Question 1: Realized return on the Equity Investment (20

marks)
Question 2: Estimate the Cost of Capital (20 marks) W8
Question 3: Modigliani-Miller Proposition 1 and 2 – without tax
(20 marks) W9
Question 4: Modigliani-Miller Proposition 1 and 2 – with tax (20
marks) W9
Question 5: Risk and Diversification (20 marks)
Practice Questions Week 6 and 7
The realized return on the equity investment is 12%. The
1. The following table shows the one-year return distribution of
dividend yield is 10%.
Startup, Inc. Calculate
a. The expected return.
3. Using the data in the following table, calculate the return for
b. The standard deviation of the return. investing in Boeing stock (BA) from January 2, 2008, to January
2, 2009, and also from January 3, 2011, to January 3, 2012,
assuming all dividends are reinvested in the stock immediately.
Probability 40% 20% 20% 10% 10% Historical Stock and Dividend Data for Boeing
Returns -120% -85% -40% -30% 1000% Date Price Dividend Date Price Dividend
1/2/2008 86.62 1/3/2011 66.40
2/6/2008 79.91 0.40 2/9/2011 72.63 0.42
a.
5/7/2008 84.55 0.40 5/11/2011 79.08 0.42
E ( R )=−1.2 ( 0.4 )−0.85 ( 0.2 )−0.4 ( 0.20 )−0.3 ( 0.10 )+10 ( 0.1 ) =0.24=24 %
8/6/2008 65.40 0.40 8/10/2011 57.41 0.42
b. 11/5/2008 49.55 0.40 11/8/2011 66.65 0.42
Variance ( R )= [ (−1.2−0.24 )2 × 0.4 ]+ [ (−0.85−0.24 )2 ×0.2 ] + [ (−0.4−0.24 ) 2
×0.2 ] +
1/2/2009 45.25 [ (−0.3−0.24 ) 2
× 0.1 ] + [ ( 10−0.24 )2
×0.1 ]
1/3/2012 74.22
Variance ( R )=0.82944+0.23762+ 0.08192+ 0.02916+9.52576=0.018475
3/e # 2/e # Pick Up? Revised? New? Excel icon?
Standard deviation= √10.7039=3.2716=327.16 % 1 1x x
2 2x x
2. You bought a stock one year ago for $50 per share and sold it 3 3x
4 4x
today for $55 per share. It paid a $1 per share dividend today.
5 5x
a. What was your realized return? 6 6 x x
7 7x
b. How much of the return came from dividend yield and how 8 8 x x
much came from capital gain? 9 x
Compute the realized return and dividend yield on this equity 10 x
investment. 11 9x
12 10 x (problem text thx
13 11 x (problem text thx
a. 14 12 x (problem text the same but solution different
15 13 x (problem text thx
16 14 x
17 15 x (problem text thx
18 16 x (problem text thx
b. 19 17 x (problem text thx
 6. How does the relationship between the average return and the
4. The last four years of returns for a stock are as follows: historical volatility of individual stocks differ from the
relationship between the average return and the historical
Year 1 2 3 4 volatility of large, well-diversified portfolios?
Return -4.4% +27.8% +11.6% +3.9% For large portfolios there is a relationship between returns and
volatility—portfolios with higher returns have higher volatilities.
For stocks, no clear relation exists.
a. What is the average annual return?
b. What is the variance of the stock’s returns? 7. Consider two local banks. Bank A has 100 loans outstanding,
c. What is the standard deviation of the stock’s returns? each for $1 million, that it expects will be repaid today. Each
loan has a 5% probability of default, in which case the bank is
a. not repaid anything. The chance of default is independent
−4.4 %+27.8 % +11.6 %+3.9 % across all the loans. Bank B has only one loan of $100 million
Average annual return= =9.73 %
4 outstanding, which it also expects will be repaid today. It also
b. has a 5% probability of not being repaid. Explain the difference
Variance of returns= (−0.044−0.0973 ) + ( 0.278−0.0973 ) + ( 0.116−0.0973 ) +between the type
)2 of risk each bank faces. Which bank faces less
2 2 2
( 0.039−0.0973
risk? Why?
Variance of returns=0.01996569+0.03265249+0.00034969+ 0.00339889=0.05637
The expected payoffs are the same, but bank A is less risky.
c.
Standard deviation of returns=
√0.05636676
4−1
=0.1371=13.71%
8. Consider the following two, completely separate, economies.
The expected return and volatility of all stocks in both
economies is the same. In the first economy, all stocks move
5. Using the data in Table 2 (in the Lecture Slides), together—in good times all prices rise together and in bad
times they all fall together. In the second economy, stock
a. What was the average annual return of Microsoft stock from returns are independent—one stock increasing in price has no
2005–2017? effect on the prices of other stocks. Assuming you are risk-
b. What was the annual volatility for Microsoft stock from averse and you could choose one of the two economies in
2005–2017? which to invest, which one would you choose? Explain.
A risk-averse investor would choose the economy in which stock
a. Average annual return returns are independent because this risk can be diversified away
=-0.9% + 15.8% + 20.8% –44.4% + 60.5% – 6.5% –4.5% + 5.8% in a large portfolio.
+ 44.3% + 27.6% + 22.7% + 15.1% + 40.7%) = 15.15%
b. Annual volatility of returns = 9. Explain why the risk premium of a stock does not depend on its
diversifiable risk.
Investors can costlessly remove diversifiable risk from their
portfolio by diversifying. They, therefore, do not demand a risk
premium for it.
10. Identify each of the following risks as most likely to be severe market downturn: (1) A $2000 investment in Hershey,
systematic risk or diversifiable risk: (2) a $1500 investment in Macy’s, or (3) a $1000 investment in
Amazon.
a. The risk that your main production plant is shut down due
For each 10% market decline,
to a tornado.
Hershey down 10%*0.33 = 3.3%,
b. The risk that the economy slows, decreasing demand for 3.3% × 2,000 = $66 loss;
your firm’s products. Macy’s down 10%*.75 = 7.5%,
c. The risk that your best employees will be hired away. 7.5% × 1,500 = $112.50 loss;
Amazon down 10%*1.62 = 16.2%,
d. The risk that the new product you expect your R&D division 16.2% × 1,000 = $162 loss;
to produce will not materialize. Amazon investment will lose most.
a. diversifiable risk
15. Suppose the market portfolio is equally likely to increase by
b. systematic risk
30% or decrease by 10%.
c. diversifiable risk
a. Calculate the beta of a firm that goes up on average by 43%
d. diversifiable risk when the market goes up and goes down by 17% when the
market goes down.
11. What is an efficient portfolio? b. Calculate the beta of a firm that goes up on average by 18%
An efficient portfolio is any portfolio that only contains systemic when the market goes down and goes down by 22% when
risk; it contains no diversifiable risk. the market goes up.
c. Calculate the beta of a firm that is expected to go up by 4%
12. What does the beta of a stock measure?
independently of the market.
Beta measures the amount of systemic risk in a stock

