Study Guides (258,838)
CA (124,997)
UTM (5,134)
ECO (241)
ECO359H5 (14)
Sun (12)

5 Pages
171 Views

Department
Economics
Course Code
ECO359H5
Professor
Sun

This preview shows pages 1-2. Sign up to view the full 5 pages of the document.
ECO359/2011î€ƒî€ƒUniversityî€ƒofî€ƒTorontoî€ƒ
Practiceî€ƒProblemsî€ƒ3î€ƒ î€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒ Departmentî€ƒofî€ƒEconomicsî€ƒ
1î€ƒ
î€ƒ
ECO 359 Practice Problems 3
Solutions to selected Textbook questions
Question 16.1
a. Since Alpha Corporation is an all-equity firm, its value is equal to the market value of its outstanding
shares. Alpha has 5,000 shares of common stock outstanding, worth \$20 per share.
Therefore, the value of Alpha Corporation is \$100,000 (= 5,000 shares * \$20 per share).
b. Modiglianiâ€“Miller Proposition I states that in the absence of taxes, the value of a levered firm equals
the value of an otherwise identical unlevered firm. Since Beta Corporation is identical to Alpha
Corporation in every way except its capital structure and neither firm pays taxes, the value of the two
firms should be equal.
Modiglianiâ€“Miller Proposition I (No Taxes): VL =VU.
Alpha Corporation, an unlevered firm, is worth \$100,000 = VU.
Therefore, the value of Beta Corporation (VL) is \$100,000.
c. The value of a levered firm equals the market value of its debt plus the market value of its equity. VL
= B + S. The value of Beta Corporation is \$100,000 (VL), and the market value of the firmâ€™s debt is
\$25,000 (B). The value of Betaâ€™s equity is S= VL â€“ B = \$100,000 â€“ \$25,000 = \$75,000. Therefore,
the market value of Beta Corporationâ€™s equity (S) is \$75,000.
d. Since the market value of Alpha Corporationâ€™s equity is \$100,000, it will cost \$20,000 (= 0.20*
\$100,000) to purchase 20% of the firmâ€™s equity.
Since the market value of Beta Corporationâ€™s equity is \$75,000, it will cost \$15,000 (= 0.20*
\$75,000) to purchase 20% of the firmâ€™s equity.
e. Since Alpha Corporation expects to earn \$35,000 this year and owes no interest payments, the dollar
return to an investor who owns 20% of the firmâ€™s equity is expected to be \$7,000 (= 0.20*\$35,000)
over the next year.
While Beta Corporation also expects to earn \$35,000 before interest this year, it must pay 13%
interest on its debt. Since the market value of Betaâ€™s debt at the beginning of the year is \$25,000,
Beta must pay \$3,250 (= 0.13*\$25,000) in interest at the end of the year. Therefore, the amount of
the firmâ€™s earnings available to equity holders is \$31,750 (=\$35,000 â€“ \$3,250). The dollar return to
an investor who owns 20% of the firmâ€™s equity is \$6,350 (= 0.20*\$31,750).
f. The initial cost of purchasing 20% of Alpha Corporationâ€™s equity is \$20,000, but the cost to an
investor of purchasing 20% of Beta Corporationâ€™s equity is only \$15,000 (see part d).
www.notesolution.com
ECO359/2011î€ƒî€ƒUniversityî€ƒofî€ƒTorontoî€ƒ
Practiceî€ƒProblemsî€ƒ3î€ƒ î€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒî€ƒ Departmentî€ƒofî€ƒEconomicsî€ƒ
2î€ƒ
î€ƒ
In order to purchase \$20,000 worth of Alphaâ€™s equity using only \$15,000 of his own money, the
investor must borrow \$5,000 to cover the difference. The investor must pay 13% interest on his
borrowings at the end of the year.
Since the investor now owns 20% of Alphaâ€™s equity, the dollar return on his equity investment at the
end of the year is \$7,000 (= 0.20*\$35,000). However, since he borrowed \$5,000 at 13% per annum,
he must pay \$650 (= 0.13* \$5,000) at the end of the year.
Therefore, the cash flow to the investor at the end of the year is \$6,350 (= \$7,000 - \$650). Notice
that this amount exactly matches the dollar return to an investor who purchases 20% of Betaâ€™s equity.
Strategy Summary:
1. Borrow \$5,000 at 13%.
2. Purchase 20% of Alphaâ€™s stock for a net cost of \$15,000 (= \$20,000 â€“ \$5,000 borrowed).
g. The equity of Beta Corporation is riskier. Beta must pay off its debt holders before its equity holders
receive any of the firmâ€™s earnings. If the firm does not do particularly well, all of the firmâ€™s earnings
may be needed to repay its debt holders, and equity holders will receive nothing.
Question 16.2
a. A firmâ€™s debtâ€“equity ratio is the market value of the firmâ€™s debt divided by the market value of a
firmâ€™s equity. The market value of Acetateâ€™s debt \$9 million, and the market value of Acetateâ€™s
equity is \$30 million.
Debt-Equity Ratio = Market Value of Debt/Market Value of Equity = \$9M/\$30M = 0.03. Therefore,
Acetateâ€™s Debtâ€“Equity Ratio is 30%.
b. By CAPM, the cost of Acetateâ€™s equity is:
rS = rf + î€•S[E(rm) â€“ rf] = 0.07 + 0.85( 0.21- 0.07) = 0.189. The cost of Acetateâ€™s equity (rS) is 18.9%.
Assume a cost of debt of 14% (missing in the statement of the problem).
Acetateâ€™s weighted average cost of capital equals:
rwacc = {B / (B+S)} rB + {S / (B+S)}rS = (\$9M/\$39M)(0.14) + (\$30M/\$39M)(0.189) = (0.23)(0.14) +
(.77)(0.189) = 0.1777. Therefore, Acetateâ€™s weighted average cost of capital is 17.77%.
c. According to Modiglianiâ€“Miller Proposition II (No Taxes):
rS = r0 + (B/S)(r0 â€“ rB). Thus, 0.189= r0 + (9/30)(r0 â€“ 0.14). Solving for r0 = 0.1777. Therefore, the
cost of capital for an otherwise identical allâ€“equity firm is 17.77%. This is consistent with
Modiglianiâ€“Millerâ€™s proposition that, in the absence of taxes, the cost of capital for an allâ€“equity
firm is equal to the weighted average cost of capital of an otherwise identical levered firm.
www.notesolution.com

