ChapterTool KitChapter 1411/21/18Distributions to Shareholders: Dividends and Repurchases14-2 Procedures for Cash DistributionsDeclaration date:Thursday, November 21, 2019Dividend goes with stock:Tuesday, December 17, 2019Ex-dividend date:Wednesday, December 18, 2019Thursday, December 19, 2019Holder-of-record date:Friday, December 20, 2019Payment date:Friday, January 10, 202014-7 Setting the Target Distribution Level: The Residual Distribution ModelThe optimal distribution ratio for a firm is a function of four factors. (1) Investors' preferences for dividends versus capital gains. (2) The firm's investment opportunities. (3) Its target capital structure. And (4), the availability and cost of external capital.The last three elements can be combined into the residual distribution model. Within the residual model, firms must determine the optimal capital budget, determine the amount of equity needed to fund the capital budget (based upon the target capital structure), use reinvested earnings to meet equity requirements whenever possible, and make distributions to shareholders only if more earnings are available than are needed for dividends. The residual model can be expressed as:Distributions =Net Income - [(Target equity ratio) * (Total capital budget)]Consider a firm whose net income for the current year is $100 million, their target equity ratio is 60%, and the expected capital budget is $50 million. What are its distributions to be made to shareholders, according to the residual model? Net Income$100Target equity ratio60%Total capital budget$50Distributions =Net Income - [(Target equity ratio) * (Total capital budget)]=$100-60%*$50=$70Distribution =70.0%What if the expected capital budget rose to $166.67 million?Total capital budget$166.67Distributions = =Net Income - [(Target equity ratio) * (Total capital budget)] =$100-60%*$167 =$0Distribution =0.0%The firm could not have a negative dividend, so a negative distribution must be a stock issue rather than a stock repurchase. Under the residual policy, if investment opportunities exceed net income, the firm should pay zero dividends and issue stock (or else increase its debt ratio to fund the investment opportunities).T&W's Distribution RatioNet income =$60Target equity ratio (ws) =60%PoorAverageGoodCapital budget$40$70$150Required equity (ws X Capital budget)$24$42$90Net income$60$60$60Required equity (ws X Capital budget)$24$42$90Distributions paid (NI – Required equity)$36$18−$30Note: a negative distribution means T&W would pay no dividends but would issue stock.Distribution ratio (Dividend/NI)60%30%0%14-9 A Tale of Two Cash Distributions: Dividends versus Stock RepurchasesFigure 14-1Projecting Benson Conglomerate's Financial Statements: Distributions as Dividends (Millions of Dollars)1. InputsActualProjected12/31/192020202120222023Sales growth rate5%5%5%5%Costs / Sales75.00%75.00%75.00%75.00%75.00%Depreciation / Net PPE10.00%10.00%10.00%10.00%10.00%Cas ...

1. ChapterTool KitChapter 1411/21/18Distributions to
Shareholders: Dividends and Repurchases14-2 Procedures for
Cash DistributionsDeclaration date:Thursday, November 21,
2019Dividend goes with stock:Tuesday, December 17, 2019Ex-
dividend date:Wednesday, December 18, 2019Thursday,
December 19, 2019Holder-of-record date:Friday, December 20,
2019Payment date:Friday, January 10, 202014-7 Setting the
Target Distribution Level: The Residual Distribution ModelThe
optimal distribution ratio for a firm is a function of four factors.
(1) Investors' preferences for dividends versus capital gains.
(2) The firm's investment opportunities. (3) Its target capital
structure. And (4), the availability and cost of external
capital.The last three elements can be combined into the
residual distribution model. Within the residual model, firms
must determine the optimal capital budget, determine the
amount of equity needed to fund the capital budget (based upon
the target capital structure), use reinvested earnings to meet
equity requirements whenever possible, and make distributions
to shareholders only if more earnings are available than are
needed for dividends. The residual model can be expressed
as:Distributions =Net Income - [(Target equity ratio) * (Total
capital budget)]Consider a firm whose net income for the
current year is $100 million, their target equity ratio is 60%,
and the expected capital budget is $50 million. What are its
distributions to be made to shareholders, according to the
residual model? Net Income$100Target equity ratio60%Total
capital budget$50Distributions =Net Income - [(Target
equity ratio) * (Total capital budget)]=$100-
60%*$50=$70Distribution =70.0%What if the expected
capital budget rose to $166.67 million?Total capital
budget$166.67Distributions = =Net Income - [(Target
equity ratio) * (Total capital budget)] =$100-60%*$167
=$0Distribution =0.0%The firm could not have a negative
dividend, so a negative distribution must be a stock issue rather

2. than a stock repurchase. Under the residual policy, if
investment opportunities exceed net income, the firm should
pay zero dividends and issue stock (or else increase its debt
ratio to fund the investment opportunities).T&W's Distribution
RatioNet income =$60Target equity ratio (ws)
=60%PoorAverageGoodCapital budget$40$70$150Required
equity (ws X Capital budget)$24$42$90Net
income$60$60$60Required equity (ws X Capital
budget)$24$42$90Distributions paid (NI – Required
equity)$36$18−$30Note: a negative distribution means T&W
would pay no dividends but would issue stock.Distribution ratio
(Dividend/NI)60%30%0%14-9 A Tale of Two Cash
Distributions: Dividends versus Stock RepurchasesFigure 14-
1Projecting Benson Conglomerate's Financial Statements:
Distributions as Dividends (Millions of Dollars)1.
InputsActualProjected12/31/192020202120222023Sales growth
rate5%5%5%5%Costs /
Sales75.00%75.00%75.00%75.00%75.00%Depreciation / Net
PPE10.00%10.00%10.00%10.00%10.00%Cash /
Sales1.00%1.00%1.00%1.00%1.00%Acct. rec. + Inv. /
Sales27.00%27.00%27.00%27.00%27.00%Net PPE /
Sales85.00%85.00%85.00%85.00%85.00%Acct. pay. + Accr. /
Sales10.00%10.00%10.00%10.00%10.00%Tax
rate25%25%25%25%25%2. Income
Statement12/31/201912/31/202012/31/202112/31/202212/31/20
23Net Sales$8,000.0$8,400.0$8,820.0$9,261.0$9,724.1Costs
(except depr.)6,000.06,300.06,615.06,945.87,293.0Depreciation
680.0 714.0 749.7 787.2
826.5EBIT$1,320.0$1,386.0$1,455.3$1,528.1$1,604.5Interest
expensea 0.0 0.0 0.0 0.0 0.0Pre-tax
earnings$1,320.0$1,386.0$1,455.3$1,528.1$1,604.5Taxes
330.0 346.5 363.8 382.0 401.1Net
income$990.0$1,039.5$1,091.5$1,146.0$1,203.4Regular
dividends$0.0$0.0$0.0$0.0$0.0Special
dividends$627.5$658.9$691.8$726.4Addition to
RE$412.0$432.6$454.2$476.93. Balance

3. Sheets12/31/192020202120222023Assets12/3012/3112/3012/31
12/3012/3112/3012/31Cash$80.0$84.0$84.0$88.2$88.2$92.6$92
.6$97.2$97.2Short-term
investmentsb0.0627.50.0658.90.0691.80.0726.40.0Acct. rec. +
Inv. 2,160.0 2,268.0 2,268.0 2,381.4 2,381.4
2,500.5 2,500.5 2,625.5 2,625.5Total current
assets$2,240.0$2,979.5$2,352.0$3,128.5$2,469.6$3,284.9$2,593
.1$3,449.1$2,722.7Net plant and equipment 6,800.0 7,140.0
7,140.0 7,497.0 7,497.0 7,871.9 7,871.9 8,265.4
8,265.4Total
assets$9,040.0$10,119.5$9,492.0$10,625.5$9,966.6$11,156.7$1
0,464.9$11,714.6$10,988.2Liabilities & EquityAcct. pay. +
Accr.$800.0$840.0$840.0$882.0$882.0$926.1$926.1$972.4$972
.4Line of credit 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0Total current
liabilities$800.0$840.0$840.0$882.0$882.0$926.1$926.1$972.4
$972.4Long-term debt 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0Total
liabilities$800.0$840.0$840.0$882.0$882.0$926.1$926.1$972.4
$972.4Common
stock2,400.02,400.02,400.02,400.02,400.02,400.02,400.02,400.
02,400.0Retained earningsc 5,840.0 6,879.5 6,252.0
7,343.5 6,684.6 7,830.6 7,138.8 8,342.2 7,615.8Total
common
equity$8,240.0$9,279.5$8,652.0$9,743.5$9,084.6$10,230.6$9,5
38.8$10,742.2$10,015.8Total liabilities &
equity$9,040.0$10,119.5$9,492.0$10,625.5$9,966.6$11,156.7$1
0,464.9$11,714.6$10,988.2Check for
balancing:YesYesYesYesYesYesYesYes4. Financial Deficit or
Surplus12/30/2012/31/2012/30/2112/31/2112/30/2212/31/2212/
30/2312/31/23Incr. spon. liab.$40.0$42.0$44.1$46.3+ Incr. LT
debt and stock$0.0$0.0$0.0$0.0− Previous line of
credit$0.0$0.0$0.0$0.0+ NI minus regular
dividends$1,039.5$1,091.5$1,146.0$1,203.4Increase in
financing$1,079.5$1,133.5$1,190.1$1,249.7− Increase in
operating assets$452.0$474.6$498.3$523.2Amount of deficit or