13. You turn on the news and find out the stock market has gone up a.
10%. Based on the data in Table 10.6, by how much do you
expect each of the following stocks to have gone up or down:
(1) Starbucks, (2) Tiffany & Co., (3) Hershey, and (4) McDonald’s. b.
Beta*10% c. A firm that moves independently has no systemic risk, so beta
Starbucks 8% =0
Tiffany & Co. 17.7%
Hershey 3.3%
McDonald’s 6.3%

14. Based on the data in Table 10.6, estimate which of the following
investments you expect to lose the most in the event of a
16. Suppose the risk-free interest rate is 4%. 18. Why don’t all investors hold Autodesk’s stock rather than
Hershey’s stock?
a. i. Use the beta you calculated for the stock in Problem 33(a)
Hershey’s stock has less market risk, so investors don’t need as
to estimate its expected return.
high an expected return to hold it. Hershey’s stock will perform
ii. How does this compare with the stock’s actual expected much better in a market downturn.
return?
b. i. Use the beta you calculated for the stock in Problem 33(b) 20. Consider an economy with two types of firms, S and I. S firms all
to estimate its expected return. move together. I firms move independently. For both types of
firms, there is a 60% probability that the firms will have a 15%
ii. How does this compare with the stock’s actual expected return and a 40% probability that the firms will have a −10%
return? return. What is the volatility (standard deviation) of a portfolio
a. E[RM] = ½ (30%) + ½ (–10%) = 10% that consists of an equal investment in 20 firms of (a) type S,
and (b) type I?
i.. E[R] = 4% + 1.5 (10% – 4%) = 13%
ii. Actual Expected return = a.
(43% – 17%) / 2 = 13%
b. i. E[R] = 4% – 1(10% – 4%) = –2%
Because all S firms in the portfolio move together there is no
ii. Actual l expected Return = diversification benefit. So the standard deviation of the
(–22% + 18%) / 2 = –2% portfolio is the same as the standard deviation of the stocks—
12.25%.

17. Suppose the market risk premium is 5% and the risk-free b.

interest rate is 4%. Using the data in Table 10.6, calculate the
expected return of investing in
a. Starbucks’ stock. Type I stocks move independently. Hence the standard
deviation of the portfolio is
b. Hershey’s stock.
c. Autodesk’s stock.
a. 4% + 0.80 × 5% = 8%
b. 4% + 0.33 × 5% = 5.7%
c. 4% + 1.76 × 5% = 12.8%
Practice Question Week 8 No, expected return of this portfolio would be lower due to
bonds. Compute the historical excess return of this new index.
1. Suppose Pepsico’s stock has a beta of 0.72. If the risk-free rate is
2% and the expected return of the market portfolio is 6%, what is 5. You need to estimate the equity cost of capital for XYZ Corp. You
Pepsico’s equity cost of capital? have the following data available regarding past returns:
Answer: Year Risk-free Market XYZ Return
r i=r f + β i × ( E [ R Mkt ] −r f ) Return Return
2017 4% 7% 8%
r Pepsico =2 %+0.72 × ( 6 %−2% )=4.88 %
2018 1% -43% -37%
a. What was XYZ’s average historical return?
2. Suppose the market portfolio has an expected return of 10% and a
b. Compute the market’s and XYZ’s excess returns for each
volatility of 20%, while Microsoft’s stock has a volatility of 30%.
year. Estimate XYZ’s beta.
a. Given its higher volatility, should we expect Microsoft to
c. Suppose the current risk-free rate is 4%, and you expect the
have an equity cost of capital that is higher than 10%?
market’s return to be 8%. Use the CAPM to estimate an
b. What would have to be true for Microsoft’s equity cost of
expected return for XYZ Corp.’s stock.
capital to be equal to 10%?
d. Would you base your estimate of XYZ’s equity cost of capital
Answer:
on your answer in part (a) or in part (d)? How does your
a. No, volatility includes diversifiable risk, so it cannot be used
answer to part (c) affect your estimate? Explain.
to assess the equity cost of capital.
Answer:
b. Microsoft stock would need to have a beta of 1.
( 8 %−37 % )
a. XYZ average historical returns= =−14.5 %
2
3. Aluminum maker Alcoa has a beta of about 1.73, whereas Hormel
Foods has a beta of 1.68. If the expected excess return of the
b. Market excess return 2017 = 7% - 4% = 3%
marker portfolio is 3%, which of these firms has a higher equity cost
Market excess return 2018 = -43% - 1% = -44%
of capital, and how much higher is it?
Answer:
XYZ excess return 2017 = 8% - 4% = 4%
r i= βi × ( E [ R Mkt ]−r f )
XYZ excess return 2018 = -37% - 1% = -38%
r Alcoa =1.73 × ( 3 % )=5.19 %
r Hormel =1.68 × ( 3 % )=5.04 % ( 4−(−38 ) )
Beta= =0.89
( 3−(−44 ) )
Alcoa’s cost of capital is higher by 0.15%.
a. E ( r XYZ ) =4 %+0.89 × ( 8 %−4 % ) =7.56 %
4. Suppose that in place of the S&P 500, you wanted to use a broader
market portfolio of all U.S. stocks and bonds as the market proxy.
d. Use (c)— because the CAPM provides a better estimate of
Could you use the same estimate for the market risk premium
expected returns.
when applying the CAPM? If not, how would you estimate the
correct risk premium to use?
Answer:
6. In mid-2017, Ralston Purina had AA-rated, 10-year bonds premium was 5%, estimate the expected return of KB Home’s debt
outstanding with a yield to maturity of 2.36%. using two different methods. How do your results compare?
a. What is the highest expected return these bonds could Answer:
have? Given the low rating of debt, as well as the recessionary
b. At the time, similar maturity Treasuries have a yield of economic conditions at the time, we know the yield to maturity
1.36%. Could these bonds actually have an expected return of KB Home’s debt is likely to significantly overstate its expected
equal to your answer in part (a)? return. Using the recession estimates in Table 12.2 and an
c. If you believe Ralston Purina’s bonds have 0.5% chance of expected loss rate of 60%, from Eq. 12.7 we have
default per year, and that expected loss rate in the event of
default is 48%, what is your estimate of the expected return Alternatively, we can estimate the bond’s expected return using
for these bonds? the CAPM and an estimated beta of 0.17 from Table 12.3. In that
Answer: case,
a. Highest expected returns for the bonds would be 2.36%
While both estimates are rough approximations, they both
b. No, if the bonds are risk-free, the expected return equals confirm that the expected return of KB Home’s debt is well below
the risk-free rate, and if they are not risk-free the its promised yield.
expected return is less than the yield.

