Problem Set_ Cost of Capital

The Cost of Capital The Equity Cost of Capital

Use the following information to answer the question(s) below.

"Eenie" "Meenie" "Miney" "Moe"

Beta 0.45 0.75 1.05 1.20

Volatility 20% 18% 35% 25%

Assume that the risk-free rate of interest is 3% and you estimate the m arket's expected return to be 9%. 1) Which firm has the most total risk? A) Eenie B) Meenie C) Miney D) Moe Answer: C Explanation: C) Total risk is measured using volatility and Miney has the highest volatility, hence the most total risk. Diff: 1 Section: 12.1 The Equity Cost of Capital Skill: Analytical 2) Which firm has the least market risk? A) Eenie B) Meenie C) Miney D) Moe Answer: A Explanation: A) Market risk is measured using beta and Eenie has the lowest beta, hence the lowest market risk. Diff: 1 Section: 12.1 The Equity Cost of Capital Skill: Analytical

1 Copyright © 2014 Pearson Education, Inc.

3) Which firm has the highest cost of equity capital? A) Eenie B) Meenie C) Miney D) Moe Answer: D Explanation: D) Cost of capital is measured using the CAPM and is a linear function of beta. Therefore the firm with the highest beta (Moe) has the highest cost of equity capital. Diff: 1 Section: 12.1 The Equity Cost of Capital Skill: Analytical 4) The equity cost of capital for "Miney" is closest to: A) 6.30% B) 7.50% C) 9.30% D) 9.75% Answer: C Explanation: C) r Miney = 3% + 1.05(9% - 3%) = 9.3% Diff: 1 Section: 12.1 The Equity Cost of Capital Skill: Analytical 5) The equity cost of capital for "Meenie" is closest to: A) 4.50% B) 7.50% C) 9.30% D) 9.75% Answer: B Explanation: B) r Meenie = 3% + 0.75(9% - 3%) = 7.5% Diff: 1 Section: 12.1 The Equity Cost of Capital Skill: Analytical 6) The risk premium for "Meenie" is closest to: A) 4.50% B) 7.50% C) 9.30% D) 9.75% Answer: A Explanation: A) risk premiumMeenie = 0.75(9% - 3%) = 4.5% Diff: 2 Section: 12.1 The Equity Cost of Capital Skill: Analytical


Beta Estimation


Year 2007 2008 2009

Risk-free Return 3.0% 1.5% 1.0%

Market Return 6.0% -38.5% 22.5%

Wyatt Oil Return 5.5% -32.6% 19.6%

Market Excess Return 3.0% .40% 21.5%

Wyatt Oil Excess Return 2.5% -34.1% 18.6%

Beta 0.833 0.853 0.865

1) Wyatt Oil's average historical return is closest to: A) -2.50% B) -3.33% C) -4.33% D) -5.17% Answer: A Explanation: A) r average = Risk-free Return 3.0% 1.5% 1.0% 1.83%

Market Return 6.0% -38.5% 22.5% -3.33%

Year 2007 2008 2009 Average Diff: 1 Section: 12.3 Beta Estimation Skill: Analytical

Wyatt Oil Return 5.5% -32.6% 19.6% -2.50%

Market Excess Return 3.0% -40.0% 21.5% -5.17%


Wyatt Oil Excess Return 2.5% -34.1% 18.6% -4.33%

2) The Market's average historical return is closest to: A) -2.50% B) -3.33% C) -4.33% D) -5.17% Answer: B Explanation: B) r average = Risk-free Return 3.0% 1.5% 1.0% 1.83%

Market Return 6.0% -38.5% 22.5% -3.33%


Wyatt Oil Return 5.5% -32.6% 19.6% -2.50%



3) Wyatt Oil's average historical excess return is closest to: A) -2.50% B) -3.33% C) -4.33% D) -5.17% Answer: C Explanation: C) excess returnaverage = Risk-free Return 3.0% 1.5% 1.0% 1.83%

