Problem Set_ Cost of Capital

5/26/2018 Problem Set_ Cost of Capital

1/19

1Copyright 2014 Pearson Education, Inc.

The Cost of Capital

The Equity Cost of Capital

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

Beta Volatility

"Eenie" 0.45 20%

"Meenie" 0.75 18%

"Miney" 1.05 35%

"Moe" 1.20 25%

Assume that the risk-free rate of interest is 3% and you estimate the market's expected return tobe 9%.

1) Which firm has the most total risk?A) EenieB) MeenieC) MineyD) MoeAnswer: CExplanation: C) Total risk is measured using volatility and Miney has the highest volatility,hence the most total risk.Diff: 1Section: 12.1 The Equity Cost of CapitalSkill: Analytical

2) Which firm has the least market risk?A) EenieB) MeenieC) MineyD) MoeAnswer: AExplanation: A) Market risk is measured using beta and Eenie has the lowest beta, hence thelowest market risk.Diff: 1Section: 12.1 The Equity Cost of Capital

Skill: Analytical


2/19


3) Which firm has the highest cost of equity capital?A) EenieB) MeenieC) MineyD) Moe

Answer: DExplanation: 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: 1Section: 12.1 The Equity Cost of CapitalSkill: 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: CExplanation: C) rMiney= 3% + 1.05(9% - 3%) = 9.3%

Diff: 1Section: 12.1 The Equity Cost of CapitalSkill: 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: BExplanation: B) rMeenie= 3% + 0.75(9% - 3%) = 7.5%


6) The risk premium for "Meenie" is closest to:A) 4.50%B) 7.50%C) 9.30%

D) 9.75%Answer: AExplanation: A) risk premiumMeenie= 0.75(9% - 3%) = 4.5%



3/19


Beta Estimation


YearRisk-freeReturn

MarketReturn

Wyatt OilReturn

Market

ExcessReturn

Wyatt Oil

ExcessReturn Beta

2007 3.0% 6.0% 5.5% 3.0% 2.5% 0.833

2008 1.5% -38.5% -32.6% .40% -34.1% 0.853

2009 1.0% 22.5% 19.6% 21.5% 18.6% 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) raverage=

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

Market

Excess

Return

Wyatt Oil

Excess

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%

Diff: 1

Section: 12.3 Beta EstimationSkill: Analytical


4/19


2) The Market's average historical return is closest to:A) -2.50%B) -3.33%C) -4.33%D) -5.17%

Answer: BExplanation: B) raverage=

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

Market

Excess

Return

Wyatt Oil

Excess

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%

Diff: 1


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=

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

MarketExcess

Return

Wyatt OilExcess

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%

Diff: 2Section: 12.3 Beta EstimationSkill: Analytical


5/19


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

Answer: DExplanation: D) excess returnaverage=

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

Market

Excess

Return

Wyatt

Oil

Excess

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%


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

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

Market

Excess

Return

Wyatt

Oil

Excess

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%



6/19


6) The Market's excess return for 2008 is closest to:A) -40.0%B) -38.5%C) -37.0%D) -34.1%

Answer: AExplanation: A) excess returne= (rWO- rrf)2009

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

Market

Excess

Return

Wyatt Oil

Excess

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%

Diff: 1


7) Using just the return data for 2009, your estimate of Wyatt Oil's Beta is closest to:A) 0.84B) 0.87C) 1.00D) 1.16Answer: BExplanation: B)

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

MarketExcess

Return

Wyatt OilExcess

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%

WO = = = .8651


8) Using just the return data for 2008, your estimate of Wyatt Oil's Beta is closest to:A) 0.85B) 0.87C) 1.00D) 1.17Answer: A


7/19


Explanation: A)

Year

Risk-free

Return

Market

Return

Wyatt Oil

Return

Market

Excess

Return

Wyatt Oil

Excess

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%

WO = - = .8525


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 returnsversus the market excess return.D) The statistical technique that identifies the bets-fitting line through a set of points is calledlinear regression.Answer: ADiff: 2Section: 12.3 Beta EstimationSkill: Conceptual

The Debt Cost of Capital


Consider the following information regarding corporate bonds:

Rating AAA AA A BBB BB B CCC

Average Default Rate 0.0% 0.1% 0.2% 0.5% 2.2% 5.5% 12.2%

Recession Default Rate 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 48.0%

