ws)]
374
375 b= 1.107
376
377 Repeating this process for each capital structure provides an estimate of the levered beta for each capital structure:
378
379 wd = 0% 10% 20% 30%
380 b= 0.932 1.010 1.107 1.232
381
382 The cost of equity is:
383 rs = rRF + b(RPM)
384
385 Risk-free rate (rRF) = 6.670%
386 Mkt. risk prem. (RPM) = 5.940%
387
388 The cost of equity for each capital structure is:
389
390 wd = 0% 10% 20% 30%
391 rs = 12.21% 12.6694% 13.25% 13.99%
392
393
394 Figure 15-5 charts the relationship between the cost of equity and the amount of debt financing.
395
396 Data for Figure 15-5
397 wd 0% 10% 20% 30%
398 rRF 6.67% 6.67% 6.67% 6.67%
399 bU ´ RPM 5.54% 5.54% 5.54% 5.54%

400 (b − bU)´ RPM 0.00% 0.46% 1.04% 1.78%

401
402 Figure 15-5
403 Strasburg’s Required Rate of Return on Equity at Different Debt Levels
404
Required
Return on
Equity
18%
16% Premium for
Financial Risk:
14% (b − bU) x RPM
12%
10% Premium for
8% Business Risk:
bU x RPM = 5.54%
 A B C D E
405 Required
406 Return on
407 Equity
408 18%
409
410 16% Premium for
411 Financial Risk:
412 14% (b − bU) x RPM
413 12%
414
415 10% Premium for
416 Business Risk:
417 8%
bU x RPM = 5.54%
418 6%
419
420 4% Risk-Free
421 2% Rate:
422 rRF = 6.67%
423 0%
424
425 -2%0% 10% 20% 30% 40% 50%
426
427
428 Percent Financed with Debt
429
430
431
432 Estimating the Cost of Debt (rd)
433
434 Investment bankers and commercial bankers can provide estimates of the expected interest rate for each capital structure under considerat
435 Discussions with its bankers indicate that Strasburg's cost of debt goes up as the percentage of debt goes up. The investment bankers' estim
shown in Line 4 of Figure 15-6. Note: the percentages are based on market values.
436
437
438 Figure 15-6 also shows the previously calculated betas and costs of equity. The following sections explain the remaining information in the
439
440
441 Figure 15-6
442 Estimating Strasburg's Optimal Capital Structure (Millions of Dollars)
443 Percent of Firm Financed with Debt (w d)
444 0% 10% 20% 30%
445 1. ws 100.00% 90.00% 80.00% 70.00%
446 2. b 0.932 1.010 1.107 1.232
447 3. rs 12.21% 12.67% 13.25% 13.99%
448 4. rd 7.80% 8.00% 8.20% 8.70%
449 5. rd (1−T) 5.85% 6.00% 6.15% 6.53%
450 6. WACC 12.21% 12.00% 11.83% 11.75%
451 7. Vop $2,457.00 $2,500.00 $2,535.93 $2,553.19
452 8. Debt $0.00 $250.00 $507.19 $765.96
453 9. Equity $2,457.00 $2,250.00 $2,028.74 $1,787.23
454 10. # Shares 111.33 100.00 88.75 77.60
455 11. Stock price $22.07 $22.50 $22.86 $23.03
456 12. Net income $300.00 $285.00 $268.81 $250.02
 A B C D E
457 13. EPS $2.69 $2.85 $3.03 $3.22
458 Numbers are reported as rounded values for clarity but are calculated using Excel’s full precision unless
459 otherwise noted. Thus, intermediate calculations using the figure’s rounded values will be inexact.
460 Notes:
461 1. The percent financed with equity is: w s = 1 − wd
462 2. The levered beta for each proposed capital structure is estimated by Hamada's formula with a 25% federal-
463 plus-state tax rate, the unlevered beta (0.9323), and the propsed capital structure:
b = bU [1 + (1-T) (wd/ws)]
464 The unlevered beta is found by using a version of Hamada's formula with the current capital structure (w d
465 = 10%) and current levered beta (1.01) as shown in the blue range of cells:
466 bU = b/ [1 + (1-T) (wd/ws)].
467
468
469
470 3. The cost of equity is estimated using the CAPM formula with a risk-free rate of 6.67% and a market risk
471 premium of 5.94%: rs = rRF + (RPM)b.
472 4. The cost of debt, rd, is obtained from investment bankers.

473 5. The after-tax cost of debt is rd (1−T), where T = 25%.

474 6. The weighted average cost of capital is calculated as:

WACC = ws rs + wd rd (1-T)
475 and is rounded to 4 decimal places.
476
477 7. The value of the firm's operations is calculated as:
Vop = [FCF(1+gL)] / (WACC − gL), where FCF = $300 million and g L = 0.
478
479 8. Debt = wd x Vop
480 9. The intrinsic value of equity after the recapitalization and repurchase is S Post = Vop − Debt = ws x Vop
481
482 10. The number of shares after the recap has been completed is found using:
483 nPost = nPrior [(VopNew - DNew) / (VopNew-DOld)].
The subscript "Old" indicates values from the original capital structure where w d = 10%, the subscript
484
"New" indicates values at the current capital structure after the recap & repurchase, and the subscript
485 "Post" indicates values after the recap & repurchase.
486
487
488 11. The price after the recap & repurchase is: P Post = SPost/nPost. But we can also find the price as:
PPost = (VopNew − DOld)/nPrior.
489
490 12. The EBIT is $400 million; see Figure 15-4. Net income is: NI = (EBIT − r dD)(1 − T).
491 13. Earnings per share: EPS = NI/nPost.
492
493
494
495 Data for Figure 15-7
496 wd 0% 10% 20% 30%
497 After-Tax Cost of De 5.85% 6.00% 6.15% 6.53%
498 Cost of Equity 12.21% 12.67% 13.25% 13.99%
499 WACC 12.21% 12.00% 11.83% 11.75%
500
501
502 Figure 15-7
503 Effects of Capital Structure on Cost of Capital
504
505
Cost of Capital