Market Return 6.0% -38.5% 22.5% -3.33%


Wyatt Oil Return 5.5% -32.6% 19.6% -2.50%




4) The Market's average historical excess return is closest to: A) -2.50% B) -3.33% C) -4.33% D) -5.17% Answer: D Explanation: D) excess returnaverage =

Risk-free Market Year Return Return 2007 3.0% 6.0% 2008 1.5% -38.5% 2009 1.0% 22.5% Average 1.83% -3.33% Diff: 2 Section: 12.3 Beta Estimation Skill: Analytical

Wyatt Oil Return 5.5% -32.6% 19.6% -2.50%





5) Wyatt Oil's excess return for 2009 is closest to: A) 18.6% B) 19.6% C) 20.0% D) 21.5% Answer: A Explanation: A) excess returne = (r WO - r rf )2009

Risk-free Market Year Return Return 2007 3.0% 6.0% 2008 1.5% -38.5% 2009 1.0% 22.5% Average 1.83% -3.33% Diff: 1 Section: 12.3 Beta Estimation Skill: Analytical

Wyatt Oil Return 5.5% -32.6% 19.6% -2.50%


6) The Market's excess return for 2008 is closest to: A) -40.0% B) -38.5% C) -37.0% D) -34.1% Answer: A Explanation: A) excess returne = (r WO - r rf )2009

Risk-free Return 3.0% 1.5% 1.0% 1.83%

Market Return 6.0% -38.5% 22.5% -3.33%


Wyatt Oil Return 5.5% -32.6% 19.6% -2.50%



7) Using just the return data for 2009, your estimate of Wyatt Oil's Beta is closest to: A) 0.84 B) 0.87 C) 1.00 D) 1.16 Answer: B Explanation: B) Market Wyatt Oil Risk-free Market Wyatt Oil Excess Excess Year Return Return Return Return Return 2007 3.0% 6.0% 5.5% 3.0% 2.5% 2008 1.5% -38.5% -32.6% -40.0% -34.1% 2009 1.0% 22.5% 19.6% 21.5% 18.6% Average 1.83% -3.33% -2.50% -5.17% -4.33% β WO =

=

= .8651

Diff: 2 Section: 12.3 Beta Estimation Skill: Analytical 8) Using just the return data for 2008, your estimate of Wyatt Oil's Beta is closest to: A) 0.85 B) 0.87 C) 1.00 D) 1.17 Answer: A 6 Copyright © 2014 Pearson Education, Inc.

Explanation: A)

Year 2007 2008 2009 Average

β WO =

Risk-free Return 3.0% 1.5% 1.0% 1.83%

Market Return 6.0% -38.5% 22.5% -3.33%

-


Wyatt Oil Return 5.5% -32.6% 19.6% -2.50%


= .8525

Diff: 2 Section: 12.3 Beta Estimation Skill: Analytical 13) Which of the following statements is FALSE? A) Securities that tend to move more than the market have betas higher than 0. B) Securities whose returns tend to move in tandem with the market on average have a beta of 1. C) Beta corresponds to the slope of the best fitting line in the plot of the securities excess returns versus the market excess return. D) The statistical technique that identifies the bets-fitting line through a set of points is called linear regression. Answer: A Diff: 2 Section: 12.3 Beta Estimation Skill: Conceptual

The Debt Cost of Capital


Consider the following information regarding corporate bonds: Rating Average Default Rate Recession Default Rate Average Beta

AAA 0.0% 0.0% 0.05

AA 0.1% 1.0% 0.05

A 0.2% 3.0% 0.05

BBB 0.5% 3.0% 0.10

BB B CCC 2.2% 5.5% 12.2% 8.0% 16.0% 48.0% 0.17 0.26 0.31

1) Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of 7.0%, and a BBB rating. The corresponding risk-free rate is 3% and the market risk premium is 5%. Assuming a normal economy, the expected return on Wyatt Oil's debt is closest to: A) 3.0% B) 3.5% C) 4.9% D) 5.5% Answer: B 7 Copyright © 2014 Pearson Education, Inc.