4. surplus financing:$627.5$658.9$691.8$726.4Line of
credit$0.0$0.0$0.0$0.0$0.0$0.0$0.0$0.0Short-term
investment$627.5$0.0$658.9$0.0$691.8$0.0$726.4$0.0Special
dividend$0.0$627.5$0.0$658.9$0.0$691.8$0.0$726.4 Source:
Numbers in the figure are shown as rounded values for clarity in
reporting. However, unrounded values are used for all
calculations, so columns may not total exactly.Notes:a To
simplify the example, we assume any short-term investment are
held for only part of the year and earn no interest.b If there is a
financial surplus, it is shown as a short-term investment on
December 30. These funds are distributed to investors on
December 31, so the balance of short-term investments goes to
zero on December 31.c Because no special dividends have been
paid out as of December 30, the retained earnings balance for
that date is equal to the previous year's retained earnings
balance plus the current year's net income less the regular
dividends. When short-term investments are sold and their
proceeds are used to make the special cash dividend payments
on December 31, the balance of retained earnings is reduced by
the amount of the total dividend payments (which is equal to the
regular dividend and the reduction in short-term investments
that funded the special dividend). Figure 14-2 Projecting
Benson Conglomerate's Liabilities & Equity: Distributions as
Stock Repurchases (Millions of
Dollars)ActualProjected12/31/192020202120222023Liabilities
& Equity12/3012/3112/3012/3112/3012/3112/3012/31Acct. pay.
+
Accr.$800.0$840.0$840.0$882.0$882.0$926.1$926.1$972.4$972
.4Line of credit 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0Total current
liabilities$800.0$840.0$840.0$882.0$882.0$926.1$926.1$972.4
$972.4Long-term debt 0.0 0.0 0.0 0.0 0.0 0.0 0.0
0.0 0.0Total
liabilities$800.0$840.0$840.0$882.0$882.0$926.1$926.1$972.4
$972.4Common
stock2,400.02,400.02,400.02,400.02,400.02,400.02,400.02,400.

5. 02,400.0Treasury stocka 0.0 0.0 ─627.5 ─627.5
─1,286.4 ─1,286.4 ─1,978.2 ─1,978.2 ─2,704.6Retained
earningsb$5,840.0$6,879.5$6,879.5$7,971.0$7,971.0$9,117.0$9
,117.0$10,320.4$10,320.4Total common
equity$8,240.0$9,279.5$8,652.0$9,743.5$9,084.6$10,230.6$9,5
38.8$10,742.2$10,015.8Total liabilities & equity$
9,040.0$10,119.5$ 9,492.0$10,625.5$ 9,966.6$11,156.7$
10,464.9$11,714.6$ 10,988.2Check for
balancing:YesYesYesYesYesYesYesYesNotes:All significant
digits in are used in calculations, but numbers in the Figure are
rounded, so columns may not total exactly. See Figure 14-1 for
income statements and assets.aWhen distributions are made as
repurchases, the treasury stock account is reduced by the dollar
value of the repurchase at the time of the repurchase, which
occurs when short-term investments are liquidated and used to
repurchase stock.bBecause no funds are paid out in dividends,
the retained earnings balance is equal to the previous balance
plus the year's net income because all net income is being
retained.Application of the Residual Distribution Model to
Benson Conglomerate (Millions of
Dollars)Projected12/31/202012/31/202112/31/202212/31/2023
Δcash$4.0$4.2$4.4$4.6 + Δ(Accts. rec. +
Inv.)$108.0$113.4$119.1$125.0 + ΔNet plant &
equipment$340.0$357.0$374.8$393.6 − Δ(Accts. pay. +
Accr.).$40.0$42.0$44.1$46.3Capital
budgeta$412.0$432.6$454.2$476.9Target equity
ratio100%100%100%100%Net
incomeb$1,039.5$1,091.5$1,146.0$1,203.4Required additional
equityc$412.0$432.6$454.2$476.9Residual distribution: NI −
Req. equ.$627.5$658.9$691.8$726.4Notes:aSee Figure 14-1 for
balance sheet projections. The capital budget is equal to the net
addition to total operating capital: ΔCash + Δ(Accts. rec. Inv) +
ΔNet plant & equipment − Δ(Accts. pay. + Accr.).bSee Figure
14-1 for income statement projections.cRequired additional
equity = Capital budget x Target equity ratio.12.00%Figure 14-
3 Benson Conglomerate's Value of Operations Under (Millions

6. of Dollars)WACC =
11.50%Projected12/31/201912/31/202012/31/202112/31/202212
/31/20231. Calculation of Free Cash FlowOperating current
assetsa$2,240.00$2,352.00$2,352.00$2,469.60$2,469.60$2,593.
08$2,593.08$2,722.73$2,722.73Operating current
liabilitiesb800.00840.00840.00882.00882.00926.10926.10972.4
1972.41NOWCc$1,440.00$1,512.00$1,512.00$1,587.60$1,587.6
0$1,666.98$1,666.98$1,750.33$1,750.33Net plant &
equipment6,800.007,140.007,140.007,497.007,497.007,871.857,
871.858,265.448,265.44Total net operating
capitald$8,240.00$8,652.00$8,652.00$9,084.60$9,084.60$9,538
.83$9,538.83$10,015.77$10,015.77NOPATe$990.00$1,039.50$0
.00$1,091.48$0.00$1,146.05$0.00$1,203.35$0.00Inv. in
operating capitalf412.00432.60454.23476.94Free cash flow
(FCF)g$627.50$658.88$691.82$726.412. Performance
Measures12/31/1912/31/2012/31/9912/31/2112/31/9912/31/2212
/31/9912/31/2312/31/99Expected
ROICh12.62%12.62%12.62%12.62%Growth in
FCFna5.00%5.00%5.00%Growth in
sales5.00%5.00%5.00%5.00%3.
Valuation12/31/1912/31/2012/31/9912/31/2112/31/9912/31/221
2/31/9912/31/2312/31/99Horizon value at 12/31/2023 (after
FCF paid)i$11,734.31Note: we can apply the horizon value
formula before the last projected year because FCF is growing
at a constant rate from the beginning.Value of
operationsj$9,653.85$10,136.54$10,643.37$11,175.53$11,734.3
1Notes:Numbers in the figure are shown as rounded values for
clarity in reporting. However, unrounded values are used for all
calculations. aSum of cash, accounts receivable, and
inventories.bSum of accounts payable and accruals.cNet
operating working capital is equal to operating current assets
minus operating current liabilities.dSum of NOWC and net plant
& equipmenteNet operating profit after taxes = (EBIT)(1−T).
Notice that NOPAT is equal to net income in this example
because there is no interest expense or income.fChange in net
operating capital from previous year.gFCF = NOPAT −