Average Beta 0.05 0.05 0.05 0.10 0.17 0.26 0.31

1) Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of7.0%, and a BBB rating. The corresponding risk-free rate is 3% and the market risk premium is5%. 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


8/19


Explanation: B) rd= rrf+ (rm- rrf) = 3% + 0.1(5%) = 3.5%

Diff: 1Section: 12.4 The Debt Cost of CapitalSkill: Analytical

2) Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of7.0%, 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: DExplanation: D) rd= ytm - prob(default) loss rate = 7% - 0.4%(70%) = 6.72%

Diff: 2Section: 12.4 The Debt Cost of Capital

Skill: Analytical


9/19


3) Wyatt Oil has a bond issue outstanding with seven years to maturity, a yield to maturity of7.0%, 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: BExplanation: B) rd= ytm - prob(default) loss rate = 7% - 3.0%(70%) = 4.9%


4) Rearden Metal has a bond issue outstanding with ten years to maturity, a yield to maturity of8.6%, 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: CExplanation: C) rd= rrf+ (rm- rrf) = 3% + 0.26(6%) = 4.56%


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: DExplanation: D) rd= ytm - prob(default) loss rate = 8.6% - 5.2%(50%) = 6.00%



10/19


6) Rearden Metal has a bond issue outstanding with ten years to maturity, a yield to maturity of8.6%, 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 isclosest to:A) 0.6%

B) 1.6%C) 4.6%D) 6.0%Answer: AExplanation: A) rd= ytm - prob(default) loss rate = 8.6% - 16.0%(50%) = 0.6%


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 yieldthat 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: CExplanation: C) For AAA rd= rrf+ (rm- rrf) = rrf+ 0.05(5%) = 3.5% rrf= 3.25%

For BBB rd= rrf+ (rm- rrf) = 3.25% + 0.10(5%) = 3.75%

rd= ytm -prob(default) loss rate 3.75% = ytm - 0.4%(60%) ytm = 3.99%

Diff: 3

Section: 12.4 The Debt Cost of CapitalSkill: 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 riskpremium is 5% and the expected loss rate in the event of default on the bonds is 60%. The yieldthat 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: DExplanation: D) For AAA rd= rrf+ (rm- rrf) = rrf+ 0.05(5%) = 3.5% rrf= 3.25%

For BBB rd= rrf+ (rm- rrf) = 3.25% + 0.10(5%) = 3.75%

rd= ytm -prob(default) loss rate 3.75% = ytm - 3.0%(60%) ytm = 5.55%



11/19


A Project's Cost of Capital


Consider the following information regarding corporate bonds:

Rating AAA AA A BBB BB B CCC

Average Default Rate 0.0% 0.1% 0.2% 0.45% 2.2% 5.5% 12.2%

Recession Default Rate 0.0% 1.0% 3.0% 3.0% 8.0% 16.0% 48.0%

Average Beta 0.05 0.05 0.05 0.10 0.17 0.26 0.31

Company

Market

Capitalization

($mm)

Total

Enterprise

Value ($mm)

Equity

Beta

Debt

Rating

Taggart Transcontinental $4,500 8,000 1.1 BBB

Rearden Metal $3,800 7,200 1.3 AAA

Wyatt Oil $2,400 3,800 0.9 ANielson Motors $1,500 4,400 1.75 BB

1) Your estimate of the debt beta for Taggart Transcontinental would be:A) 0.05B) 0.10C) 0.17D) 1.00Answer: BExplanation: B) Since Taggart has a rating of BBB, the appropriate debt beta from the table is0.10.

Diff: 1Section: 12.5 A Project's Cost of CapitalSkill: Analytical

2) Your estimate of the debt beta for Nielson Motors would be:A) 0.10B) 0.17C) 1.00D) 1.68Answer: BExplanation: B) Since Nielson has a rating of BB, the appropriate debt beta from the table is

0.17.Diff: 1Section: 12.5 A Project's Cost of CapitalSkill: Analytical


12/19


3) Your estimate of the asset beta for Taggart Transcontinental is closest to:A) 0.42B) 0.59C) 0.66D) 0.71

Answer: CExplanation: C) Since Taggart has a rating of BBB, the appropriate debt beta from the table is0.10.