c. 2.36 %−( 0.005 × 48 % )=2.12 %

7. In mid-2012, Rite Aid had CCC-rated, 6-year bonds outstanding with

a yield to maturity of 17.3%. At the time, similar maturity
Treasuries had a yield of 3%. Suppose the market risk premium is
6% and you believe Rite Aid’s bonds have a beta of 0.31. The
expected loss rate of these bonds in the event of default is 58%.
a. What annual probability of default would be consistent with
the yield to maturity of these bonds in mid-2009?
b. In mid-2015, Rite-Aid’s bonds had a yield of 6.6%, while
similar maturity Treasuries had a yield of 1.6%. What
probability of default would you estimate now?
Answer:
a. Rd = 3% + 0.31(6%) = 4.86% = y – pL = 17.3% – p(0.58)
p = (17.3% – 4.86%)/0.58 = 21.45%
b. p = (6.6% – 1.6% – 0.31(6%))/0.58 = 5.41%

8. During the recession in mid-2009, homebuilder KB Home had

outstanding 6-year bonds with a yield to maturity of 8.5% and a BB
rating. If corresponding risk-free rates were 3%, and the market risk
9. The Dunley Corp. plans to issue 5-year bonds. It believes the bonds Answer:
will have a BBB rating. Suppose AAA bonds with the same maturity Project beta = 0.85 (using all equity comp)
have a 4% yield. Assume the market risk premium is 5% and use the Thus, rp = 4% + 0.85(5%) = 8.25%
data in Table 12.2 and Table 12.3.
a. Estimate the yield Dunley will have to pay, assuming an 11. You decided to look for other comparables to reduce estimation
expected 60% loss rate in the event of default during error in your cost of capital estimate. You find a second firm,
average economic times. What spread over AAA bonds will Thurbinar Design, which is also engaged in a similar line of
it have to pay? business. Thurbinar has a stock price of $20 per share, with 15
b. Estimate the yield Dunley would have to pay if it were a million shares outstanding. It also has $100 million in outstanding
recession, assuming the expected loss rate is 80% at that debt, with a yield on the debt of 4.5%. Thurbinar’s equity beta is
time, but the beta of debt and market risk premium are the 1.00. The risk-free rate is 4% and the market risk premium is 5%.
same as in average economic times. What is Dunley’s spread a. Assume Thurbinar’s debt has a beta of zero. Estimate
over AAA now? Thurbinar’s unlevered beta. Use the unlevered beta and the
c. In fact, one might expect risk premia and betas to increase CAPM to estimate Thurbinar’s unlevered cost of capital.
in recessions. Redo part (b) assuming that the market risk b. Estimate Thurbinar’s equity cost of capital using the CAPM.
premium and the beta of debt both increase by 20%; that is, Then assume its debt cost of capital equals its yield, and
they equal 1.2 times their value in recessions. using these results, estimate Thurbinar’s unlevered cost of
Answer: capital.
a. Use CAPM to estimate expected return, using AAA rate as rf c. Explain the difference between your estimate in part (a) and
rate: r + 0.1 ´ rp = 4% + 0.10(5%) = 4.5% part (b).
So, y – p ´ l = 4.5% d. You decide to average your results in part (a) and part (b),
y = 4.5% + p(60%) = 4.5% + 0.4%(60%) = 4.74% and then average this result with your estimate from
Spread = 0.74% Problem 17. What is your estimate for the cost of capital of
b. Use CAPM to estimate expected return, using AAA rate as rf your firm’s project?
rate: r + 0.1 ´ rp = 4% + 0.10(5%) = 4.5% Answer:
y = 4.5% + 3%(80%) = 6.90% a. E = 20 ´ 15 = 300
Spread = 2.9% E + D = 400
c. Use CAPM to estimate expected return, using AAA rate as rf Bu = 300/400 ´ 1.00 + 100/400 ´ 0 = 0.75
rate: r +0.1 ´ 1.2 ´ rp ´ 1.2 = 4% + 0.10(5%)1.22 = 4.72% Ru = 4% + 0.75(5%) = 7.75%
So, y – p ´ l = 4.5% b. Re = 4% + 1.0 ´ 5% = 9%
y = 4.72% + p(80%) = 4.72% + 3%(80%) = 7.12% Ru = 300/400 ´ 9% + 100/400 ´ 4.5% = 7.875%
Spread = 3.12% c. In the first case, we assumed the debt had a beta of zero, so
rd = rf = 4%
10. Your firm is planning to invest in an automated packaging plant. In the second case, we assumed rd = ytm = 4.5%
Harburtin Industries is an all-equity firm that specializes in this d. Thurbinar Ru = (7.75 + 7.875)/2 = 7.8125%
business. Suppose Harburtin’s equity beta is 0.85, the risk-free rate Harburtin Ru = 8.25%
is 4%, and the market risk premium is 5%. If your firm’s project is all Estimate = (8.25% + 7.8125%)/2 = 8.03%
equity financed, estimate its cost of capital.
 12. IDX Tech is looking to expand its investment in advanced security
systems. The project will be financed with equity. You are trying to
assess the value of the investment, and must estimate its cost of
capital. You find the following data for a publicly traded firm in the 14. Consider the following airline industry data from mid-2009:
same line of business: Total
Market Enterprise
$423 million Company Capitalization Value Equity Debt
Debt Outstanding (book value, AA- Name ($mm) ($mm) Beta Ratings
rated) Delta Air 4,938.5 17,026.5 2.04 BB
Number of shares of common 67 million Lines (DAL)
stock Southwest 4,896.8 6,372.8 0.966 A/BBB
Stock price per share $17.29 Airlines (LUV)
Book value of equity per share $6.24 JetBlue 1,245.5 3,833.5 1.91 B/CCC
eta of equity 1.19 Airways
(JBLU)
Continental 1,124.0 4,414.0 1.99 B
What is your estimate of the project’s beta? What assumptions do you Airlines (CAL)
need to make? a. Use the estimates in Table 12.3 to estimate the debt beta
Answer: for each firm (use an average if multiple ratings are listed).