18%

16%

14%

12%

10%
 A B C D E
506
507 Cost of Capital
508
509 18%
510
511 16%
512
513
514 14%
515
516 12%
517
518
519 10%
520
521 8%
522
523
524 6%
525
526 4%
527
528
529 2%
530
531 0%
532
533 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%
534
535 Percent Financed with Debt
536
537
538
539
540 Data for Figure below
541 wd 0% 10% 20% 30%
542 Vop $2,457.00 $2,500.00 $2,535.93 $2,553.19
543 Debt $0.00 $250.00 $507.19 $765.96
544 Equity (S) $2,457.00 $2,250.00 $2,028.74 $1,787.23
545 V for chart $2,458.00 $2,501.00 $2,536.93 $2,554.19
546 $1.00 $1.00 $1.00 $1.00
547
548 Figure 15-8
549 Effects of Capital Structure on the Value of Operations
550
551
552
553
554
Value
555
556
557
$3,000
of
558 $2,500 Oper
$2,000 ation
$1,500
s
$1,000

$500
 Value
$3,000
of
559
A $2,500 B C
Oper D E

560
561
562
$2,000 ation
563
564 $1,500
s
565
566
567 $1,000
568
569
570
$500
571
572
573
574 $0
575 0% 10% 20% 30% 40% 50%
576 Percent Financed with Debt
577
578
579
580
581
582
583
584
585 15-6 Anatomy of a Recapitalization
586
587 Strasburg will issue additional debt and use the proceeds to repurchase stock. This is a recapitalization, often called a "recap." When Stras
588 announces its planned recapitalization, investors realize that the company will be worth more after the recap because it will have a lower co
capital. Therefore, the stock price will increase when the plans are announced, even though the actual repurchase has not yet occurred. If t
589 price did not increase until after the actual repurchase, it would be possible for an investor to buy the stock immediately prior to the repurc
590 then reap a reward the next day when the repurchase occurred. Current stockholders realize this, and refuse to sell the stock unless they ar
591 price that is expected immediately after the repurchase occurs.
592
593
594
595
596
597
598 Figure 15-9
599 Anatomy of a Recapitalization (Millions, Except Per Share Data)
600
601
602 Before Issuing After Debt Issue, but Post
603 Additional Debt Prior to Repurchase Repurchase
604 (1) (2) (3)
605
606 Percent financed with debt: wd 10% 30% 30%
607
608 Value of operations $2,500.00 $2,553.19 ###
609 + Value of ST investments $0.00 $515.96 $0.00
610 Estimated total intrinsic value $2,500.00 $3,069.15 ###
 A B C D E
611 − Debt $250.00 $765.96 $765.96
612 Estimated intrinsic value of equity $2,250.00 $2,303.19 ###
613 ÷ Number of shares $100.00 $100.00 $77.60
614 Estimated intrinsic price per share $22.50 $23.03 $23.03
615
616 Value of stock $2,250.00 $2,303.19 ###
617 + Cash distributed in repurchase $0.00 $0.00 $515.96
618 Wealth of shareholders $2,250.00 $2,303.19 ###
619
620 Numbers in the figure are shown as rounded values for clarity in reporting. However,
621 unrounded values are used for all calculations.
622
623 Notes: 1. The value of ST investments in Column 2 is equal to the amount of cash raised by issuing
624 additional debt but that has not been used to repurchase shares:
ST investments = DNew − DOld.
625
626
627 2. The value of ST investments in Column 3 is zero because the funds have been used to
628 repurchase shares of stock.
629 3. The number of shares in Column 3 reflects the shares repurchased:
630 nPost = nPrior − (CashRep/PPrior) = nPrior − ([DNew − DOld]/PPrior).
631
632
633
634 Figure 15-10
635 Effect of Capital Structure on Intrinsic Stock Price and Earnings per Share
636
637
638
639
640 Stock Price EPS
641
642 $25 $6
643
644 $20 $5
645
646 $4
$15
647
648 $3
649 $10
650 $2
651 $5 $1
652
653 $0 $0
654 0% 10% 20% 30% 40% 50%
655
656 Percent Financed with Debt
657
658
659
660
661 Shortcut Formulas Applied to Change in Capital Structure: w d Prior = 10%, wd Post = 30%
662
 A B C D E
663 Inputs:
664 wd = 30%
665 VopNew = $2,553.19
666 nPrior = 100.00
667 DNew = $765.96
668 DOld = $250.00
669
670
671 Shortcuts:
672 SPost = VopNew (1-wd) = $1,787.23
673 nPost = nPrior (VopNew - DNew) / (VopNew - DOld) = 77.60
674 PPost = (VopNew - DOld) / nPrior = $23.03
675
676
677
678 15-8 Risky Debt and Equity as an Option
679
680 If we relax the MM assumption that debt is risk free, then we allow for management to make the decision of whether or not to default on the
681 This is like an option: If management decides NOT to default on the debt, i.e. if management decides to make a required interest or principal