7. investment in operating capitalhExpected return on invested
capital = NOPAT divided by beginning capital.iHorizon value at
2023 is immediately after the FCF at 2023 has been paid, which
makes the horizon value at 2023 the present value of all FCF
from 2024 and beyond discounted back to 12/31/2023: HV2023
= [FCF2023 (1+gL)]/(WACC−gL).jValue of operations before
horizon = Vop(t) = (Vop(t + 1) + FCFt + 1)/(1+WACC).Figure
14-4 Benson Conglomerate's Intrinsic Stock Price for Each
Method of Distribution (Millions of Dollars, Except for Per-
Share Data)Section 1. Distribute as
DividendsProjected202020212022202312/31/1912/3012/3112/30
12/3112/3012/3112/3012/31Value of
operations$9,654$10,137$10,137$10,643$10,643$11,176$11,17
6$11,734$11,734+ Value of nonoperating
assets$0$628$0$659$0$692$0$726$0Total intrinsic value of
firm$9,654$10,764$10,137$11,302$10,643$11,867$11,176$12,4
61$11,734− Debt$0$0$0$0$0$0$0$0$0− Preferred
stock$0$0$0$0$0$0$0$0$0Intrinsic value of
equity$9,654$10,764$10,137$11,302$10,643$11,867$11,176$12
,461$11,734÷ Number of
shares$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,000$1,
000Intrinsic price per
sharea$9.65$10.76$10.14$11.30$10.64$11.87$11.18$12.46$11.
73Dividend per share$0.63$0.66$0.69$0.73Section 2. Distribute
as
Repurchase202020212022202312/31/1912/3012/3112/3012/3112
/3012/3112/3012/31Value of
operations$9,654$10,137$10,137$10,643$10,643$11,176$11,17
6$11,734$11,734+ Value of nonoperating
assets$0$628$0$659$0$692$0$726$0Total intrinsic value of
firm$9,654$10,764$10,137$11,302$10,643$11,867$11,176$12,4
61$11,734− Debt$0$0$0$0$0$0$0$0− Preferred
stock$0$0$0$0$0$0$0$0$0Intrinsic value of
equity$9,654$10,764$10,137$11,302$10,643$11,867$11,176$12
,461$11,734÷ Number of
sharesb1,000$1,000$942$942$887$887$835$835$786Intrinsic

8. price per
sharea$9.65$10.76$10.76$12.00$12.00$13.38$13.38$14.92$14.
92Notes:Numbers in the figure are shown as rounded values for
clarity in reporting. However, unrounded values are used for all
calculations. aThe projected intrinsic stock prices for four years
are shown in Ch14 Tool Kit.xls.bThe number of shares after the
repurchase is: nPost = nPrior − (CashRep/PPrior). In this
example, the entire amount of ST investments (i.e., the balance
of nonoperating assets) is used to repurchase stock.
Price per share (Dividends)
Price per share (Dividends)
43830 44195 44196 44560 44561 44925
44926 45290 45291 9.6538461538459881
10.764038461538277 10.136538461538278
11.30224038461518 10.64336538461518
11.867352403845926 11.175533653845925
12.460720024038206 11.734310336538206 Price
per share (Repurchase)
Price per share (Repurchase)
43830 44195 44196 44560 44561 44925
44926 45290 45291 9.6538461538459881
10.764038461538277 10.764038461538277
12.001902884615179 12.001902884615179
13.382121716345926 13.382121716345925
14.921065713725707 14.921065713725705
End of Month
Stock
Price
14-7SECTION 14-7SOLUTIONS TO SELF-TESTHamilton
Corporation has a target equity ratio of 65%. Its capital budget
is $2 million. If Hamilton has net income of $1.6 million and
follows a residual distribution model, how much will its
distribution be?Capital budget =$2,000,000Target equity ratio

9. =65%Net income =$1,600,000Residual distribution =$300,000
14-9SECTION 14-9SOLUTIONS TO SELF-TESTA firm's most
recent FCF was $2.4 million; the FCF is expected to grow at a
constant rate of 5%. The WACC is 14% and there are 2 million
shares outstanding. The firm has $12 million in short-term
investments which it plans to liquidate distribute in a stock
repurchase; the firm has no other financial investments or debt.
Verify that the value of operations is $28 million. Immediately
prior to the repurchase, what are the intrinsic value of equity
and the intrinsic stock price? How many shares will be
repurchased? How many shares will remain after the
repurchase? Immediately after the repurchase, what are the
intrinsic value of equity and the intrinsic stock price?Note: All
values in millions except per share data.FCF =$2.4milliong
=5%WACC = 14%nPrior =2.0millionShort-term investments
(Extra cash) =$12millionNote: All values in millions except per
share data.Prior RepurchaseAfter RepurchaseValue of
operations$28.0$28.0million+ Value of nonoperating
assets12.00.0millionTotal intrinsic value of
firm$40.0$28.0million− Debt0.00.0million− Preferred
stock0.00.0millionIntrinsic value of equity$40.0$28.0million÷
Number of shares2.01.4millionIntrinsic stock
price$20.00$20.00# shares repurchased =0.6
14-13SECTION 14-13SOLUTIONS TO SELF-TEST Suppose
you have 1,000 common shares of Burnside Bakeries. The EPS
is $6.00, the DPS is $3.00, and the stock sells for $90 per share.
Burnside announces a 3-for-1 split. Immediately after the split,
how many shares will you have, what will the adjusted EPS and
DPS be, and what would you expect the stock price to
be?Shares1,000EPS$6DPS$3Stock price$90Split factor (n-for-
1)3Shares3,000EPS$2.00DPS$1.00Price$30.00
Reflection and Discussion Forum Week 6
Reflect on the assigned readings for the week. Identify what you
thought was the most important concept(s), method(s), term(s),
and/or any other thing that you felt was worthy of your

10. understanding.
Also, provide a graduate-level response to each of the following
questions:
a. American Airlines and British Airways are proposing to
merge. If British pilots and American pilots are represented by
different unions, how would this merger affect airline costs?
Respond to the post of at least two peers, using 100
words minimum each.
[Your initial post should be based upon the assigned reading for
the week, so the textbook should be a source listed in your
reference section and cited within the body of the text. Other
sources are not required but feel free to use them if they aid in
your discussion].
[Your initial post should be at least 450+ words and in APA
format (including Times New Roman with font size 12 and
double spaced). Post the actual body of your paper in the
discussion thread then attach a Word version of the paper for
APA review].
[Your initial posting should be completed by Thursday at 11:59
p.m. EST. All peer replies must be completed by Sunday at
11:59 p.m. EST].
[Your post must be substantive and demonstrate insight gained
from the course material. A peer response such as “I agree with
her,” or “I liked what he said about that” is not considered
substantive and will not be counted for course credit. A blank
post just to review other submissions will not be tolerated].
Problem Set #6
1. Describe a decision a company has made when facing
uncertainty. Compute the expected costs and benefits of the
decision. Offer advice on how to proceed. Compute the profit
consequences of the advice
2. Identify something you buy or sell that could be bought or
sold using an auction. How would you run the auction? Do a
benefit-cost analysis of the auction relative to how you

11. currently buy or sell.
The assignment is to answer the question provided above in
essay form. This is to be in narrative form. Bullet points should
not to be used. The paper should be at least 1.5 - 2 pages in
length, Times New Roman 12-pt font, double-spaced, 1 inch
margins and utilizing at least one outside scholarly or
professional source related to organizational behavior. This
does not mean blogs or websites. This source should be a
published article in a scholarly journal. This source should
provide substance and not just be mentioned briefly to fulfill
this criteria. The textbook should also be utilized. Do not use
quotes. Do not insert excess line spacing. APA formatting and
citation should be used.
Problem Set #14
Question 1
Integrated Waveguide Technologies (IWT) is a 6-year-old
company founded by Hunt Jackson and David Smithfield to
exploit metamaterial plasmonic technology to develop and
manufacture miniature microwave frequency directional
transmitters and receivers for use in mobile Internet and
communications applications. IWT’s technology, although
highly advanced, is relatively inexpensive to implement, and its
patented manufacturing techniques require little capital as
compared to many electronics fabrication ventures. Because of
the low capital requirement, Jackson and Smithfield have been
able to avoid issuing new stock and thus own all of the shares.
Because of the explosion in demand for its mobile Internet
applications, IWT must now access outside equity capital to
fund its growth, and Jackson and Smithfield have decided to
take the company public. Until now, Jackson and Smithfield
have paid themselves reasonable salaries but routinely
reinvested all after-tax earnings in the firm, so dividend policy
has not been an issue. However, before talking with potential
outside investors, they must decide on a dividend policy. Your