E=67 × $ 17.29=$ 1,158.43 b. Estimate the asset beta for each firm.
D=$ 423 c. What is the average asset beta for the industry, based on
Be = 1.19, BD = 0 these firms?
E+ D=$ 1,158.43+$ 423=$ 1,581.43 Answer:
1,158.43 423
B u= × 1.19+ ×0=0.87
1,581.43 1,581.43
Risk-free Rate Market Return XYZ Return Excess
13. In mid-2015, Cisco Systems had a market capitalization of $123 2007 3% 6% 10% 3% 7%
2008 1% -37% -45% -38% -46%
billion. It had A-rated debt of $21 billion as well as cash and short-
term investments of $62 billion, and its estimated equity beta at
the time was 1.32.
a. What is Cisco’s enterprise value?
b. Assuming Cisco’s debt has a beta of zero, estimate the beta
of Cisco’s underlying business enterprise.
Answer:
a. EV = E + D – C = $123 + $21 – $62 = $82 billion
123 −41
b. B u= × 1.32+ ×0=1 .98
82 82
 16. Unida Systems has 32 million shares outstanding trading for $9 per
15. Harrison Holdings, Inc. (HHI) is publicly traded, with a current share share. In addition, Unida has $85 million in outstanding debt.
price of $30 per share. HHI has 23 million shares outstanding, as Suppose Unida’s equity cost of capital is 13%, its debt cost of
well as $70 million in debt. The founder of HHI, Harry Harrison, capital is 9%, and the corporate tax rate is 32%.
made his fortune in the fast food business. He sold off part of his a. What is Unida’s unlevered cost of capital?
fast food empire, and purchased a professional hockey team. HHI’s b. What is Unida’s after-tax debt cost of capital?
only assets are the hockey team, together with 50% of the c. What is Unida’s weighted average cost of capital?
outstanding shares of Harry’s Hotdogs restaurant chain. Harry’s Answer:
Hotdogs (HDG) has a market capitalization of $803 million, and an a. E = 32 x $9 = $288 million
enterprise value of $1.05 billion. After a little research, you find D = $85 million
that the average asset beta of other fast food restaurant chains is Ru = 288 /(288 + 85) x 13% + 85/(288 + 85) x 9% = 12.1%
0.72. You also find that the debt of HHI and HDG is highly rated,
and so you decide to estimate the beta of both firms’ debt as zero. b. Rd = 9% x (1 – 32%) = 6.1%
Finally, you do a regression analysis on HHI’s historical stock
returns in comparison to the S&P 500, and estimate an equity beta c. Rwacc = 288/(288 + 85) x 13% + 85/(288 + 85) x 6.1% =
of 1.32. Given this information, estimate the beta of HHI’s 11.4%
investment in the hockey team. d.
Answer: 17. You would like to estimate the weighted average cost of capital for
HHI Equity = 30 x 23 = $690 a new airline business. Based on its industry asset beta, you have
HHI debt = $70 already estimated an unlevered cost of capital for the firm of 9%.
HHI asset beta = (690/(690 + 70))1.32 + (70/(690 + 70))0 = 1.20 However, the new business will be 24% debt financed, and you
Holdings of Hotdogs = $803/2 = 401.5 anticipate its debt cost of capital will be 6%. If its corporate tax rate
Value of Hockey Team = (690 + 70) – 401.5 = $358.5 is 32%, what is your estimate of its WACC?
Hotdog equity beta: (803/1,050) x Be + ((1050 − 803)/1,050) x 0 = Answer:
0.72 Ru = 9% = 76% Re + 24%Rd = 76% Re + 24%(6%)
0.7647Be = 0.72 Re = (9% – 24%(6%))/76% = 9.95%
Be = 0.74 / 0.7647 = 0.941 for hotdog equity Rwacc = 76%(9.95%) + 24%(6%)(1 – 32%) = 6.19%
So, if B = hockey team beta, Rwacc = 7.562% + 0.9792% = 8.5%
(401.5/(401.5 + 358.5))0.941 + (358.5/(401.5 + 358.5)) x B = 1.2
0.4971 + 0.4717B = 1.2
0.4717B = 1.2 – 0.4971 = 0.7029
Beta of hockey team = 0.7029 / 0.4717 = 1.49
Practice Question Week 9
2. You are an entrepreneur starting a biotechnology firm. If your
research is successful, the technology can be sold for $35
1. Consider a project with free cash flows in one year of $141,494 million. If your research is unsuccessful, it will be worth
or $182,105, with each outcome being equally likely. The initial nothing. To fund your research, you need to raise $2.7 million.
investment required for the project is $100,368, and the Investors are willing to provide you with $2.7 million in initial
project’s cost of capital is 20%. The risk-free interest rate is 5%. capital in exchange for 25% of the unlevered equity in the firm.
a. What is the NPV of this project? a. What is the total market value of the firm without leverage?
b. Suppose that to raise the funds for the initial investment, b. Suppose you borrow $0.9 million. According to MM, what
the project is sold to investors as an all-equity firm. The fraction of the firm’s equity will you need to sell to raise the
equity holders will receive the cash flows of the project in additional $1.8 million you need?
one year. How much money can be raised in this way—that
is, what is the initial market value of the unlevered equity? c. What is the value of your share of the firm’s equity in cases
(a) and (b)?
c. Suppose the initial $100,368 is instead raised by borrowing 100
at the risk-free interest rate. What are the cash flows of the a. Total value of equity=$ 2.7 million × =$ 10.8 million
25
levered equity, and what is its initial value according to b. MM says total value of firm is still $10.8. $0.9 million of debt
MM? implies total value of equity is $9.9 million. Therefore,

a. Estimated cash flow = (0.5 x $141,494) + (0.5 x $182,105) =

$161,800
(
1.8
9.9 )
× 100 18.18% of equity must be sold to raise the

additional $1.8 million.