then the stockholders get to keep the firm. If management defaults on the the interest or principal payment, then the stockholders lose the f
682
683
684
685 Kunkel's situation
686
687 Face value of zero coupon debt $10,000,000
688 Time to maturity (years) 5
689
690 When the debt comes due, Kunkel will repay the $10,000,000 only if the value of the firm exceeds $10,000,000 at the time the
691 debt comes due. This is like exercising an option on the value of the firm with an exercise price equal to $10,000,000. Today,
owning the equity in Kunkel is like owning a call option on the value of the firm that has five years to expiration and a strike
692 price of $10 million. This can be valued using the Black-Scholes Option Pricing Model (BSOPM). See Chapter 8 for more details
693 on the BSOPM.
694
695
696
697 Black-Scholes Option Pricing Model
698
699 Suppose the total value of the company at the time it issus the zero coupon debt is $20 million (this is the value of existing
700 assets plus the proceeds raised when the debt is issued).
701
702 Total value of firm when debt is issued = Value of operating assets + proceeds from issuing debt
703 = Value of debt + value of equity
704 = $20,000,000
705
706 The inputs to the Black-Schole model are:
707
708 Total value of firm (P) $20.00 Analogous to the stock price from the BSOPM
709 Face value of debt (X) $10.00 Analogous to the exercise price
710 Risk free rate (rRF) 6.0%
711 Maturity of debt in years (T) 5.00 Analogous to time to expiration of option
 A B C D E
712 Standard deviation of total value's return (σ) 0.40 This is the standard deviation of the total value of the firm'
713
714
715 Applying the Black-Schole model:
716
717 d1 1.5576
718 d2 0.6632
719 N(d1) 0.9403
720 N(d2) 0.7464
721 Call Price = Equity Value = $13.28
722
723 How much did Kunkel receive for issuing face value $10 million in zero coupon debt?
724
725 If the total value of the firm is $20 million, and the equity is worth
726 then the value of the debt should be what is left over:
727
728 Therefore, the proceeds on the debt at the time it is issued are: $6.72
729
730
731 The yield on zero coupon debt is calculated like the rate on a single future value:
732
733 PV(1+I)N = FV
734
735 Soving for the rate, I:
736
737 I = [(FV/PV)(1/N)]-1
738
739 Therefore, the yield on the debt at the time it is issued is:
740
741 FV = Face value of debt $10.00
742 N = Number of years until maturity on date when issued = $5.00
743 PV = Present value of debt when issued = $6.72
744 Yield on Debt 8.266%
745
746
747 If management can change the riskiness of its projects--i.e. change the volatility of the total company, then it can change the
748 relative values of the debt, equity, and the yield on the debt.
749
750
751
752 Table 15-2
753 The Value of Kunkel’s Debt and Equity for Various Levels of Volatility (Millions
754 of Dollars)
755
756
757 Standard Deviation
758 Of Total Value Total Value Equity Value Debt Value Yield on Debt
Base Case values to
759 right $20 $13.28 $6.72 $0.08
760 20% $20 $12.62 $7.38 6.25%
761 40% 20 13.28 6.72 8.27%
 A B C D E
762 60% 20 14.51 5.49 12.74%
763 80% 20 15.81 4.19 18.99%
764 100% 20 16.96 3.04 26.92%
765
766
767
768 Debt and Equity Values for Various Levels of Volatility When the Total Value is $11 Million
769
770 Total Value of Firm $11.00 Analogous to the stock price from the BSOPM
771 Face Value of Debt $10.00 Analogous to the exercise price
772 Risk Free rate 0.06
773 Maturity of debt (years) 5.00 Analogous to time to expiration of option
774 Standard Dev. 0.40 This is the standard dev. of the total value of the firm, not just the stock.
775 d1 0.8892
776 d2 -0.0052
777 N(d1) 0.8130
778 N(d2) 0.4979
779 Call Price = Equity Value $5.25
780
781 If the total value of the firm is $10 million, and the equity is worth
782 then the value of the debt should be what is left over:
783
784 FV = Face value of debt $10.00
785 N = Number of years until maturity on date when issued = 5.00
786 PV = Present value of debt when issued = $5.75
787 Yield on Debt 11.723%
788
789
790
791 Not Reported in Textbook
792 The Value of Kunkel’s Debt and Equity for Various Levels of Volatility if Total
793 Value is $11 (Millions of Dollars)
794
Standard Deviation
795 Of Total Value Total Value Equity Value Debt Value Yield on Debt