Loved by over 2.2 million students

Over 90% improved by at least one letter grade.

OneClass has been such a huge help in my studies at UofT especially since I am a transfer student. OneClass is the study buddy I never had before and definitely gives me the extra push to get from a B to an A!

Leah â€” University of Toronto

Balancing social life With academics can be difficult, that is why I'm so glad that OneClass is out there where I can find the top notes for all of my classes. Now I can be the all-star student I want to be.

Saarim â€” University of Michigan

As a college student living on a college budget, I love how easy it is to earn gift cards just by submitting my notes.

Jenna â€” University of Wisconsin

OneClass has allowed me to catch up with my most difficult course! #lifesaver

Anne â€” University of California
Description
ECO3592011 UniversityofToronto PracticeProblems3 DepartmentofEconomics ECO 359 Practice Problems 3 Solutions to selected Textbook questions Question 16.1 a. Since Alpha Corporation is an all-equity firm, its value is equal to the market value of its outstanding shares. Alpha has 5,000 shares of common stock outstanding, worth \$20 per share. Therefore, the value of Alpha Corporation is \$100,000 (= 5,000 shares * \$20 per share). b. ModiglianiMiller Proposition I states that in the absence of taxes, the value of a levered firm equals the value of an otherwise identical unlevered firm. Since Beta Corporation is identical to Alpha Corporation in every way except its capital structure and neither firm pays taxes, the value of the two firms should be equal. ModiglianiMiller Proposition I (No Taxes): V L =V U. Alpha Corporation, an unlevered firm, is worth \$100,000 = V . U Therefore, the value of Beta Corporation (V L) is \$100,000. c. The value of a levered firm equals the market value of its debt plus the market value of its equity. V L = B + S. The value of Beta Corporation is \$100,000 (V ), Lnd the market value of the firms debt is \$25,000 (B). The value of Betas equity is S= V L B = \$100,000 \$25,000 = \$75,000. Therefore, the market value of Beta Corporations equity (S) is \$75,000. d. Since the market value of Alpha Corporations equity is \$100,000, it will cost \$20,000 (= 0.20* \$100,000) to purchase 20% of the firms equity. Since the market value of Beta Corporations equity is \$75,000, it will cost \$15,000 (= 0.20* \$75,000) to purchase 20% of the firms equity. e. Since Alpha Corporation expects to earn \$35,000 this year and owes no interest payments, the dollar return to an investor who owns 20% of the firms equity is expected to be \$7,000 (= 0.20*\$35,000) over the next year. While Beta Corporation also expects to earn \$35,000 before interest this year, it must pay 13% interest on its debt. Since the market value of Betas debt at the beginning of the year is \$25,000, Beta must pay \$3,250 (= 0.13*\$25,000) in interest at the end of the year. Therefore, the amount of the firms earnings available to equity holders is \$31,750 (=\$35,000 \$3,250). The dollar return to an investor who owns 20% of the firms equity is \$6,350 (= 0.20*\$31,750). f. The initial cost of purchasing 20% of Alpha Corporations equity is \$20,000, but the cost to an investor of purchasing 20% of Beta Corporations equity is only \$15,000 (see part d). 1 www.notesolution.com
More Less

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

Unlock Document

Unlock to view full version

Unlock Document
Notes
Practice
Earn
Me

OR

Don't have an account?

Join OneClass

Access over 10 million pages of study
documents for 1.3 million courses.

Join to view

OR

By registering, I agree to the Terms and Privacy Policies
Just a few more details

So we can recommend you notes for your school.