$ 161,800
NPV =−$ 100,368+ =$ 34,465
1.2
c. In (a), it is $10.8 million - $2.7 million = $8.1 million. In (b), it is
$10.8 million - $0.9 million - $1.8 million = $8.1 million.
$ 161,800
b. PV ( Equity )= =$ 134,833
1.2

c. Total amount needed to be paid for debt = $100,368 x 1.05 =

$105,386
Cash flows for the levered equity is
$141,494 - $105,386 = $36,108
$182,105 - $105,386 = $76,719
Initial value, by MM, is $134,833 – $100,368 = $34,465.
3. Acort Industries owns assets that will have an 80% probability
of having a market value of $50 million in one year. There is a 4. Wolfrum Technology (WT) has no debt. Its assets will be worth
20% chance that the assets will be worth only $20 million. The $476 million in one year if the economy is strong, but only $262
current risk-free rate is 5%, and Acort’s assets have a cost of million in one year if the economy is weak. Both events are
capital of 10%. equally likely. The market value today of its assets is $286
million.
a. If Acort is unlevered, what is the current market value of its
equity? a. What is the expected return of WT stock without leverage?
b. Suppose instead that Acort has debt with a face value of $20 b. Suppose the risk-free interest rate is 5%. If WT borrows $93
million due in one year. According to MM, what is the value million today at this rate and uses the proceeds to pay an
of Acort’s equity in this case? immediate cash dividend, what will be the market value of
its equity just after the dividend is paid, according to MM?
c. What is the expected return of Acort’s equity without
leverage? What is the expected return of Acort’s equity with c. What is the expected return of WT stock after the dividend
leverage? is paid in part (b)?
d. What is the lowest possible realized return of Acort’s equity Answer:
with and without leverage?
a. Estimated market value in one year = (0.5 x $476 million) +
Answer:
(0.5 x $262 million) = $369 million
$ 369 million
Expected return= −1=0.2902=29.02 %
a. E[Value in one year] . $ 286 million
b. Market value of equity after the dividend is paid = $286
million - $93 million = $193 million.
b. D = . Therefore,
c. Estimated market value in one year = (0.5 x $476 million) +
(0.5 x $262 million) – ($93 million x 1.05) = $369 million
c. Without leverage, r = , with leverage, r = $ 271.35 million
Expected return= −1=0.4059=40.59 %
$ 193 million

d. Without leverage, r = , with leverage, r =

5. Suppose there are no taxes. Firm ABC has no debt, and firm XYZ a. According to MM Proposition I, what is the stock price for
has debt of $5000 on which it pays interest of 10% each year. Omega Technology?
Both companies have identical projects that generate free cash b. Suppose Omega Technology stock currently trades for $11
flows of $800 or $1000 each year. After paying any interest on per share. What arbitrage opportunity is available? What
debt, both companies use all remaining free cash flows to pay assumptions are necessary to exploit this opportunity?
dividends each year.
a. V(Alpha) = 10 22 = 220m = V(Omega) = D + E  E = 220 – 60
a. Fill in the table below showing the payments debt and = 160m  p = $8 per share.
equity holders of each firm will receive given each of the
two possible levels of free cash flows. b. Omega is overpriced. Sell 20 Omega, buy 10 Alpha, and
borrow 60. Initial = 220 – 220 + 60 = 60. Assumes we can
trade shares at current prices and that we can borrow at the
same terms as Omega (or own Omega debt and can sell at
same price).
b. Suppose you hold 10% of the equity of ABC. What is another
portfolio you could hold that would provide the same cash 7. Cisoft is a highly profitable technology firm that currently has $2
flows? billion in cash. The firm has decided to use this cash to
repurchase shares from investors, and it has already announced
c. Suppose you hold 10% of the equity of XYZ. If you can
these plans to investors. Currently, Cisoft is an all-equity firm
borrow at 10%, what is an alternative strategy that would
with 2 billion shares outstanding. These shares currently trade
provide the same cash flows?
for $20 per share. Cisoft has issued no other securities except
a. for stock options given to its employees. The current market
value of these options is $6 billion.
Debt
Paymen a. What is the market value of Cisoft’s non-cash assets?
ts
Equity Ddividends
Debt Pa payments Equity Ddividends
b. With perfect capital markets, what is the market value of
Cisoft’s equity after the share repurchase? What is the value
per share?
b. Unlevered Equity = Debt + Levered Equity. Buy 10% of XYZ a. Total value of Cisoft = (2 billion shares x $20 per share) + $6
debt and 10% of XYZ Equity, get 50 + (30, 50) = (80,100) billion = $46 billion.
c. Levered Equity = Unlevered Equity + Borrowing. Borrow $500, Market value of Cisoft’s non-cash assets = $46 billion - $2
buy 10% of ABC, receive (80,100) – 50 = (30, 50) billion = $44 billion.
b.
$ 2 bilion
6. Suppose Alpha Industries and Omega Technology have identical Number of shares repurchased= =0.1 billion shares
$ 20 per share
assets that generate identical cash flows. Alpha Industries is an
all-equity firm, with 10 million shares outstanding that trade for Number of shares outstanding after repurcahse=2 billion−0.1billion
a price of $22 per share. Omega Technology has 20 million
shares outstanding as well as debt of $60 million. Market value of equity after repurchase=$ 40 billion−$ 2 billion=$
 i. Before this transaction?
$ 38 billion
Value per share= =$ 20 per share ii. After the new securities are issued but before the share
1.9billion
repurchase?
8. Schwartz Industry is an industrial company with 89.9 million iii. After the share repurchase?
shares outstanding and a market capitalization (equity value) of b. At the conclusion of this transaction, how many shares
$4.24 billion. It has $1.75 billion of debt outstanding. outstanding will Zetatron have, and what will the value of
Management have decided to delever the firm by issuing new those shares be?
equity to repay all outstanding debt.
a. How many new shares must the firm issue?
a. i.
b. Suppose you are a shareholder holding 100 shares, and you
ii.
disagree with this decision. Assuming a perfect capital
market, describe what you can do to undo the effect of this
decision.
$ 4.24 billion iii.
a. Current value per share= =$ 47.16
0.0899 billion