796
Base Case values to
right $11 $5.25 $5.75 11.72%
797 20% $11 $4.00 $7.00 7.40%
798 40% 11 5.25 5.75 11.72%
799 60% 11 6.54 4.46 17.54%
800 80% 11 7.69 3.31 24.75%
801 100% 11 8.64 2.36 33.50%
802
803
804
805
806 Expected Return Compared to Yield to Maturity on Debt
 A B C D E
807
808 Not Reported in Textbook
809
Yield to Maturity and Expected Return on Debt for Various Levels of Volatility
810 and Debt. Total Value is $20 (Millions of Dollars)
811
812
813 Total Value of Firm $20.00 Analogous to the stock price from the BSOPM
814 Face Value of Debt $10.00 Analogous to the exercise price
815 Risk Free rate 0.06
816 Maturity of debt (years) 5.00 Analogous to time to expiration of option
817 Standard Dev. 0.40 This is the standard dev. of the total value of the firm, not just the stock.
818 d1 1.5576
819 d2 0.6632
820 N(d1) 0.9403
821 N(d2) 0.7464
822 Call Price = Equity Value $13.28
823
824 If the total value of the firm is $10 million, and the equity is worth
825 then the value of the debt should be what is left over:
826
827 FV = Face value of debt = $10.00
828 N = Number of years until maturity on date when issued = 5.00
829 PV = Present value of debt when issued = $6.72
830 Yield to Maturity on Debt = 8.266%
831
832 The yield to maturity above is not equal to the expected (or required) return on the debt. Rather, the YTM is the
833 maximum return the bondholders will get, and they will only get that if the company doesn't default. If the
company does default, the bondholders will get less. Thus the expected return is less than the YTM.
834
835 Option pricing theory says that the expected return can be calculated from the inputs to the option pricing
836 model, but using the unlevered expected return on the stock (that is, the expected return on the entire company,
not just the equity) rather than the risk free rate to calculate the actual expected returns on the debt.
837
838
839
840
841 Options pricing theory shows that (expected payoff from zero coupon debt) =
842 (face value of debt) x (probability the equity holders fully pay back the debt) + (expected payoff if the equity
holders default on the debt).
843 These amounts are functions of N(d 1*) and N(d2*) where d1* and d2* are the same as d1 and d2 calculated with the
844 regular Black Scholes Option Pricing Model, but with the risk free rate replaced by the unlevered expected
845 return on the stock.
846
847
848
849 N(d2*) = probability of stockholders fully paying off the debt.
850 (S0ert-S0ertN(d1*)) = expected payoff to bondholders if the stockholders default where S 0 is the total value of the
851 firm at time zero.
So the overall expected payoff to bondholders is XN(d 2*)+(S0ert-S0ertN(d1*))
852 where X is the face value of the debt and r is the unlevered expected rate of return on the total value of the
853 company rather than the risk free rate.
854
855 The expected rate of return is the return calculated from investing the value of debt from the option pricing
model and receiving the expected payoff.
856
857
858
 A B C D E
859
860 Expected unlevered return on stock = 9%
861
862 d1* = 1.7253 This uses the expected unlevered return on the stock in the calculation rather tha
863 d2* = 0.8309 This uses the expected unlevered return on the stock in the calculation rather tha
864 N(d1*) = 0.9578
865 N(d2*) = 0.7970 = Probability of fully retiring the debt (probability of exercise)
866
867

Probability of retiring
868 Face Value of Debt X debt +

869 N(d2*) (S0ert-S0ertN(d1*))

870
871 $10.00 X 0.7970 +
872
873
874 Price of bond = $6.72
875 Face value of bond = $10.00 YTM =
876 Expected payoff = $9.295 Expected Return =
877
878
879
880 Yield to maturity and expected return on debt for different levels of standard deviation of total value.

881 Standard Deviation

of Total Value Total Value Equity Value Debt Value Debt YTM

882 Base Case values to

right $20.00 $13.28 $6.72 8.27%
883 10% $20.00 $12.59 $7.41 6.18%
884 20% $20.00 $12.62 $7.38 6.25%
885 30% $20.00 $12.83 $7.17 6.89%
886 40% $20.00 $13.28 $6.72 8.27%
887 50% $20.00 $13.86 $6.14 10.25%
888 60% $20.00 $14.51 $5.49 12.74%
889 70% $20.00 $15.17 $4.83 15.66%
890 80% $20.00 $15.81 $4.19 18.99%
891 90% $20.00 $16.41 $3.59 22.74%
892 100% $20.00 $16.96 $3.04 26.92%
893
894
895 Yield to maturity and expected return on debt for different face values of debt.

896 Standard Deviation

Face Value of Debt of Total Value Total Value Equity Value Debt Value

897 Base Case values to

right 40% $20.00 $13.28 $6.72
898 $2.00 40% $20.00 $18.52 $1.48
899 $4.00 40% $20.00 $17.07 $2.93
900 $6.00 40% $20.00 $15.70 $4.30
901 $8.00 40% $20.00 $14.44 $5.56
 A B C D E
902 $10.00 40% $20.00 $13.28 $6.72
903 $12.00 40% $20.00 $12.22 $7.78
904 $14.00 40% $20.00 $11.27 $8.73
905 $16.00 40% $20.00 $10.40 $9.60
906 $18.00 40% $20.00 $9.62 $10.38
907 $20.00 40% $20.00 $8.91 $11.09
908 $25.00 40% $20.00 $7.41 $12.59
909 $30.00 40% $20.00 $6.22 $13.78
910 $35.00 40% $20.00 $5.27 $14.73
911 $40.00 40% $20.00 $4.50 $15.50
912 $45.00 40% $20.00 $3.87 $16.13
913 $50.00 40% $20.00 $3.35 $16.65
914 $55.00 40% $20.00 $2.92 $17.08
915 $60.00 40% $20.00 $2.55 $17.45
916 $65.00 40% $20.00 $2.25 $17.75
917
918
919
Note that as the face value of debt increases, the expected return on the debt approaches the unlevered expected
920 return on the stock. This is because as the face value of debt increases, the probability that the stockholders will
921 default on the debt and turn the company over to the bondholders approaches 1 and the debt's payoffs
922 approach those of simply owning the company without any debt at all.
 F G H I
1 11/21/2018
ructure Decisions
2
3
4
5
6 if a high percentage of a firm's costs are fixed, hence
firm's operations. Thus,
7
ating leverage. High operating leverage produces a situation where a small
8 two operational plans with different degrees of
ollowing example compares
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
ty. 50
51
 F G H I
52
53 V)
54 $1.50
55
56
57
58 V)
59 $1.00
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
Panel B: Financial Leverage
79
80
ROE 81
50.0% 82
83
40.0% 84
85
30.0% 86
Crossover at 76
87 Units
Million