12. new boss at the consulting firm Flick and Associates, which has
been retained to help IWT prepare for its public offering, has
asked you to make a presentation to Jackson and Smithfield in
which you review the theory of dividend policy and discuss the
following issues.
a. (1) What is meant by the term “distribution policy”?
How has the mix of dividend payouts and stock repurchases
changed over time?
(2) The terms “irrelevance,” “dividend preference” (or “bird-in-
the-hand”), and “tax effect” have been used to describe three
major theories regarding the way dividend payouts affect a
firm’s value. Explain these terms, and briefly describe each
theory.
(3) What do the three theories indicate regarding the actions
management should take with respect to dividend payouts?
(4) What results have empirical studies of the dividend theories
produced? How does all this affect what we can tell managers
about dividend payouts?
b. Discuss the effects on distribution policy consistent with: (1)
the signaling hypothesis (also called the information content
hypothesis) and (2) the clientele effect.
c. (1) Assume that IWT has completed its IPO and has a
$112.5 million capital bud-get planned for the coming year. You
have determined that its present capital structure (80% equity
and 20% debt) is optimal, and its net income is forecasted at
$140 million. Use the residual distribution approach to
determine IWT’s total dollar distribution. Assume for now that
the distribution is in the form of a dividend. Suppose IWT has
100 million shares of stock outstanding. What is the forecasted
dividend payout ratio? What is the forecasted dividend per
share? What would happen to the payout ratio and DPS if net
income were forecasted to decrease to $90 million? To increase
to $160 million?
(2) In general terms, how would a change in investment
opportunities affect the payout ratio under the residual
distribution policy?

13. (3) What are the advantages and disadvantages of the residual
policy? (Hint: Don’t neglect signaling and clientele effects.)
d. (1) Describe the procedures a company follows when it
makes a distribution through dividend payments.
(2) What is a stock repurchase? Describe the procedures a
company follows when it makes a distribution through a stock
repurchase.
e. Discuss the advantages and disadvantages of a firm
repurchasing its own shares.
f. Suppose IWT has decided to distribute $50 million, which it
presently is holding in liquid short-term investments. IWT’s
value of operations is estimated to be about $1,937.5 million; it
has $387.5 million in debt and zero preferred stock. As
mentioned previously, IWT has 100 million shares of stock
outstanding.
(1) Assume that IWT has not yet made the distribution. What is
IWT’s intrinsic value of equity? What is its intrinsic stock price
per share?
2) Now suppose that IWT has just made the $50 million
distribution in the form of dividends. What is IWT’s intrinsic
value of equity? What is its intrinsic stock price per share?
(3) Suppose instead that IWT has just made the $50 million
distribution in the form of a stock repurchase. Now what is
IWT’s intrinsic value of equity? How many shares did IWT
repurchase? How many shares remained outstanding after the
repurchase? What is its intrinsic stock price per share after the
repurchase?
g. Describe the series of steps that most firms take when setting
dividend policy.
h. What are stock splits and stock dividends? What are the
advantages and disadvantages of each?
i. What is a dividend reinvestment plan (DRIP), and how does it
work?
Question 2
Gamut Satellite Inc. produces satellite earth stations that sell
for $150,000 each. The firm’s fixed costs, F, are $1.5 million,

14. 20 earth stations are produced and sold each year, profits total
$400,000, and the firm’s assets (all equity financed) are $5
million. The firm estimates that it can change its production
process, adding $10 million to assets and $500,000 to fixed
operating costs. This change will reduce variable costs per unit
by $5,000 and increase output by 30 units. However, the sales
price on all units must be lowered to $140,000 to permit sales of
the additional output. The firm has tax loss carryforwards that
render its tax rate zero, its cost of equity is 18%, and it uses no
debt.
a. Determine the variable cost per unit
b. Determine the new profit if the change is made
c. What is the incremental profit?
d. What is the projects expected rate of return for the next year
(defined as the incremental profit divided by the investment)?
e. Should the firm make the investment? Why or why not?
f. Would the firm’s break-even point increase or decrease if it
made the change?
g. Would the new situation expose the firm to more or less
business risk than the old one? Show workings
Submit your answers in a Word document.
ChapterTool KitChapter 1511/21/18Capital Structure
Decisions15-2 Business Risk and Financial RiskOperating
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, hence continue even if sales decline, then the firm is
said to have high operating leverage. High operating leverage
produces a situation where a small change in sales can result in
a large change in operating profit. The following example
compares two operational plans with different degrees of
operating leverage. Figure 15-1Illustration of Operating and
Financial Leverage (Millions of Dollars and Millions of Units,
Except Per Unit Data)1. Input Data Plan A Plan U Plan
LRequired operating current assets$3$3$3Req uired long-term

15. assets$199$199$199Total assets$202$202$202Resulting
operating current liabilities$2$2$2Required capital (TA − Op.
CL)$200$200$200Book
equity$200$200$150Debt$0$0$50Interest rate8%8%8%Sales
price (P)$2.00$2.00$2.00Tax rate (T)25%25%25%Expected
units sold (Q)100100100Fixed costs (F)$20$60$60Variable
costs (V)$1.50$1.00$1.002. Income Statements Plan A Plan U
Plan LSales revenue (P x Q)$200.0$200.0$200.0Fixed
costs20.060.060.0Variable costs (V x
Q)150.0100.0100.0EBIT$30.0$40.0$40.0Interest0.00.04.0Pre-
tax earnings$30.0$40.0$36.0Tax7.510.09.0Net
income$22.5$30.0$27.03. Key Performance Measures Plan A
Plan U Plan LNOPAT = EBIT(1 − T)$22.5$30.0$30.0ROIC =
NOPAT/Capital11.3%15.0%15.0%ROA = NI/Total
assets11.1%14.9%13.4%ROE =
NI/Equity11.3%15.0%18.0%Numbers are reported as rounded
values for clarity but are calculated using Excel’s full precision.
Thus, intermediate calculations using the figure’s rounded
values will be inexact.Note: ROA is not exactly equal to ROE
for the Plan L or Plan U because total assets is not quite 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.We can use the following
formula to find the exact break-even quantity.QBE =F ÷ (P-
V)Plan AQBE =F÷( P−V )QBE =$20÷$2.00−$1.50QBE
=40 Units.Plan UQBE =F÷( P−V )QBE
=$60÷$2.00−$1.00QBE =60Units.Crossover Q for A vs. U
=80QBE for levered firm =(F + Int) ÷ (P-V)Plan LQBE =F −
Int÷P − VQBE =$56÷$1.00QBE =56Units.Crossover Q for
U vs. L =76Leverage magnifies the ROE. See Panel b of Figure
15-2 below.Figure 15-2Operating Leverage and Financial
LeverageData Table for Figurex-axis for both panels.ROE for
Panel AROE for Panel bROICPlan APlan UPlan UPlan LPlan
UPlan LLine at 0Q11.3%15.0%15.0%18.0%Q15.0%15.0%0-
7.5%-22.5%-22.5%-32.0%0-22.5%-22.5%020-3.8%-15.0%-
15.0%-22.0%20-15.0%-15.0%0400.0%-7.5%-7.5%-12.0%40-