Explanation: B) r d = r rf + β (r m - r rf ) = 3% + 0.1(5%) = 3.5% Diff: 1 Section: 12.4 The Debt Cost of Capital Skill: Analytical 2) Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of 7.0%, and a BBB rating. The bondholders' expected loss rate in the event of default is 70%. Assuming a normal economy the expected return on Wyatt Oil's debt is closest to: A) 3.0% B) 3.5% C) 4.9% D) 6.7% Answer: D Explanation: D) r d = ytm - prob(default) × loss rate = 7% - 0.4%(70%) = 6.72% Diff: 2 Section: 12.4 The Debt Cost of Capital Skill: Analytical


3) Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of 7.0%, and a BBB rating. The bondholders' expected loss rate in the event of default is 70%. Assuming the economy is in recession, then the expected return on Wyatt Oil's debt is closest to: A) 3.5% B) 4.9% C) 5.5% D) 7.0% Answer: B Explanation: B) r d = ytm - prob(default) × loss rate = 7% - 3.0%(70%) = 4.9% Diff: 2 Section: 12.4 The Debt Cost of Capital Skill: Analytical 4) Rearden Metal has a bond issue outstanding with ten years to maturity, a yield to maturity of 8.6%, and a B rating. The corresponding risk-free rate is 3% and the market risk premium is 6%. Assuming a normal economy, the expected return on Rearden Metal's debt is closest to: A) 0.6% B) 1.6% C) 4.6% D) 6.0% Answer: C Explanation: C) r d = r rf + β (r m - r rf ) = 3% + 0.26(6%) = 4.56% Diff: 1 Section: 12.4 The Debt Cost of Capital Skill: Analytical 5) Rearden Metal has a bond issue outstanding with ten years to maturity, a yield to maturity of 8.6%, and a B rating. The bondholders expected loss rate in the event of default is 50%. Assuming a normal economy the expected return on Rearden Metal's debt is closest to: A) 0.6% B) 1.6% C) 4.6% D) 6.0% Answer: D Explanation: D) r d = ytm - prob(default) × loss rate = 8.6% - 5.2%(50%) = 6.00% Diff: 2 Section: 12.4 The Debt Cost of Capital Skill: Analytical


6) Rearden Metal has a bond issue outstanding with ten years to maturity, a yield to maturity of 8.6%, and a B rating. The bondholders expected loss rate in the event of default is 50%. Assuming the economy is in recession, then the expected return on Rearden Metal's debt is closest to: A) 0.6% B) 1.6% C) 4.6% D) 6.0% Answer: A Explanation: A) r d = ytm - prob(default) × loss rate = 8.6% - 16.0%(50%) = 0.6% Diff: 2 Section: 12.4 The Debt Cost of Capital Skill: Analytical 7) Nielson Motors plans to issue 10-year bonds that it believes will have an BBB rating. Suppose AAA bonds with the same maturity have a 3.5% yield. Assume that the market risk premium is 5% and the expected loss rate in the event of default on the bonds is 60%. The yield that these bonds will have to pay during average economic times is closest to: A) 3.50% B) 3.75% C) 4.00% D) 5.50% Answer: C Explanation: C) For AAA r d = r rf + β (r m - r rf ) = r rf + 0.05(5%) = 3.5% → r rf = 3.25% For BBB r d = r rf + β (r m - r rf ) = 3.25% + 0.10(5%) = 3.75% r d = ytm - prob(default) × loss rate → 3.75% = ytm - 0.4%(60%) → ytm = 3.99% Diff: 3 Section: 12.4 The Debt Cost of Capital Skill: Analytical 8) Nielson Motors plans to issue 10-year bonds that it believes will have an BBB rating. Suppose AAA bonds with the same maturity have a 3.5% yield. Assume that the market risk premium is 5% and the expected loss rate in the event of default on the bonds is 60%. The yield that these bonds will have to pay during a recession is closest to: A) 3.50% B) 3.75% C) 4.00% D) 5.50% Answer: D Explanation: D) For AAA r d = r rf + β (r m - r rf ) = r rf + 0.05(5%) = 3.5% → r rf = 3.25% For BBB r d = r rf + β (r m - r rf ) = 3.25% + 0.10(5%) = 3.75% r d = ytm - prob(default) × loss rate → 3.75% = ytm - 3.0%(60%) → ytm = 5.55% Diff: 3 Section: 12.4 The Debt Cost of Capital Skill: Analytical