20.0%
88
Plan U
Break-even at8960
10.0%
90
Million Units
91
0.0%
92
93
10.0%
94
95
20.0%
96
97 Plan L
98Break-even at 64
30.0%
99 Million Units
100
40.0%
0 20 40 60 80 100 120 140

Units Sold (Millions)

 0.0%

10.0%

20.0%
Plan L
Break-even at 64
30.0% Million Units
F G H I
40.0%
101
0 20 40 60 80 100 120 140
102
103
Units Sold (Millions)
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125 Data for Graph

ate Taxes 126 Debt VU

127 $0 $100
128 $15 $100
129 $30 $100
130 $45 $100
131 $60 $100
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
e
 F G H I
e 152
153
154
155
156
157
158
deductibility to 30% of159
EBITDA for the years 2018-2021 and 30% of EBIT for
ied forward to offset future
160 taxes. When applying this rule to EBIT and using
tax shield immediately is:
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193 TCJA rates
194 VU = $100
195 Combined federal plus state corporate tax rate = T C = 25.0%
196 Personal tax rate on debt = Td = 32.0%
197 Effective personal tax rate on stock = T s = 12.0%
198 Value in bracket = 2.9%
199
200
 F G H I
201
202
203
204
205
206
207 Data for Graph
208 Debt
209 $0
210 $10
211 $20
212 $30
213 $40
214 $50
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
Value Reduced by
243
Banruptcy-Related Costs
244
245
246
247
248
249
250
251
252
253
254

l Structure:
helter Benefits =
ruptcy-Related Costs
 F G H I
255
256
257
258
259
260
261
262
263
l Structure: 264
helter Benefits = 265
ruptcy-Related Costs 266
267
268
269
270
271
272
273
274
ble) but also increases275
the cost of debt (because the
r risk as measured by276
beta and the cost of equity.
areholder wealth and implement that capital structure
277
try, current market conditions, etc.).
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296 Note: WACC is rounded to 4 decimal places.
297
298
299
300
301
302
303
304
 F G H I
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
market values) that corresponds with each capital structure
he unlevered beta (b U)320
because it will be needed to identify
321
322
323
324
325
326
es Under Consideration 327
(w d)
328 40% 50%
329
330
331
gliani-Miller model. We 332use the model to determine beta at different amount of
333of equity associated with those debt ratios. Here is a
ebt ratios to find the cost
334
335
336
337
t used no debt, T is the338
marginal tax rate, D is the market value of the debt, and S
339
340
341
342
343
344
will be used to estimate345
the unlevered beta.
346
347
348
349
350
351
352
353
354
355
 F G H I
356
each capital structure357
under consideration: (1) Estimate
cost of debt. (3) Calculate
358 the weighted average cost of
ue of free cash flows discounted by the new WACC. The
alue of operations. 359
360
361
362
363
364
15-11a to determine the 365levered beta for each of the capital
tal structure with 20% 366
debt is:
367
368
369
370
371
372
373
374
375
376
377
e of the levered beta for each capital structure:
378
379 40% 50%
380 1.398 1.632
381
382
383
384
385
386
387
388
389
390 40% 50%
391 14.98% 16.36%
392
393
394
395
396
397 40% 50%
398 6.67% 6.67%
399 5.54% 5.54%

400 2.77% 4.15%

401
402
403
404

Premium for
Financial Risk:
(b − bU ) x RPM

Premium for
Business Risk:
bU x RPM = 5.54%
 F G H I
405
406
407
408
409
410Premium for
411Financial Risk:
412(b − bU ) x RPM
413
414
415
Premium for
416
Business Risk:
417
bU x RPM = 5.54%
418
419
420
Risk-Free
421
Rate:
422
rRF = 6.67%
423
40% 50% 424
425
426
427
428
429
430
431
432
433
434
of the expected interest rate for each capital structure under consideration.
es up as the percentage
435of debt goes up. The investment bankers' estimates are
arket values.
436
437
438 explain the remaining information in the figure.
quity. The following sections
439
440
441
442
443
m Financed with Debt (w d
)
444 40% 50%
445 60.00% 50.00%
446 1.398 1.632
447 14.98% 16.36%
448 10.10% 12.20%
449 7.58% 9.15%
450 12.02% 12.76%
451 $2,495.84 $2,351.10
452 $998.34 $1,175.55
453 $1,497.50 $1,175.55
454 66.68 55.95
455 $22.46 $21.011
456 $224.38 $192.44
 F G H I
457 $3.37 $3.44
rity but are calculated458 using Excel’s full precision unless
459 values will be inexact.
s using the figure’s rounded
460
461
462
ture is estimated by Hamada's formula with a 25% federal-
and the propsed capital 463structure:

f Hamada's formula with 464the current capital structure (w

465
n in the blue range of cells:
d

466
467
468
469
ormula with a risk-free470 rate of 6.67% and a market risk
471
472
473
d as: 474
475
476
s: 477
300 million and g L = 0.
478
479
ation and repurchase 480 is S Post = Vop − Debt = ws x Vop
481
ompleted is found using: 482
483
iginal capital structure where w d = 10%, the subscript
484
ucture after the recap & repurchase, and the subscript
hase. 485
486
487
SPost/nPost. But we can also
488find the price as:
489
come is: NI = (EBIT − r490
d
D)(1 − T).
491
492
493
494
495
496 40% 50%
497 7.58% 9.15%
498 14.98% 16.36%
499 12.02% 12.76%
500
501
502
503
504
505
 F G H I
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
40% 45% 50% 533
534
ebt 535
536
537
538
539
540
541 40% 50%
542 $2,495.84 $2,351.10
543 $998.34 $1,175.55
544 $1,497.50 $1,175.55
545 $2,496.84 $2,352.10
546 $1.00 $1.00
547
548
549
550
551
552
553
554
555
556
557
558
 F G H I
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
40% 50%
575
nt Financed with Debt 576
577
578
579
580
581
582
583
584
585
586
587
ase stock. This is a recapitalization, often called a "recap." When Strasburg
mpany will be worth more
588 after the recap because it will have a lower cost of
nnounced, even though the actual repurchase has not yet occurred. If the stock
ossible for an investor589
to buy the stock immediately prior to the repurchase, and
590this, and refuse to sell the stock unless they are paid the
rent stockholders realize
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
 F G H I
611
612
613
614
615
616
617
618
619
620 However,
ues for clarity in reporting.
621
622
623raised by issuing
ual to the amount of cash
purchase shares: 624
625
626
627 been used to
ro because the funds have
628
e shares repurchased:629
ld
]/PPrior). 630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
 F G H I
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
r management to make 680the decision of whether or not to default on the debt.
ebt, i.e. if management681
decides to make a required interest or principal payment,
n the the interest or principal payment, then the stockholders lose the firm.
682
683
684
685
686
687
688
689
690 $10,000,000 at the time the
the value of the firm exceeds
irm with an exercise price
691 equal to $10,000,000. Today,
of the firm that has five years to expiration and a strike
692 See Chapter 8 for more details
on Pricing Model (BSOPM).
693
694
695
696
697
698
699(this is the value of existing
oupon debt is $20 million
700
701
702 from issuing debt
perating assets + proceeds
703
704
705
706
707
708
Analogous to the stock price from the BSOPM
709
Analogous to the exercise price
710
711
Analogous to time to expiration of option
 F G H I
712
This is the standard deviation of the total value of the firm's total value, not just the standard deviation of its stock.
713
714
715
716
717
718
719
720
721
722
723
724
725 $13.28 million,
726 $6.72 million.
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
e volatility of the total747
company, then it can change the
748
749
750
751
752
753
754
755
756 Percentage
Change in
757 Equity Value
758 from Base Case
759 Note: this row has the links to outputs for the data table below the row, but the font is yellow so you can't see them. This is a
760 -4.98%
761 0.00%
 F G H I
762 9.27%
763 19.06%
764 27.77%
765
766
767
the Total Value is $11 768 Million
769
770
to the stock price from the BSOPM
771
772
to time to expiration 773
of option
774value of the firm, not just the stock.
standard dev. of the total
775
776
777
778
779
780
781 $5.25 million,
782 $5.75 million.
783
784
785
786
787
788
789
790
791
792
793
794
795

Percentage
796 Change in
Equity Value
from Base Case
797 -24%
798 0%
799 25%
800 46%
801 64%
802
803
804
805
806
 F G H I
807
808
809
810
811
812
to the stock price from813the BSOPM
814
815
to time to expiration 816
of option
817value of the firm, not just the stock.
standard dev. of the total
818
819
820
821
822
823
824 $13.28
825 $6.72
826
827
828
829
830
831
832 the YTM is the
) return on the debt. Rather,
if the company doesn't833default. If the
ed return is less than the YTM.
834
from the inputs to the835
option pricing
the expected return on the entire company,
836
al expected returns on the debt.
837
838
839
840
n debt) = 841
he debt) + (expected payoff
842 if the equity
e the same as d1 and d843
2
calculated with the
844 expected
e replaced by the unlevered
845
846
847
848
849
850
s default where S 0 is the total value of the

(d1*))
851
852
rate of return on the total value of the
853
854
he value of debt from the
855option pricing
856
857
858
 F G H I
859
860
861
he expected unlevered 862
return on the stock in the calculation rather than the risk free rate.
863
he expected unlevered return on the stock in the calculation rather than the risk free rate.
864
ity of fully retiring the865
debt (probability of exercise)
866
867
Expected
payoff if Expected payoff from
868 stockholders = bond
default

869 (S0e -S0e N(d1 ))

rt rt *

870
871 $1.32483 = $9.2946
872
873
874
875 8.266%
876 6.693% Note that Expected return will always be less than YTM.
877
878
879
880 value.
tandard deviation of total