16. 7.5%-7.5%0603.8%0.0%0.0%-
2.0%600.0%0.0%0644.5%1.5%1.5%0.0%641.5%1.5%0766.8%6.
0%6.0%6.0%766.0%6.0%0807.5%7.5%7.5%8.0%807.5%7.5%01
0011.3%15.0%15.0%18.0%10015.0%15.0%012015.0%22.5%22.
5%28.0%12022.5%22.5%014018.8%30.0%30.0%38.0%14030.0
%30.0%015-3 Capital Structure Theory: The Modigliani and
Miller ModelsFollowing are descriptions of the M&M
models.15-3a Modigliani and Miller: No TaxesV L = V U 15-3b
Modigliani and Miller: The Effect of Corporate TaxesV L = V U
+ TDVU = $100Federal-plus-state corporate tax rate =25%Pre-
TCJA federal-plus-state corporate tax rate =40%This figure is
not shown in the textbook.Data for GraphDebtVUVLPre-TCJA
VLwd$0$100$100$1000%$15$100$103.75$10614%$30$100$10
7.50$11228%$45$100$111.25$11840%$60$100$115.00$12452
%Interest expense deduction limitationThe TCJA limits
deductibility of interest expenses for purpose of tax
deductibility to 30% of EBITDA for the years 2018-2021 and
30% of EBIT for subsequent years. Interest expenses exceeding
this level may be carried forward to offset future taxes. When
applying this rule to EBIT and using reasonable values for rsu
and rd, the maximum wd that can utilize the tax shield
immediately is:Reasonable values of:T =25%rsu =12%rd
=8%Interest expense deduction limit (IntLim)=30%Max wd
=[(IntLim)(rsu)] / [ { (1-T)rd } + {IntLim)(rsu)T} ]Max wd
=52.2%Check:wd =52.2%VU = $100Debt given wd =[w d (V U
)]/[1 − (w d T)]= $60.00Interest based on D =$4.80EBIT
implied by VU =(VU rsU)/(1 - T)= $16Interest / EBIT
=30.0%15-3c Miller: The Effect of Corporate and Personal
TaxesTCJA ratesPre-TCJA ratesThis figure is not shown in the
textbook.VU =$100$100Combined federal plus state corporate
tax rate = TC =25.0%40.0%Personal tax rate on debt = Td
=32.0%33.0%Effective personal tax rate on stock = Ts
=12.0%12.0%Value in bracket =2.9%21.2%Data for GraphPre-
TCJA
wdDebtVUVLPre-TCJA
VLwd$0$100$100$1000%0%$10$100$100.2 9$102.1210%10%$

17. 20$100$100.59$104.2420%19%$30$100$100.88$106.3630%28
%$40$100$101.18$108.4840%37%$50$100$101.47$110.6049%
45%15-4A Trade-Off TheoryV L = V U + TD + Financial
distress costsVU =$100Federal plus state corporate tax rate
=25%Figure 15-3Effect of Financial Leverage on ValueData for
GraphThis formula gives a reasonable result for financial
distress costs: Fin dis = a -(1-ae^ZD)Note: Cell heigth and
width are locked for cells colored Parameter for reasonable
financial distress function = Z =0.09Data to create graph and
other dataLeverage (D)VU M&M II
Michael Ehrhardt: M&M Result Incorporating the Effects of
Corporate Taxation: Value if There Were No Bankruptcy-
Related CostsActual ValueHorzontal axiswdTDFin dis
costs$0$100$100$100.00600%$0.00$0.00$6$100$101.50$101.3
0606%$1.50$0.20$12$100$103.00$102.406012%$3.00$0.60$18
$100$104.50$103.506017%$4.50$1.00$24$100$106.00$104.286
023%$6.00$1.72$30$100$107.50$104.566028%$7.50$2.94$36$
100$109.00$103.956033%$9.00$5.05$42$100$110.50$101.8360
38%$10.50$8.67$48$100$112.00$97.126043%$12.00$14.88$54
$100$113.50$87.976048%$13.50$25.5315-6 Estimating the
Optimal Capital StructureAdding debt decreases taxes (because
interest expenses are deductible) but also increases the cost of
debt (because the 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 (wd)
that maximizes shareholder wealth and implement that capital
structure unless there are other compelling reasons (e.g,
information asymmetry, current market conditions, etc.).15-6a
Current Value and Capital StructureFigure 15-4 shows
Strasburg's current situation.Figure 15-4Strasburg’s Current
Value and Capital Structure
(Millions of Dollars Except Per Share Data)Input DataCapital
Structure and Cost of CapitalStock price (P)$22.50Market value
of equity (S = P x n)$2,250# of shares (n)100Total value (V = D

18. + S)$2,500Market value of debt (D)$250.00% financed with
debt (wd = D/V)10.00%Tax rate25%% financed with stock (ws
= S/V)90.00%EBIT$400Cost of equity: rs = rRF + b(RPM
)12.67%Net operating capital$2,000Growth rate
(gL)0%Weighted average cost of capital:Cost of debt
(rd)8.00%WACC = rd (1 − T)(wd) + rs (ws)12.00%Note: WACC
is rounded to 4 decimal places.Beta (b)1.01Risk-free rate
(rRF)6.67%Mkt. risk prem. (RPM)5.94%ROIC and Free Cash
FlowEstimated Intrinsic ValueNOPAT = EBIT(1 − T)$300Vop =
[FCF(1 + gL)]/(WACC − gL):$2,500.00ROIC = NOPAT/Op.
Cap.15%+ Value of ST investments$0.00Inv. in Op. Cap. = Δ
Cap.$0Estimated total intrinsic value$2,500.00−
Debt$250.00Free cash flow:Estimated intrinsic value of
equity$2,250.00FCF = NOPAT − Δ Cap.$300÷ Number of
shares$100.00Estimated intrinsic price per share$22.50Numbers
are reported as rounded values for clarity but are calculated
using Excel’s full precision. Thus, intermediate calculations
using the figure’s rounded values will be inexact.Notes:1. The
weighted average cost of capital is rounded to 4 decimal
places.2. Strasburg's sales, earnings, and assets are not growing,
so it does not need investments in operating capital. Therefore,
FCF = NOPAT − Investment in operating capital = EBIT(1 − T)
− $0 = EBIT(1 − T) . The growth in FCF also is 0.15-6b
Preliminary Steps to Identify the Optimal Capital
StructureBegin the process by choosing the percentage of debt
(wd, based on market values) that corresponds with each capital
structure to be considered. Also, use the current capital
structure to estimate the unlevered beta (bU) because it will be
needed to identify the cost of equity for each capital structure
under consideration.Capital Structures to be ConsideredCapital
Structures Under Consideration
(wd)0%10%20%30%40%50%Estimating the Unlevered Beta
with the Hamada EquationHamada developed his equation by
merging the CAPM with the Modigliani-Miller model. We use
the model to determine beta at different amount of financial
leverage, and then use the betas associated with different debt

19. ratios to find the cost of equity associated with those debt
ratios. Here is a version of the Hamada equation: bU = b / [1
+ (1-T) x (D/S)] 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 debt, and S is the market value
of the equity. Most analysts use the following version based on
market weights of debt and equity: bU = b / [1 + (1-T) x
(wd/ws)] Following is information about the current capital
structure, which will be used to estimate the unlevered
beta.Levered beta (b) =1.01000Current percentage financing
provided by debt (wd) =10%Current financing provided by
equity (ws) =90%Federal-plus-state tax rate (T) =25%bU
=0.9323115-6c Steps to Identify the Optimal Capital
StructureTo identify the optimal capital structure, apply the
following steps to each capital structure under consideration:
(1) Estimate 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 objective is to find the amount of debt
financing that maximizes the value of operations.Estimating the
Levered Beta and Cost of Equity (rs)Use the previously
calculated unlevered beta (1.0526) and Equation 15-11a to
determine the levered beta for each of the capital structures
being considered. For example, the levered beta for a capital
structure with 20% debt is: bU = 0.9323T = 25%wd = 20%ws
= 80%b = bU x [1 + (1-T) x (wd/ws)] b =1.107Repeating this
process for each capital structure provides an estimate of the
levered beta for each capital structure:wd =
0%10%20%30%40%50%b
=0.9321.0101.1071.2321.3981.632The cost of equity is:rs = rRF
+ b(RPM)Risk-free rate (rRF) =6.670%Mkt. risk prem. (RPM)
=5.940%The cost of equity for each capital structure is:wd =
0%10%20%30%40%50%rs
=12.21%12.6694%13.25%13.99%14.98%16.36%Figure 15-5
charts the relationship between the cost of equity and the