A Project's Cost of Capital


Consider the following information regarding corporate bonds: Rating Average Default Rate Recession Default Rate Average Beta

AAA 0.0% 0.0% 0.05

AA 0.1% 1.0% 0.05

A BBB BB B CCC 0.2% 0.45% 2.2% 5.5% 12.2% 3.0% 3.0% 8.0% 16.0% 48.0% 0.05 0.10 0.17 0.26 0.31

Market Total Capitalization Enterprise Company ($mm) Value ($mm) Taggart Transcontinental $4,500 8,000 Rearden Metal $3,800 7,200 Wyatt Oil $2,400 3,800 Nielson Motors $1,500 4,400

Equity Beta 1.1 1.3 0.9 1.75

Debt Rating BBB AAA A BB

1) Your estimate of the debt beta for Taggart Transcontinental would be: A) 0.05 B) 0.10 C) 0.17 D) 1.00 Answer: B Explanation: B) Since Taggart has a rating of BBB, the appropriate debt beta from the table is 0.10. Diff: 1 Section: 12.5 A Project's Cost of Capital Skill: Analytical 2) Your estimate of the debt beta for Nielson Motors would be: A) 0.10 B) 0.17 C) 1.00 D) 1.68 Answer: B Explanation: B) Since Nielson has a rating of BB, the appropriate debt beta from the table is 0.17. Diff: 1 Section: 12.5 A Project's Cost of Capital Skill: Analytical


3) Your estimate of the asset beta for Taggart Transcontinental is closest to: A) 0.42 B) 0.59 C) 0.66 D) 0.71 Answer: C Explanation: C) Since Taggart has a rating of BBB, the appropriate debt beta from the table is 0.10. β U = β E + β D =

× 1.1 +

× 0.10 = 0.6625

Diff: 2 Section: 12.5 A Project's Cost of Capital Skill: Analytical 4) Your estimate of the asset beta for Rearden Metal is closest to: A) 0.42 B) 0.59 C) 0.66 D) 0.71 Answer: D Explanation: D) Since Rearden has a rating of AAA, the appropriate debt beta from the table is 0.05. β U = β E + β D =

× 1.3 +

× 0.05 = 0.709722

Diff: 2 Section: 12.5 A Project's Cost of Capital Skill: Analytical 5) Your estimate of the asset beta for Wyatt Oil is closest to: A) 0.59 B) 0.66 C) 0.71 D) 0.90 Answer: A Explanation: A) Since Wyatt has a rating of A, the appropriate debt beta from the table is 0.05. β U = β E + β D =

× 0.9 +

× 0.05 = 0.586842

Diff: 2 Section: 12.5 A Project's Cost of Capital Skill: Analytical


6) Your estimate of the asset beta for Nielson Motors is closest to: A) 0.59 B) 0.66 C) 0.71 D) 1.75 Answer: C Explanation: C) Since Nielson has a rating of BB, the appropriate debt beta from the table is 0.17. β U = β E + β D =

× 1.75 +

× 0.17 = 0.708636

Diff: 2 Section: 12.5 A Project's Cost of Capital Skill: Analytical 7) Suppose that because of the large need for steel in building railroad infrastructure, Taggart Transcontinental and Rearden Metal decide to form into one large conglomerate. Your estimate of the asset beta for this new conglomerate is closest to: A) 0.42 B) 0.59 C) 0.66 D) 0.68 Answer: D Explanation: D) Since Taggart has a rating of BBB, the appropriate debt beta from the table is 0.10. β U = β E + β D =