881 Expected
Return on Debt

882 6.69%
883 6.18%
884 6.23%
885 6.44%
886 6.69%
887 6.90%
888 7.06%
889 7.18%
890 7.27%
891 7.35%
892 7.41%
893
894
895
Expected
896 Return on
Debt YTM Debt

897 8.27% 6.69%

898 6.22% 6.20%
899 6.45% 6.27%
900 6.91% 6.40%
901 7.54% 6.54%
 F G H I
902 8.27% 6.69%
903 9.06% 6.84%
904 9.90% 6.98%
905 10.77% 7.11%
906 11.64% 7.24%
907 12.52% 7.35%
908 14.71% 7.61%
909 16.84% 7.82%
910 18.90% 8.01%
911 20.88% 8.16%
912 22.78% 8.29%
913 24.60% 8.41%
914 26.35% 8.51%
915 28.02% 8.59%
916 29.63% 8.67%
917
918
919
he debt approaches the unlevered expected
920
s, the probability that the stockholders will
921 payoffs
pproaches 1 and the debt's
l. 922
 J K L M N O
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78 Data Table for Figure
79 x-axis for both ROE for Panel A ROE for Panel b
80 panels. Plan A Plan U Plan U
81 Q 11.3% 15.0% 15.0%
82 0 -7.5% -22.5% -22.5%
83 20 -3.8% -15.0% -15.0%
84 40 0.0% -7.5% -7.5%
85 60 3.8% 0.0% 0.0%
86 64 4.5% 1.5% 1.5%
87 76 6.8% 6.0% 6.0%
88 80 7.5% 7.5% 7.5%
89 100 11.3% 15.0% 15.0%
90 120 15.0% 22.5% 22.5%
91 140 18.8% 30.0% 30.0%
92
93
94
95
96
97
98
99
100
 J K L M N O
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126 VL Pre-TCJA VL wd
127 $100 $100 0%
128 $103.75 $106 14%
129 $107.50 $112 28%
130 $111.25 $118 40%
131 $115.00 $124 52%
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
 J K L M N O
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193 Pre-TCJA rates
194 $100
195 40.0%
196 33.0%
197 12.0%
198 21.2%
199
200
 J K L M N O
201
202
203
204
205
206
Data for207
Graph Pre-TCJA
208 VU VL Pre-TCJA VL wd wd
209 $100 $100 $100 0% 0%
210 $100 $100.29 $102.12 10% 10%
211 $100 $100.59 $104.24 20% 19%
212 $100 $100.88 $106.36 30% 28%
213 $100 $101.18 $108.48 40% 37%
214 $100 $101.47 $110.60 49% 45%
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233 Data for Graph This formula gives a reasonable result for financial distress costs: Fin dis =
234 Note: Cell heigth and width are locked for cells colored Parameter for reasonable financial distress function = Z =
235 M&M II
236 Leverage (D) VU Actual Value Horzontal axis
237 $0 $100 $100 $100.00 60
238 $6 $100 $101.50 $101.30 60
239 $12 $100 $103.00 $102.40 60
240 $18 $100 $104.50 $103.50 60
241 $24 $100 $106.00 $104.28 60
242 $30 $100 $107.50 $104.56 60
243 $36 $100 $109.00 $103.95 60
244 $42 $100 $110.50 $101.83 60
245 $48 $100 $112.00 $97.12 60
246 $54 $100 $113.50 $87.97 60
247
248
249
250
251
252
253
254
 J K L M N O
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
 J K L M N O
712
rm's total value, not just the standard deviation of its stock.
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
nks to outputs for the 759
data table below the row, but the font is yellow so you can't see them. This is a good way to "hide" material you don't want to show in a presentatio
760
761
 J K L M N O
859
860
861
862
863
864
865
866
867

868

869
870
871
872
873
874
875
rn will always be less 876
than YTM.
877
878
879
880

881

882
883
884
885
886
887
888
889
890
891
892
893
894
895

896

897
898
899
900
901
 P Q R S T
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79for Panel b
ROE ROIC
80 Plan L Plan U Plan L Line at 0
81 18.0% Q 15.0% 15.0%
82 -32.0% 0 -22.5% -22.5% 0
83 -22.0% 20 -15.0% -15.0% 0
84 -12.0% 40 -7.5% -7.5% 0
85 -2.0% 60 0.0% 0.0% 0
86 0.0% 64 1.5% 1.5% 0
87 6.0% 76 6.0% 6.0% 0
88 8.0% 80 7.5% 7.5% 0
89 18.0% 100 15.0% 15.0% 0
90 28.0% 120 22.5% 22.5% 0
91 38.0% 140 30.0% 30.0% 0
92
93
94
95
96
97
98
99
100
 P Q R S T
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233 result for financial distress costs: Fin dis = a -(1-ae^ZD)
s formula gives a reasonable
Parameter for 234
reasonable financial distress function = Z = 0.09
235 Data to create graph and other data
236 wd TD Fin dis costs
237 0% $0.00 $0.00
238 6% $1.50 $0.20
239 12% $3.00 $0.60
240 17% $4.50 $1.00
241 23% $6.00 $1.72
242 28% $7.50 $2.94
243 33% $9.00 $5.05
244 38% $10.50 $8.67
245 43% $12.00 $14.88
246 48% $13.50 $25.53
247
248
249
250
251
252
253
254
 P Q R S T
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759you don't want to show in a presentation.
od way to "hide" material
760
761
SECTION 15-2
SOLUTIONS TO SELF-TEST

A firm has fixed operating costs of $100,000 and variable costs of $4 per unit. If it sells the product for $6 per unit, what is the
breakeven quantity?