20. amount of debt financing.Data for Figure 15-
5wd0%10%20%30%40%50%rRF6.67%6.67%6.67%6.67%6.67%
6.67%bU ´ RPM5.54%5.54%5.54%5.54%5.54%5.54%(b − bU)´
RPM0.00%0.46%1.04%1.78%2.77%4.15%Figure 15-
5Strasburg’s Required Rate of Return on Equity at Different
Debt LevelsEstimating the Cost of Debt (rd)Investment bankers
and commercial bankers can provide estimates of the expected
interest rate for each capital structure under consideration.
Discussions with its bankers indicate that Strasburg's cost of
debt goes up as the percentage of debt goes up. The investment
bankers' estimates are shown in Line 4 of Figure 15-6. Note: the
percentages are based on market values.Figure 15-6 also shows
the previously calculated betas and costs of equity. The
following sections explain the remaining information in the
figure.Figure 15-6Estimating Strasburg's Optimal Capital
Structure (Millions of Dollars)Percent of Firm Financed with
Debt (wd)0%10%20%30%40%50% 1.
ws100.00%90.00%80.00%70.00%60.00%50.00% 2.
b0.9321.0101.1071.2321.3981.632 3.
rs12.21%12.67%13.25%13.99%14.98%16.36% 4.
rd7.80%8.00%8.20%8.70%10.10%12.20% 5. rd
(1−T)5.85%6.00%6.15%6.53%7.58%9.15% 6.
WACC12.21%12.00%11.83%11.75%12.02%12.76% 7.
Vop$2,457.00$2,500.00$2,535.93$2,553.19$2,495.84$2,351.10
8. Debt$0.00$250.00$507.19$765.96$998.34$1,175.55 9.
Equity$2,457.00$2,250.00$2,028.74$1,787.23$1,497.50$1,175.
5510. # Shares111.33100.0088.7577.6066.6855.9511. Stock
price$22.07$22.50$22.86$23.03$22.46$21.01112. Net
income$300.00$285.00$268.81$250.02$224.38$192.4413.
EPS$2.69$2.85$3.03$3.22$3.37$3.44Numbers are reported as
rounded values for clarity but are calculated using Excel’s full
precision unless otherwise noted. Thus, intermediate
calculations using the figure’s rounded values will be
inexact.Notes:1.The percent financed with equity is: ws = 1 −
wd2.The levered beta for each proposed capital structure is
estimated by Hamada's formula with a 25% federal-plus-state

21. tax rate, the unlevered beta (0.9323), and the propsed capital
structure:
b = bU [1 + (1-T) (wd/ws)]
The unlevered beta is found by using a version of Hamada's
formula with the current capital structure (wd = 10%) and
current levered beta (1.01) as shown in the blue range of cells:
bU = b/ [1 + (1-T) (wd/ws)]. 3.The cost
of equity is estimated using the CAPM formula with a risk-free
rate of 6.67% and a market risk premium of 5.94%: rs = rRF +
(RPM)b. 4.The cost of debt, rd, is obtained from investment
bankers. 5.The after-tax cost of debt is rd (1−T), where T =
25%. 6.The weighted average cost of capital is calculated as:
WACC = ws rs + wd rd (1-T)
and is rounded to 4 decimal places. 7.The value of the firm's
operations is calculated as:
Vop = [FCF(1+gL)] / (WACC − gL), where FCF = $300
million and gL = 0. 8.Debt = wd x Vop9.The intrinsic value of
equity after the recapitalization and repurchase is SPost = Vop
− Debt = ws x Vop 10.The number of shares after the recap has
been completed is found using:
nPost = nPrior [(VopNew - DNew) / (VopNew-DOld)].
The subscript "Old" indicates values from the original capital
structure where wd = 10%, the subscript "New" indicates values
at the current capital structure after the recap & repurchase, and
the subscript "Post" indicates values after the recap &
repurchase.11.The price after the recap & repurchase is: PPost =
SPost/nPost. But we can also find the price as:
PPost = (VopNew − DOld)/nPrior.12.The EBIT is $400 million;
see Figure 15-4. Net income is: NI = (EBIT − rdD)(1 −
T).13.Earnings per share: EPS = NI/nPost.Data for Figure 15-
7wd0%10%20%30%40%50%After-Tax Cost of
Debt5.85%6.00%6.15%6.53%7.58%9.15%Cost of
Equity12.21%12.67%13.25%13.99%14.98%16.36%WACC12.21
%12.00%11.83%11.75%12.02%12.76%Figure 15-7 Effects of
Capital Structure on Cost of CapitalData for Figure
belowwd0%10%20%30%40%50%Vop$2,457.00$2,500.00$2,535

22. .93$2,553.19$2,495.84$2,351.10Debt$0.00$250.00$507.19$765.
96$998.34$1,175.55Equity
(S)$2,457.00$2,250.00$2,028.74$1,787.23$1,497.50$1,175.55V
for
chart$2,458.00$2,501.00$2,536.93$2,554.19$2,496.84$2,352.10
$1.00$1.00$1.00$1.00$1.00$1.00Figure 15-8Effects of Capital
Structure on the Value of Operations15-6 Anatomy of a
RecapitalizationStrasburg will issue additional debt and use the
proceeds to repurchase stock. This is a recapitalization, often
called a "recap." When Strasburg announces its planned
recapitalization, investors realize that the company will be
worth more after the recap because it will have a lower cost of
capital. Therefore, the stock price will increase when the plans
are announced, even though the actual repurchase has not yet
occurred. If the stock price did not increase until after the
actual repurchase, it would be possible for an investor to buy
the stock immediately prior to the repurchase, and then reap a
reward the next day when the repurchase occurred. Current
stockholders realize this, and refuse to sell the stock unless they
are paid the price that is expected immediately after the
repurchase occurs. Figure 15-9Anatomy of a Recapitalization
(Millions, Except Per Share Data)Before Issuing Additional
DebtAfter Debt Issue, but Prior to RepurchasePost
Repurchase(1)(2)(3)Percent financed with debt:
wd10%30%30%Value of
operations$2,500.00$2,553.19$2,553.19+ Value of ST
investments$0.00$515.96$0.00Estimated total intrinsic
value$2,500.00$3,069.15$2,553.19−
Debt$250.00$765.96$765.96Estimated intrinsic value of
equity$2,250.00$2,303.19$1,787.23÷ Number of
shares$100.00$100.00$77.60Estimated intrinsic price per
share$22.50$23.03$23.03Value of
stock$2,250.00$2,303.19$1,787.23+ Cash distributed i n
repurchase$0.00$0.00$515.96Wealth of
shareholders$2,250.00$2,303.19$2,303.19Numbers in the figure
are shown as rounded values for clarity in reporting. However,

23. unrounded values are used for all calculations. Notes:1. The
value of ST investments in Column 2 is equal to the amount of
cash raised by issuing additional debt but that has not been used
to repurchase shares:
ST investments = DNew − DOld.2. The value of ST
investments in Column 3 is zero because the funds have been
used to repurchase shares of stock.3. The number of shares in
Column 3 reflects the shares repurchased:
nPost = nPrior − (CashRep/PPrior) = nPrior − ([DNew −
DOld]/PPrior).Figure 15-10Effect of Capital Structure on
Intrinsic Stock Price and Earnings per ShareShortcut Formulas
Applied to Change in Capital Structure: wd Prior = 10%, wd
Post = 30%Inputs:wd =30%VopNew =$2,553.19nPrior
=100.00DNew =$765.96DOld =$250.00Shortcuts:SPost =
VopNew (1-wd) =$1,787.23nPost = nPrior (VopNew - DNew) /
(VopNew - DOld) =77.60PPost = (VopNew - DOld) / nPrior
=$23.0315-8 Risky Debt and Equity as an OptionIf 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 debt. 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 payment, then the stockholders get
to keep the firm. If management defaults on the the interest or
principal payment, then the stockholders lose the firm.Kunkel's
situationFace value of zero coupon debt$10,000,000Time to
maturity (years)5When 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 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 price of $10 million. This
can be valued using the Black-Scholes Option Pricing Model
(BSOPM). See Chapter 8 for more details on the
BSOPM.Black-Scholes Option Pricing ModelSuppose the total
value of the company at the time it issus the zero coupon debt is