× 1.1 +

× 0.10 = 0.6625

Since Rearden has a rating of AAA, the appropriate debt beta from the table is 0.05. β U = β E + β D =

× 1.3 +

= W TT =

× 0.05 = 0.709722

+ W RM

(0.6625) +

(0.709722) = 0.684868

Diff: 2 Section: 12.5 A Project's Cost of Capital Skill: Analytical


11) Your firm is planning to invest in a new power generation system. Galt Industries is an all equity firm that specializes in this business. Suppose Galt's equity beta is 0.75, the risk-free rate is 3%, and the market risk premium is 6%. If your firm's project is all equity financed, then your estimate of your cost of capital is closest to: A) 5.25% B) 6.00% C) 6.75% D) 7.50% Answer: D Explanation: D) r i = r rf + β (r m - r rf ) = .03 + .75(.06) = .075 or 7.5% Diff: 1 Section: 12.5 A Project's Cost of Capital Skill: Analytical 12) Your firm is planning to invest in a new electrostatic power generation system. Electrostat Inc is a firm that specializes in this business. Electrostat has a stock price of $25 per share with 16 million shares outstanding. Electrostat's equity beta is 1.18. It also has $220 million in debt outstanding with a debt beta of 0.08. Your estimate of the asset beta for electrostatic power generators is closest to: A) 0.76 B) 0.79 C) 0.93 D) 1.10 Answer: B Explanation: B) β U =

β E +

β D =

× 1.18 +

0.789677 Diff: 2 Section: 12.5 A Project's Cost of Capital Skill: Analytical


× 0.08 =

13) Your firm is planning to invest in a new electrostatic power generation system. Electrostat Inc is a firm that specializes in this business. Electrostat has a stock price of $25 per share with 16 million shares outstanding. Electrostat's equity beta is 1.18. It also has $220 million in debt outstanding with a debt beta of 0.08. If the risk-free rate is 3%, and the market risk premium is 6%, then your estimate of your cost of capital for electrostatic power generators is closest to: A) 7.50% B) 7.75% C) 9.50% D) 10.10% Answer: B Explanation: D) β U =

β E +

β D =

× 1.18 +

× 0.08 =

0.789677 r i = r rf + β (r m - r rf ) = .03 + .789677(.06) = .07738 or 7.74% Diff: 3 Section: 12.5 A Project's Cost of Capital Skill: Analytical 14) The firm's unlevered (asset) beta is: A) the weighted average of the equity beta and the debt beta. B) the weighted average of the levered beta and the equity beta. C) the debt beta minus the equity beta. D) the unlevered beta minus the cost of capital. Answer: A Diff: 1 Section: 12.5 A Project's Cost of Capital Skill: Definition 15) The firm's unlevered (asset) cost of capital is: A) the weighted average of the equity cost of capital and the debt cost of capital. B) the weighted average of the levered cost of capital and the equity cost of capital. C) the debt cost of capital minus the equity cost of capital. D) the unlevered beta minus the cost of capital. Answer: A Diff: 1 Section: 12.5 A Project's Cost of Capital Skill: Definition


Project Risk Characteristics and Financing


Division Oil Exploration Oil Refining Gas & Convenience Stores

Asset Beta 1.4 1.1 0.8

Next Period's Expected Free Cash Flow ($mm) 450 525 600

The risk-free rate of interest is 3% and the market risk premium is 5%. 1) The cost of capital for the oil exploration division is closest to: A) 6.0% B) 7.0% C) 8.5% D) 10.0% Answer: D Explanation: D) r i = r rf + β (r m - r rf ) = .03 + 1.4(.05) = .10 or 10.0% Diff: 1 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical 2) The cost of capital for the oil refining division is closest to: A) 6.5% B) 7.0% C) 8.5% D) 10.0% Answer: C Explanation: C) r i = r rf + β (r m - r rf ) = .03 + 1.1(.05) = .085 or 8.5% Diff: 1 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical 3) The value of the oil exploration division is closest to: A) $4,500 B) $7,500 C) $8,750 D) $10,000 Answer: B Explanation: B) r i = r rf + β (r m - r rf ) = .03 + 1.4(.05) = .10 or 10.0% V=

=

= $7,500

Diff: 2 Section: 12.6 Project Risk Characteristics and Financing 16 Copyright © 2014 Pearson Education, Inc.