$ 1.75 billion
Number of new shares ¿ be issued= =37.105 milion
$ 47.16
b. Repurchase shares  53.33 remain. Value is
b. You can undo the effect of the decision by borrowing to buy
additional shares, in the same proportion as the firm’s
actions, thus re-levering your own portfolio. In this case you
should buy 37.105 million new shares and borrow 37.105 x 10. Explain what is wrong with the following argument: “If a firm
$47.16 = $1,792.08. issues debt that is risk free, because there is no possibility of
default, the risk of the firm’s equity does not change. Therefore,
risk-free debt allows the firm to get the benefit of a low cost of
9. Zetatron is an all-equity firm with 100 million shares
capital of debt without raising its cost of capital of equity.”
outstanding, which are currently trading for $7.50 per share. A
month ago, Zetatron announced it will change its capital
Any leverage raises the equity cost of capital. In fact, risk-free
structure by borrowing $100 million in short-term debt,
leverage raises it the most (because it does not share any of the
borrowing $100 million in long-term debt, and issuing $100
risk).
million of preferred stock. The $300 million raised by these
issues, plus another $50 million in cash that Zetatron already
has, will be used to repurchase existing shares of stock. The
transaction is scheduled to occur today. Assume perfect capital
markets.
a. What is the market value balance sheet for Zetatron
 12. Hardmon Enterprises is currently an all-equity firm with an
11. Consider the entrepreneur described in Example 1 (in Lecture expected return of 12%. It is considering a leveraged
slides). Suppose she funds the project by borrowing $750 rather recapitalization in which it would borrow and repurchase
than $500. existing shares.
a. According to MM Proposition I, what is the value of the a. Suppose Hardmon borrows to the point that its debt-equity
equity? What are its cash flows if the economy is strong? ratio is 0.50. With this amount of debt, the debt cost of
What are its cash flows if the economy is weak? capital is 5%. What will the expected return of equity be
after this transaction?
b. What is the return of the equity in each case? What is its
expected return? b. Suppose instead Hardmon borrows to the point that its
debt-equity ratio is 1.50. With this amount of debt,
c. What is the risk premium of equity in each case? What is the
Hardmon’s debt will be much riskier. As a result, the debt
sensitivity of the levered equity return to systematic risk?
cost of capital will be 7%. What will the expected return of
How does its sensitivity compare to that of unlevered
equity be in this case?
equity? How does its risk premium compare to that of
unlevered equity? c. A senior manager argues that it is in the best interest of the
shareholders to choose the capital structure that leads to
d. What is the debt-equity ratio of the firm in this case?
the highest expected return for the stock. How would you
e. What is the firm’s WACC in this case? respond to this argument?

a. E = 1000 – 750 = 250. CF = (1400,900) – 500 (1.05) = D

a. R E=R U + ( R −R D )
E U
(612.5,112.5)
R E=12 % +0.5 ( 12 %−5 % )=15.5 %
b. Re = (145%, – 55%), E[Re] = 45%, Risk premium = 45% – 5% =
40% D
b. R E=R U + ( R −R D )
E U
c. Return sensitivity = 145% – (–55%) = 200%. This sensitivity is
4x the sensitivity of unlevered equity (50%). Its risk premium R E=12 % +1.5 ( 12%−7 % )=19.5 %
is also 4× that of unlevered equity (40% vs. 10%).
c. Returns are higher because risk is higher—the return fairly
compensates for the risk. There is no free lunch.
d.
e. 25%(45%) + 75%(5%) = 15%
13. Suppose Paypal (PYPL) has no debt and an equity cost of capital 15. Hubbard Industries is an all-equity firm whose shares have an
of 9.2%. The average debt-to-value ratio for the credit services expected return of 10.2%. Hubbard does a leveraged
industry is 15%. What would its cost of equity be if it took on recapitalization, issuing debt and repurchasing stock, until its
the average amount of debt for its industry at a cost of debt of debtequity ratio is 0.58. Due to the increased risk, shareholders
6%? now expect a return of 15.2%. Assuming there are no taxes and
Hubbard’s debt is risk free, what is the interest rate on the
At a cost of debt of 6%: debt?

E D
r WACC =r U = r E+ r
E+ D E +D D
1 0.58
r WACC =10.2 %= ( 15.2 % )+ r
1+ 0.58 1+0.58 D
10.2 %=0.6329 ( 15.2 % ) +0.3671 r D
10.2 %=9.62 %+ 0.3671r D
14. Global Pistons (GP) has common stock with a market value of 0.58 %=0.3671 r D
$200 million and debt with a value of $100 million. Investors 0.58 %
expect a 15% return on the stock and a 6% return on the debt. r D= =1.58 %
0.3671
Assume perfect capital markets.
a. Suppose GP issues $100 million of new stock to buy back the 16. Hartford Mining has 50 million shares that are currently trading
debt. What is the expected return of the stock after this for $4 per share and $200 million worth of debt. The debt is risk
transaction? free and has an interest rate of 5%, and the expected return of
Hartford stock is 11%. Suppose a mining strike causes the price
b. Suppose instead GP issues $50 million of new debt to
of Hartford stock to fall 25% to $3 per share. The value of the
repurchase stock.
risk-free debt is unchanged. Assuming there are no taxes and
i. If the risk of the debt does not change, what is the the risk (unlevered beta) of Hartford’s assets is unchanged,
expected return of the stock after this transaction? what happens to Hartford’s equity cost of capital?
ii. If the risk of the debt increases, would the expected
return of the stock be higher or lower than in part (i)?
.

a. .

b. i.
ii. if rd is higher, re is lower. The debt will share some of the
risk.
17. Mercer Corp. has 10 million shares outstanding and $100
million worth of debt outstanding. Its current share price is $75.
Mercer’s equity cost of capital is 8.5%. Mercer has just
announced that it will issue $350 million worth of debt. It will
use the proceeds from this debt to pay off its existing debt, and
use the remaining $250 million to pay an immediate dividend.
Assume perfect capital markets.
a. Estimate Mercer’s share price just after the recapitalization
is announced, but before the transaction occurs.
b. Estimate Mercer’s share price at the conclusion of the
transaction. (Hint: use the market value balance sheet.)
c. Suppose Mercer’s existing debt was risk-free with a 4.25%
expected return, and its new debt is risky with a 5%
expected return. Estimate Mercer’s equity cost of capital
after the transaction.
a. MM => no change, $75
b. Initial enterprise value = 75  10 + 100 = 850 million
New debt = 350 million
E = 850 – 350 = 500
Share price = 500/10 = $50
c. Ru = (750/850)  8.5% + (100/850)  4.25% = 8%
Re = 8% + 350/500(8% – 5%) = 10.1%
Practice Question Week 10 b. Free cash flow is not affected by interest expenses.