24. $20 million (this is the value of existing assets plus the
proceeds raised when the debt is issued).Total value of firm
when debt is issued = Value of operating assets + proceeds from
issuing debt= Value of debt + value of equity= $20,000,000The
inputs to the Black-Schole model are:Total value of firm
(P)$20.00Analogous to the stock price from the BSOPMFace
value of debt (X)$10.00Analogous to the exercise priceRisk free
rate (rRF)6.0%Maturity of debt in years (T)5.00Analogous to
time to expiration of optionStandard deviation of total value's
return (σ)0.40This is the standard deviation of the total value of
the firm's total value, not just the standard deviation of its
stock.Applying the Black-Schole
model:d11.5576d20.6632N(d1)0.9403N(d2)0.7464Call Price =
Equity Value =$13.28How much did Kunkel receive for issuing
face value $10 million in zero coupon debt?If the total value of
the firm is $20 million, and the equity is
worth$13.28million,then the value of the debt should be what is
left over:$6.72million.Therefore, the proceeds on the debt at the
time it is issued are:$6.72The yield on zero coupon debt is
calculated like the rate on a single future value:PV(1+I)N = FV
Soving for the rate, I:I =[(FV/PV)(1/N)]-1Therefore, the yield
on the debt at the time it is issued is:FV = Face value of
debt$10.00N = Number of years until maturity on date when
issued = $5.00PV = Present value of debt when issued
=$6.72Yield on Debt8.266%If management can change the
riskiness of its projects--i.e. change the volatility of the total
company, then it can change the relative values of the debt,
equity, and the yield on the debt.Table 15-2The Value of
Kunkel’s Debt and Equity for Various Levels of Volatility
(Millions of Dollars)Standard Deviation Of Total ValueTotal
ValueEquity ValueDebt ValueYield on DebtPercentage Change
in Equity Value from Base CaseBase Case values to
right$20$13.28$6.72$0.08Note: 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 good way to "hide" material you don't
want to show in a presentation.20%$20$12.62$7.386.25%-

25. 4.98%40%2013.286.728.27%0.00%60%2014.515.4912.74%9.27
%80%2015.814.1918.99%19.06%100%2016.963.0426.92%27.77
%Debt and Equity Values for Various Levels of Volatility When
the Total Value is $11 MillionTotal Value of
Firm$11.00Analogous to the stock price from the BSOPMFace
Value of Debt$10.00Analogous to the exercise priceRisk Free
rate0.06Maturity of debt (years)5.00Analogous to time to
expiration of optionStandard Dev.0.40This is the standard dev.
of the total value of the firm, not just the stock.d10.8892d2-
0.0052N(d1)0.8130N(d2)0.4979Call Price = Equity
Value$5.25If the total value of the firm is $10 million, and the
equity is worth$5.25million,then the value of the debt should be
what is left over:$5.75million.FV = Face value of debt$10.00N
= Number of years until maturity on date when issued = 5.00PV
= Present value of debt when issued =$5.75Yield on
Debt11.723%Not Reported in TextbookThe Value of Kunkel’s
Debt and Equity for Various Levels of Volatility if Total Value
is $11 (Millions of Dollars)Standard Deviation Of Total
ValueTotal ValueEquity ValueDebt ValueYield on DebtBase
Case values to right$11$5.25$5.7511.72%Percentage Change in
Equity Value from Base Case20%$11$4.00$7.007.40%-
24%40%115.255.7511.72%0%60%116.544.4617.54%25%80%11
7.693.3124.75%46%100%118.642.3633.50%64%Expected
Return Compared to Yield to Maturity on DebtNot Reported in
TextbookYield to Maturity and Expected Return on Debt for
Various Levels of Volatility and Debt. Total Value is $20
(Millions of Dollars)Total Value of Firm$20.00Analogous to the
stock price from the BSOPMFace Value of
Debt$10.00Analogous to the exercise priceRisk Free
rate0.06Maturity of debt (years)5.00Analogous to time to
expiration of optionStandard Dev.0.40This is the standard dev.
of the total value of the firm, not just the
stock.d11.5576d20.6632N(d1)0.9403N(d2)0.7464Call Price =
Equity Value$13.28If the total value of the firm is $10 million,
and the equity is worth$13.28then the value of the debt should
be what is left over:$6.72FV = Face value of debt =$10.00N =

26. Number of years until maturity on date when issued = 5.00PV =
Present value of debt when issued =$6.72Yield to Maturity on
Debt =8.266%The yield to maturity above is not equal to the
expected (or required) return on the debt. Rather, the YTM is
the 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.
Option pricing theory says that the expected return can be
calculated from the inputs to the option pricing 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.Options pricing theory shows that (expected payoff from
zero coupon debt) =
(face value of debt) x (probability the equity holders fully pay
back the debt) + (expected payoff if the equity holders default
on the debt).
These amounts are functions of N(d1*) and N(d2*) where d1*
and d2* are the same as d1 and d2 calculated with the regular
Black Scholes Option Pricing Model, but with the risk free rate
replaced by the unlevered expected return on the stock. N(d2*)
= probability of stockholders fully paying off the debt.
(S0ert-S0ertN(d1*)) = expected payoff to bondholders if the
stockholders default where S0 is the total value of the firm at
time zero.
So the overall expected payoff to bondholders is
XN(d2*)+(S0ert-S0ertN(d1*))
where X is the face value of the debt and r is the unlevered
expected rate of return on the total value of the company rather
than the risk free rate.
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.Expected unlevered return on

27. stock =9%d1* =1.7253This uses the expected unlevered return
on the stock in the calculation rather than the risk free rate.d2*
=0.8309This uses the expected unlevered return on the stock in
the calculation rather than the risk free rate.N(d1*)
=0.9578N(d2*) =0.7970= Probability of fully retiring the debt
(probability of exercise)Face Value of DebtXProbability of
retiring debt+Expected payoff if stockholders default=Expected
payoff from bondN(d2*) (S0ert-S0ertN(d1*))
$10.00X0.7970+$1.32483=$9.2946Price of bond =$6.72Face
value of bond =$10.00YTM =8.266%Expected payoff
=$9.295Expected Return = 6.693%Note that Expected return
will always be less than YTM.Yield to maturity and expected
return on debt for different levels of standard deviation of total
value.Standard Deviation of Total ValueTotal ValueEquity
ValueDebt ValueDebt YTMExpected Return on DebtBase Case
values to
right$20.00$13.28$6.728.27%6.69%10%$20.00$12.59$7.416.18
%6.18%20%$20.00$12.62$7.386.25%6.23%30%$20.00$12.83$7
.176.89%6.44%40%$20.00$13.28$6.728.27%6.69%50%$20.00$
13.86$6.1410.25%6.90%60%$20.00$14.51$5.4912.74%7.06%70
%$20.00$15.17$4.8315.66%7.18%80%$20.00$15.81$4.1918.99
%7.27%90%$20.00$16.41$3.5922.74%7.35%100%$20.00$16.96
$3.0426.92%7.41%Yield to maturity and expected return on
debt for different face values of debt.Face Value of
DebtStandard Deviation of Total ValueTotal ValueEquity
ValueDebt ValueDebt YTMExpected Return on DebtBase Case
values to
right40%$20.00$13.28$6.728.27%6.69%$2.0040%$20.00$18.52
$1.486.22%6.20%$4.0040%$20.00$17.07$2.936.45%6.27%$6.0
040%$20.00$15.70$4.306.91%6.40%$8.0040%$20.00$14.44$5.
567.54%6.54%$10.0040%$20.00$13.28$6.728.27%6.69%$12.00
40%$20.00$12.22$7.789.06%6.84%$14.00 40%$20.00$11.27$8.
739.90%6.98%$16.0040%$20.00$10.40$9.6010.77%7.11%$18.0
040%$20.00$9.62$10.3811.64%7.24%$20.0040%$20.00$8.91$1
1.0912.52%7.35%$25.0040%$20.00$7.41$12.5914.71%7.61%$3
0.0040%$20.00$6.22$13.7816.84%7.82%$35.0040%$20.00$5.2

28. 7$14.7318.90%8.01%$40.0040%$20.00$4.50$15.5020.88%8.16
%$45.0040%$20.00$3.87$16.1322.78%8.29%$50.0040%$20.00
$3.35$16.6524.60%8.41%$55.0040%$20.00$2.92$17.0826.35%
8.51%$60.0040%$20.00$2.55$17.4528.02%8.59%$65.0040%$2
0.00$2.25$17.7529.63%8.67%Note that as the face value of
debt increases, the expected return on the debt approaches the
unlevered expected return on the stock. This is because as the
face value of debt increases, the probability that the
stockholders will default on the debt and turn the company over
to the bondholders approaches 1 and the debt's payoffs approach
those of simply owning the company without any debt at all.
After-Tax Cost of Debt
[SERIES NAME]
After-Tax
Cost of Debt
0 0.1 0.2 0.3 0.4 0.5 5.8499999999999996E-2 0.06
6.1499999999999999E-2 6.5250000000000002E-2
7.5750000000000012E-2 9.1499999999999998E-2 Cost of
Equity
[SERIES NAME]
0 0.1 0.2 0.3 0.4 0.5 0.12207907692307693
0.126694 0.13246265384615385 0.13987949450549453
0.14976861538461539 0.1636133846153846 WACC
[SERIES NAME]
0 0.1 0.2 0.3 0.4 0.5 0.1221 0.12 0.1183
0.11749999999999999 0.1202 0.12759999999999999
Percent Financed with Debt
Cost of Capital
Debt
0 0.1 0.2 0.3 0.4 0.5 0 250 507.18512256973793
765.95744680851067 998.33610648918477