Expected Growth Rate 4.0% 2.5% 3.0%

Skill: Analytical 4) The value of the gas and convenience store division is closest to: A) $4,500 B) $6,000 C) $8,600 D) $15,000 Answer: D Explanation: D) r i = r rf + β (r m - r rf ) = .03 + 0.8(.05) = .07 or 7.0% V=

=

= $15,000

Diff: 2 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical 5) The overall value of Wyatt Oil (in $ millions) is closest to: A) $25,000 B) $18,846 C) $31,250 D) $15,000 Answer: C Explanation: C) Oil Exploration Division: r i = r rf + β (r m - r rf ) = .03 + 1.4(.05) = .10 or 10.0% V=

=

= $7,500

Oil Refining: r i = r rf + β (r m - r rf ) = .03 + 1.1(.05) = .085 or 8.5% V=

=

= $8,750

Convenience Store; r i = r rf + β (r m - r rf ) = .03 + 0.8(.05) = .07 or 7.0% V=

=

= $15,000

Total Value = 7,500 + 8,750 + 15,000 = $31,250 Diff: 3 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical


6) The overall asset beta for Wyatt Oil is closest to: A) 0.95 B) 1.05 C) 1.15 D) 1.25 Answer: B Explanation: B) Oil Exploration Division: r i = r rf + β (r m - r rf ) = .03 + 1.4(.05) = .10 or 10.0% V=

=

= $7,500


=

= $8,750

Convenience Store: r i = r rf + β (r m - r rf ) = .03 + 0.8(.05) = .07 or 7.0% V=

=

= $15,000

Total Value = 7,500 + 8,750 + 15,000 = $31,250 β WO = wOE β OE+ wOR β OR + wCS β CS

=

(1.4) +

(1.1) +

(0.8) = 1.028

Diff: 3 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical 7) The overall cost of capital for Wyatt Oil is closest to: A) 8.1% B) 8.5% C) 8.8% D) 9.3% Answer: A Explanation: A) Oil Exploration Division: r i = r rf + β (r m - r rf ) = .03 + 1.4(.05) = .10 or 10.0% V=

=

= $7,500


=

= $8,750

Convenience Store: r i = r rf + β (r m - r rf ) = .03 + 0.8(.05) = .07 or 7.0% V=

=

= $15,000

Total Value = 7,500 + 8,750 + 15,000 = $31,250 18 Copyright © 2014 Pearson Education, Inc.

r WO = wOE r OE+ wOR r OR + wCS r CS =

(.10) +

(.085) +

(.07) = .0814

Diff: 3 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical


Luther Industries has 25 million shares outstanding trading at $18 per share. In addition, Luther has $150 million in outstanding debt. Suppose Luther's equity cost of capital is 13%, its debt cost of capital is 7%, and the corporate tax rate is 40%.

15) Luther's after-tax debt cost of capital is closest to: A) 4.2% B) 5.4% C) 7.0% D) 9.8% Answer: A Explanation: A) Effective after-tax interest rate = r(1 - Tc) = .07(1 - .40) = .042 or 4.2% Diff: 1 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical 16) Luther's weighted average cost of capital is closest to: A) 9.8% B) 10.8% C) 11.5% D) 13.0% Answer: B Explanation: B) r U = =

r E + (13%) +

(1 - Tc) (7%)(1 - .4) = 10.8%

Diff: 1 Section: 12.6 Project Risk Characteristics and Financing Skill: Analytical


Problem Set_ Cost of Capital

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