F= $100,000
V= $4
P= $6

QBE 50,000
SECTION 15-6
SOLUTIONS TO SELF-TEST

JAB Industry's capital structure 20% debt. Use the following data to calculate its cost of equity: b L = 1.4; rRF = 6% and RPM =
5%.

bL 1.10
rRF 6%
RPM 5%

rs = 11.50%

Use the Hamada equation to calculate JAB's unlevered beta and unlevered cost of equity. The tax rate is 20%.

Tax rate 25%

wd 20%
ws 80%

bU 0.9263

rs,U 10.63%

What would the cost of equity be if JAB changes its capital structure to 35% debt?

wd = 35%
ws = 65%
bL = 1.30

rs,L 12.50%
SECTION 15-7
SOLUTIONS TO SELF-TEST

A firm’s value of operations is equal to $800 million after a recapitalization (the firm had no debt before the recap). It
raised $200 million in new debt and used this to buy back stock. The firm had no short-term investments before or after
the recap. After the recap, wd = 25%. The firm had 10 million shares before the recap. Its federal-plus-state tax rate is 25%.
What is S (the value of equity after the recap)? What is P Post (the stock price) after the recap? What is n Post (the number of
remaining shares) after the recap?

Vop $800
D $200
wd 25%
nPrior 10

S= $600

PPost = $80.00

nPost = 7.5
 WEB EXTENSION 15B 11/21/2018

BOND REFUNDING

This example examines the issue of replacing existing debt with newly issued debt. First, is it profitable to call an outstanding issue and
replace it with a new issue? Second, even if refunding now is profitable, would the firm's expected value be further increased if the
refunding were postponed until a later date?

The firm should refund only if the present value of the savings exceeds the cost of the refunding. The after-tax cost of debt should be
used as the discount rate, since there is relative certainty to the cash flows to be received. Using the example laid out in the chapter, we
will now evaluate such a scenario.

Figure 15B-1
Spreadsheet for the Bond Refunding Decision
Panel A: Input Data
Existing bond issue = $60,000,000 Years since old debt issued = 5
Original flotation cost = $3,000,000 Current call premium (%) = 10.0%
Maturity of original debt = 25 New bond issue = $60,000,000
Original coupon rate = 12.0% New flotation cost = $2,650,000
Call protection period = 5 New bond maturity = 20
Initial call premium (%) = 10.0% New cost of debt = 9.0%
Tax rate = 25.0% ST interest rate = 6.0%
Panel B: Investment Outlay Before-tax After-tax
1: Call premium on the old bond −$6,000,000 −$4,500,000
2: Flotation costs on new issue −$2,650,000 −$2,650,000
3: Immediate tax savings on old flotation expense $2,400,000 $600,000
4: Extra interest paid on old issue −$600,000 −$450,000
5: Interest earned on short-term investment $300,000 $225,000
6: Total after-tax initial outlay −$6,775,000

Panel C: Present Value of Annual Flotation

Cost Tax Effects: t = 1 to 20 Before-tax After-tax
7: Annual tax savings from new-issue flotation $132,500 $33,125
8: Annual lost tax savings from old-issue flotation −$120,000 −$30,000
9: Net flotation cost tax savings $12,500 $3,125 Since the annual flotation cost tax effects and inter
10: Maturity of the new bond (Nper) 20 To evaluate this project, we must find the present v
11: After-tax cost of new debt (Rate) 6.75%
12: PV of annual after-tax flotation cost savings $33,759

Panel D: Present Value of Annual Interest

Savings Due to Refunding: t = 1 to 20 Before-tax After-tax
13: Interest on old bond $7,200,000 $5,400,000
14: Interest on new bond −$5,400,000 −$4,050,000
15: Net interest savings $1,800,000 $1,350,000 Since the annual flotation cost tax effects and inter
16: Maturity of the new bond (Nper) 20 To evaluate this project, we must find the present v
17: After-tax cost of new debt (Rate) 6.75%
18: PV of annual after-tax interest savings $14,584,079

Panel E: Total Net Present Value of the Refunding After-tax

19: Total after-tax initial outlay −$6,775,000
20: PV of annual after-tax flotation cost savings $33,759
21: PV of annual after-tax interest savings $14,584,079
22: Total NPV of Bond Refunding $7,842,838
Our refunding analysis tells us that should the firm proceed with the bond refunding, the project will have a positive net
present value. However, unlike traditional capital budgeting decisions, the positive NPV does not tell the firm if it should
refund the bond issue. That decision is dependent upon several external factors, including interest rate expectations.

Scenario Analysis

Rates fall Rates stay the same Rates go up

Probability 25% 50% 25%
Rate 7% 9% 11%

NPV of refunding $20,049,044 $7,842,838 ($2,214,092)

Expected NPV $8,933,680
it profitable to call an outstanding issue and
pected value be further increased if the

nding. The after-tax cost of debt should be

sing the example laid out in the chapter, we

Since the annual flotation cost tax effects and interest savings occur for the next 20 years, they represent annuities.
To evaluate this project, we must find the present values of these savings.

Since the annual flotation cost tax effects and interest savings occur for the next 20 years, they represent annuities.
To evaluate this project, we must find the present values of these savings.
oject will have a positive net
s not tell the firm if it should
nterest rate expectations.