29. 1175.5485893416928 Equity
0 0.1 0.2 0.3 0.4 0.5 2457.002457002457 2250
2028.7404902789517 1787.2340425531916
1497.5041597337772 1175.5485893416928 0
0.1 0.2 0.3 0.4 0.5 1 1 1 1 1 1
Percent Financed with Debt
Price
0 0.1 0.2 0.3 0.4 0.5 22.070024570024568 22.5
22.859256128486894 23.031914893617024
22.458402662229616 21.010971786833856 EPS
0 0.1 0.2 0.3 0.4 0.5 2.69475 2.85
3.0288514370245139 3.2220003799392098
3.3650173322240704 3.4394960815047018 Percent
Financed with Debt
Stock Price
EPS
Panel A: Operating Leverage
Plan A
0 20 40 60 64 76 80 100 120 140 -
7.4999999999999997E-2 -3.7499999999999999E-2 0
3.7499999999999999E-2 4.4999999999999998E-2
6.7500000000000004E-2 7.4999999999999997E-2 0.1125
0.15 0.1875 Plan B Plan U
0 20 40 60 64 76 80 100 120 140 -
0.22500000000000001 -0.15 -7.4999999999999997E-2 0
1.4999999999999999E-2 0.06 7.4999999999999997E-2
0.15 0.22500000000000001 0.3 0 20 40 60 64
76 80 100 120 140 0 0 0 0 0 0 0

30. 0 0 0 Units Sold Millions
ROE
rRF 0 0.1 0.2 0.3 0.4 0.5 6.6699999999999995E-2
6.6699999999999995E-2 6.6699999999999995E-2
6.6699999999999995E-2 6.6699999999999995E-2
6.6699999999999995E-2 bU ´ RPM 0 0.1 0.2 0.3
0.4 0.5 5.5379076923076927E-2
5.5379076923076927E-2 5.5379076923076927E-2
5.5379076923076927E-2 5.5379076923076927E-2
5.5379076923076927E-2 (b − bU)´ RPM 0 0.1 0.2
0.3 0.4 0.5 0 4.6149230769230729E-3
1.0383576923076924E-2 1.7800417582417585E-2
2.7689538461538467E-2 4.153430769230769E-2 Percent
Financed with Debt
Required
Return on
Equity
Panel B: Financial Leverage
Plan B Plan U
0 20 40 60 64 76 80 100 120 140 -
0.22500000000000001 -0.15 -7.4999999999999997E-2 0
1.4999999999999999E-2 0.06 7.4999999999999997E-2
0.15 0.22500000000000001 0.3 Plan L
0 20 40 60 64 76 80 100 120 140 -0.32 -
0.22 -0.12 -0.02 0 0.06 0.08 0.18
0.28000000000000003 0.38 0 20 40 60 64 76
80 100 120 140 0 0 0 0 0 0 0 0
0 0 Units Sold (Millions)

31. ROE
Miller with Corporate and Personal Taxes
VU VU
0 10 20 30 40 50 100 100 100 100 100 100
VL VL
0 10 20 30 40 50 100 100.29411764705883
100.58823529411765 100.88235294117646
101.17647058823529 101.47058823529412 Pre-
TCJA VL Pre-TCJA VL
0 10 20 30 40 50 100 102.11940298507463
104.23880597014926 106.35820895522389
108.4776119402985 110.59701492537313 Debt
Value of Firm
M&M with Corporate Taxes
VU
0 15 30 45 60 100 100 100 100 100 VL
0 15 30 45 60 100 103.75 107.5 111.25
115 Pre-TCJA VL

32. 0 15 30 45 60 100 106 112 118 124 Leverage
Value
VU
0 6 12 18 24 30 36 42 48 54 100 100
100 100 100 100 100 100 100 100 M & M II
0 6 12 18 24 30 36 42 48 54 100 101.5
103 104.5 106 107.5 109 110.5 112 113.5
Actual Value
0 6 12 18 24 30 36 42 48 54 100 101.3
102.4 103.5 104.28399313781514
104.55532044893448 103.94690968343613
101.82886234153655 97.120268275127174
87.966278252648479 0
Leverage
0 6 12 18 24 30 36 42 48 54 60 60 60
60 60 60 60 60 60 60
Value
15-2SECTION 15-2SOLUTIONS TO SELF-TESTA 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 =$100,000V =$4P =$6QBE50,000
15-6SECTION 15-6SOLUTIONS TO SELF-TEST JAB

33. Industry's capital structure 20% debt. Use the following data to
calculate its cost of equity: bL = 1.4; rRF = 6% and RPM =
5%.bL1.10rRF6%RPM5%rs =11.50%Use the Hamada equation
to calculate JAB's unlevered beta and unlevered cost of equi ty.
The tax rate is 20%.Tax
rate25%wd20%ws80%bU0.9263rs,U10.63%What would the cost
of equity be if JAB changes its capital structure to 35% debt?wd
=35%ws =65%bL =1.30rs,L12.50%
15-7SECTION 15-7SOLUTIONS 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 PPost
(the stock price) after the recap? What is nPost (the number of
remaining shares) after the
recap?Vop$800D$200wd25%nPrior10S =$600PPost
=$80.00nPost =7.5
Web 15BWEB EXTENSION 15B11/21/18BOND
REFUNDINGThis 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-1Spreadsheet for
the Bond Refunding DecisionPanel A: Input DataExisting bond
issue =$60,000,000Years since old debt issued =5Original
flotation cost =$3,000,000Current call premium (%)
=10.0%Maturity of original debt =25New bond issue

34. =$60,000,000Original coupon rate =12.0%New flotation cost
=$2,650,000Call protection period =5New bond maturity
=20Initial call premium (%) =10.0%New cost of debt =9.0%Tax
rate =25.0%ST interest rate =6.0%Panel B: Investment
OutlayBefore-taxAfter-tax1:Call premium on the old
bond−$6,000,000−$4,500,0002:Flotation costs on new
issue−$2,650,000−$2,650,0003:Immediate tax savings on old
flotation expense$2,400,000$600,0004:Extra interest paid on
old issue−$600,000−$450,0005:Interest earned on short-term
investment$300,000$225,0006: Total after-tax initial
outlay−$6,775,000Panel C: Present Value of Annual Flotation
Cost Tax Effects: t = 1 to 20Before-taxAfter-tax7:Annual tax
savings from new-issue flotation $132,500$33,1258:Annual lost
tax savings from old-issue flotation−$120,000−$30,0009: Net
flotation cost tax savings$12,500$3,125Since 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. 10:Maturity of the
new bond (Nper)2011:After-tax cost of new debt
(Rate)6.75%12:PV of annual after-tax flotation cost
savings$33,759Panel D: Present Value of Annual Interest
Savings Due to Refunding: t = 1 to 20Before-taxAfter-
tax13:Interest on old bond$7,200,000$5,400,00014:Interest on
new bond−$5,400,000−$4,050,00015: Net interest
savings$1,800,000$1,350,000Since 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. 16:Maturity of the new bond
(Nper)2017:After-tax cost of new debt (Rate)6.75%18:PV of
annual after-tax interest savings$14,584,079Panel E: Total Net
Present Value of the RefundingAfter-tax19: Total after-tax
initial outlay−$6,775,00020:PV of annual after-tax flotation
cost savings$33,75921:PV of annual after-tax interest
savings$14,584,07922:Total NPV of Bond Refunding
$7,842,838Our refunding analysis tells us that should the firm
proceed with the bond refunding, the project will have a

35. 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 AnalysisRates fallRates stay the
sameRates go upProbability25%50%25%Rate7%9%11%NPV of
refunding$20,049,044$7,842,838($2,214,092)Expected
NPV$8,933,680
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