1. Pelamed Pharmaceuticals has EBIT of $347 million in 2018. In 3. Suppose the corporate tax rate is 40%. Consider a firm that
addition, Pelamed has interest expenses of $147 million and a earns $2500 before interest and taxes each year with no risk.
corporate tax rate of 30%. The firm’s capital expenditures equal its depreciation expenses
each year, and it will have no changes to its net working capital.
a. What is Pelamed’s 2018 net income? The risk-free interest rate is 4%.
b. What is the total of Pelamed’s 2018 net income and interest a. Suppose the firm has no debt and pays out its net income as
payments? a dividend each year. What is the value of the firm’s equity?
c. If Pelamed had no interest expenses, what would its 2018 b. Suppose instead the firm makes interest payments of $1600
net income be? How does it compare to your answer in part per year. What is the value of equity? What is the value of
b? debt?
d. What is the amount of Pelamed’s interest tax shield in c. What is the difference between the total value of the firm
2018? with leverage and without leverage?

a. Net Income=EBIT−Interest −Taxes d. The difference in part (c) is equal to what percentage of the
value of the debt?
Net Income=$ 347 million−$ 147 million × ( 1−0.3 )=$ 140 million
b. Net Income+ Interest a. Net income=$ 2,500 × ( 1−0.4 )=$ 1,500
$ 140 million+ $ 147 million=$ 287 million Thus, equity holders receive dividends of $1,500 per year with
c. Net Income=EBIT−Interest −Taxes no risk.
Net Income=$ 347 million × ( 1−0.3 )=$ 242.9 million $ 1,500
E= =$ 37,500
This is $287 million – $242.9 million = $44.1 million lower 0.04
than part (b). b. Net income=( $ 2,500−$ 1,600 ) × ( 1−0.4 ) =$ 540
$ 540
d. Interest tax shield =$ 147 million ×0.3=$ 44.1 million E= =$ 13,500
0.04
Value of equity is $13,500.
2. Grommit Engineering expects to have net income next year of
$ 1,600
$20.75 million and free cash flow of $22.15 million. Grommit’s Value of debt= =$ 40,000
0.04
marginal corporate tax rate is 20%.
c. V L=V U + PV ( Interest Tax Shield )
a. If Grommit increases leverage so that its interest expense V L=$ 13,500+ $ 40,000=$ 53,500
rises by $1 million, how will its net income change? Difference between total value of the firm with leverage and
b. For the same increase in interest expense, how will free without leverage
cash flow change? $53,500 - $37,500 = $16,000
$ 16,000
a. Net income will fall by the after-tax interest expense to d. =0.4=40 % corporate tax rate
$ 40,000
million.
 b. What is the present value of the interest tax shield,
assuming its risk is the same as the loan?
c. Suppose instead that the interest rate on the debt is 5%.
What is the present value of the interest tax shield in this
4. Braxton Enterprises currently has debt outstanding of $35 case?
million and an interest rate of 8%. Braxton plans to reduce its
debt by repaying $7 million in principal at the end of each year a. Interest tax shield million
for the next five years. If Braxton’s marginal corporate tax rate
is 25%, what is the interest tax shield from Braxton’s debt in
b. PV(Interest tax shield) million
each of the next five years?
c. Interest tax shield = $10 × 5% × 21% = $0.105 million.
Year 0 1 2 3 4 5
million.
Debt 35 28 21 14 7 0
Interest 2.80 2.24 1.68 1.12 0.56
Tax Shield 0.70 0.56 0.42 0.28 0.14 7. Ten years have passed since Arnell issued $10 million in
perpetual interest only debt with a 6% annual coupon, as in
Problem 6. Tax rates have remained the same at 35% but
5. Your firm currently has $100 million in debt outstanding with a interest rates have dropped so Arnell’s current cost of debt
10% interest rate. The terms of the loan require the firm to capital is 4%.
repay $25 million of the balance each year. Suppose that the a. What is Arnell’s annual interest tax shield?
marginal corporate tax rate is 25%, and that the interest tax
shields have the same risk as the loan. What is the present b. What is the present value of the interest tax shield today?
value of the interest tax shields from this debt?
a. Solution Interest tax shield million
Year 0 1 2 3 4 5
Debt 100 75 50 25 0 0
Interest 10 7.5 5 2.5 0 b. Solution PV(Interest tax shield) million.
Tax Shield 2.50 1.88 1.25 0.63 0 Alternatively, new market value of debt is D = (10 .06)/.04 =
PV $5.19 $15 million. Tc  D = 21%  15 = $3.15 million.

6. Arnell Industries has just issued $10 million in debt (at par). The
firm will pay interest only on this debt. Arnell’s marginal tax
rate is expected to be 21% for the foreseeable future.
a. Suppose Arnell pays interest of 6% per year on its debt.
What is its annual interest tax shield?
 E D
b. r WACC = r + r ( 1−τ c )
8. Bay Transport Systems (BTS) currently has $30 million in debt E+ D E E+ D D
outstanding. In addition to 6.5% interest, it plans to repay 5% of
the remaining balance each year. If BTS has a marginal 2.2 1.1
r WACC = ( 12 % ) + ( 6 % ) ( 1−0.4 )=9.2 %
corporate tax rate of 25%, and if the interest tax shields have 2.2+1.1 2.2+1.1
the same risk as the loan, what is the present value of the
interest tax shield from the debt? 11. Rumolt Motors has 68 million shares outstanding with a price of
Interest tax shield in year 1 = $30 × 6.5% × 25% = $0.49 million. $28 per share. In addition, Rumolt has issued bonds with a total
As the outstanding balance declines, so will the interest tax current market value of $2149 million. Suppose Rumolt’s equity
shield. Therefore, we can value the interest tax shield as a cost of capital is 15%, and its debt cost of capital is 11%.
growing perpetuity with a growth rate of g = –5% and r = 6.5%: a. What is Rumolt’s pre-tax weighted average cost of capital?
b. If Rumolt’s corporate tax rate is 38%, what is its after-tax
million
weighted average cost of capital?
9. Safeco Inc. has no debt, and maintains a policy of holding $10 a. Market value of equity = $28 per share x 68 million shares =
million in excess cash reserves, invested in risk-free Treasury $1,904 million
securities. If Safeco pays a corporate tax rate of 21%, what is E D
r WACC = r E+ r
the cost of permanently maintaining this $10 million reserve? E+ D E+ D D
(Hint: what is the present value of the additional taxes that
Safeco will pay?) 1,904 2,149
r WACC = ( 15 % ) + ( 11% )=12.88 %
D = –$10 million (negative debt) 1,904+2,149 1,904+ 2,149
So PV(Interest tax shield) = Tc  D = –$2.1 million.
This is the present value of the future taxes Safeco will pay on the E D
b. r WACC = r E+ r ( 1−τ c )
interest earned on its reserves. E+ D E+ D D

10. Rogot Instruments makes fine violins and cellos. It has $1.1 1,904 2,149
r WACC = ( 15 % ) + ( 11% )( 1−0.38 )=10.6
million in debt outstanding, equity valued at $2.2 million, and 1,904+2,149 1,904+ 2,149
pays corporate income tax at a rate of 40%. Its cost of equity is
12% and its cost of debt is 6%. 12. Summit Builders has a market debt-equity ratio of 0.65 and a
corporate tax rate of 25%, and it pays 7% interest on its debt.
a. What is Rogot’s pre-tax WACC?
The interest tax shield from its debt lowers Summit’s WACC by
b. What is Rogot’s (effective after-tax) WACC? what amount?
E D
a. r WACC = r + r
E+ D E E+ D D
.
2.2 1.1 Therefore, WACC = Pretax WACC – 0.394(7%)(0.25) = Pretax
r WACC = ( 12 % ) + ( 6 % )=10 %
2.2+1.1 2.2+1.1 WACC – 0.69%
So, it lowers it by 0.69%.
 15. Acme Storage has a market capitalization of $140 million and
debt outstanding of $94 million. Acme plans to maintain this
same debt-equity ratio in the future. The firm pays an interest
rate of 7.8% on its debt and has a corporate tax rate of 38%.
13. NatNah, a builder of acoustic accessories, has no debt and an a. If Acme’s free cash flow is expected to be $14.04 million
equity cost of capital of 15%. Suppose NatNah decides to next year and is expected to grow at a rate of 6% per year,
increase its leverage and maintain a market debt-to-value ratio what is Acme’s WACC?
of 0.5. Suppose its debt cost of capital is 9% and its corporate
tax rate is 21%. If NatNah’s pretax WACC remains constant, b. What is the value of Acme’s interest tax shield?
what will its (effective after-tax) WACC be with the increase in
leverage? FCF
a. V L=E + D=
WACC−g
V L=$ 140 million +$ 94 million=$ 234 million
14.04
234=
WACC−0.06
14. Restex maintains a debt-equity ratio of 0.85, and has an equity 234 WACC −14.04=14.04
cost of capital of 12%, and a debt cost of capital of 7%. Restex’s 234 WACC =14.04+14.04
corporate tax rate is 25%, and its market capitalization is $220 234 WACC =28.08
million. 28.08
WACC = =0.12=12 %
a. If Restex’s free cash flow is expected to be $10 million in 234
one year, what constant expected future growth rate is
consistent with the firm’s current market value? D
b. Pretax WACC =WACC + r τ
E+ D D c
b. Estimate the value of Restex’s interest tax shield. 94
Pretax WACC =12 %+ ( 7.8 % )( 0.38 )=13.19 %
Answer: 140+94
FCF $ 14.04
V U= = =$ 195.25
pretax WACC −g 0.1319−0.06

PV ( Interest Tax Shield )=V L−V U =$ 234 million−$ 195.25 million=

16. Milton Industries expects free cash flow of $5 million each year.
a.
Milton’s corporate tax rate is 21%, and its unlevered cost of
capital is 15%. The firm also has outstanding debt of $19.05
million, and it expects to maintain this level of debt
permanently.
a. What is the value of Milton Industries without leverage?
b.
b. What is the value of Milton Industries with leverage?
 Answer: a. Assets = Equity = $7.50 × 20 = $150 million
b. Assets = 150 (existing) + 50 (cash) + 25% × 50 (tax shield) =
a. $212.5 million
c. E = Assets – Debt = 212.50 – 50 = $162.5 million. Share price
b.

17. Suppose Microsoft has 8.15 billion shares outstanding and pays Kurz will repurchase million shares.
a marginal corporate tax rate of 37%. If Microsoft announces
d. Assets = 150 (existing) + 25% 50 (tax shield) = $162.5 million
that it will payout $52 billion in cash to investors through a
combination of a special dividend and a share repurchase, and if Debt = $50 million
investors had previously assumed Microsoft would retain this E = A – D = 162.5 – 50 = $112.5 million
excess cash permanently, by how much will Microsoft’s share
price change upon the announcement?
Share price (difference due to
Reducing cash is equivalent to increasing leverage by $52 billion. rounding).
PV of tax savings = 37% x $52 billion = $19.24 billion, or $19.24/
8.15 = $2.36 per share price increase.

18. Kurz Manufacturing is currently an all-equity firm with 20

million shares outstanding and a stock price of $7.50 per share.
Although investors currently expect Kurz to remain an all-equity
firm, Kurz plans to announce that it will borrow $50 million and
use the funds to repurchase shares. Kurz will pay interest only
on this debt, and it has no further plans to increase or decrease
the amount of debt. Kurz is subject to a 25% corporate tax rate.
a. What is the market value of Kurz’s existing assets before the
announcement?
b. What is the market value of Kurz’s assets (including any tax
shields) just after the debt is issued, but before the shares
are repurchased?
c. What is Kurz’s share price just before the share repurchase?
How many shares will Kurz repurchase?
d. What are Kurz’s market value balance sheet and share price
after the share repurchase?
 repurchase. Therefore, shares will be willing to sell at this
19. Rally, Inc., is an all-equity firm with assets worth $25 billion and price.
10 billion shares outstanding. Rally plans to borrow $10 billion
and use these funds to repurchase shares. The firm’s corporate
tax rate is 21%, and Rally plans to keep its outstanding debt
equal to $10 billion permanently.
a. Without the increase in leverage, what would Rally’s share
price be?
b. Suppose Rally offers $2.60 per share to repurchase its
shares. Would shareholders sell for this price?
c. Suppose Rally offers $3.00 per share, and shareholders
tender their shares at this price. What will Rally’s share
price be after the repurchase?
d. What is the lowest price Rally can offer and have
shareholders tender their shares? What will its stock price
be after the share repurchase in that case?

a. Share price per share

b. Just before the share repurchase:

Therefore, shareholders will not sell for $2.60 per share.

c. Assets = 25 (existing) + 21% 10 (tax shield) = $27.1 billion
E = 27.1 – 10 = 17.1 billion

Share price
d. From (b), fair value of the shares prior to repurchase is $2.71.

At this price, Rally will have million shares

outstanding, which will be worth after the