U= E+ D= 1.1 + 0.10 = 0.6625


4) Your estimate of the asset beta for Rearden Metal is closest to:A) 0.42

B) 0.59C) 0.66D) 0.71Answer: DExplanation: D) Since Rearden has a rating of AAA, the appropriate debt beta from the table is0.05.

U= E+ D= 1.3 + 0.05 = 0.709722


5) Your estimate of the asset beta for Wyatt Oil is closest to:A) 0.59B) 0.66C) 0.71D) 0.90

Answer: AExplanation: A) Since Wyatt has a rating of A, the appropriate debt beta from the table is 0.05.

U= E+ D= 0.9 + 0.05 = 0.586842



13/19


6) Your estimate of the asset beta for Nielson Motors is closest to:A) 0.59B) 0.66C) 0.71D) 1.75

Answer: CExplanation: C) Since Nielson has a rating of BB, the appropriate debt beta from the table is0.17.

U= E+ D= 1.75 + 0.17 = 0.708636


7) Suppose that because of the large need for steel in building railroad infrastructure, TaggartTranscontinental and Rearden Metal decide to form into one large conglomerate. Your estimate

of the asset beta for this new conglomerate is closest to:A) 0.42B) 0.59C) 0.66D) 0.68Answer: DExplanation: D) Since Taggart has a rating of BBB, the appropriate debt beta from the table is0.10.

U= E+ D= 1.1 + 0.10 = 0.6625

Since Rearden has a rating of AAA, the appropriate debt beta from the table is 0.05.

U= E+ D= 1.3 + 0.05 = 0.709722

= WTT + WRM

= (0.6625) + (0.709722) = 0.684868



14/19


11) Your firm is planning to invest in a new power generation system. Galt Industries is an allequity firm that specializes in this business. Suppose Galt's equity beta is 0.75, the risk-free rateis 3%, and the market risk premium is 6%. If your firm's project is all equity financed, then yourestimate of your cost of capital is closest to:

A) 5.25%B) 6.00%C) 6.75%D) 7.50%Answer: DExplanation: D) ri= rrf+ (rm- rrf) = .03 + .75(.06) = .075 or 7.5%


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 with16 million shares outstanding. Electrostat's equity beta is 1.18. It also has $220 million in debtoutstanding with a debt beta of 0.08. Your estimate of the asset beta for electrostatic powergenerators is closest to:A) 0.76B) 0.79C) 0.93D) 1.10Answer: B

Explanation: B) U= E+ D= 1.18 + 0.08 =

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


15/19


13) Your firm is planning to invest in a new electrostatic power generation system. ElectrostatInc is a firm that specializes in this business. Electrostat has a stock price of $25 per share with16 million shares outstanding. Electrostat's equity beta is 1.18. It also has $220 million in debtoutstanding with a debt beta of 0.08. If the risk-free rate is 3%, and the market risk premium is6%, 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) U= E+ D= 1.18 + 0.08 =

0.789677ri= rrf+ (rm- rrf) = .03 + .789677(.06) = .07738 or 7.74%

Diff: 3Section: 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: ADiff: 1Section: 12.5 A Project's Cost of CapitalSkill: 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: ADiff: 1Section: 12.5 A Project's Cost of CapitalSkill: Definition


16/19


Project Risk Characteristics and Financing


Division

Asset

Beta

Next Period's ExpectedFree Cash

Flow ($mm)

ExpectedGrowth

Rate

Oil Exploration 1.4 450 4.0%

Oil Refining 1.1 525 2.5%

Gas & Convenience Stores 0.8 600 3.0%

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: DExplanation: D) ri= rrf+ (rm- rrf) = .03 + 1.4(.05) = .10 or 10.0%

Diff: 1Section: 12.6 Project Risk Characteristics and FinancingSkill: 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: CExplanation: C) ri= rrf+ (rm- rrf) = .03 + 1.1(.05) = .085 or 8.5%


3) The value of the oil exploration division is closest to:A) $4,500

B) $7,500C) $8,750D) $10,000Answer: BExplanation: B) ri= rrf+ (rm- rrf) = .03 + 1.4(.05) = .10 or 10.0%

V = = = $7,500

Diff: 2Section: 12.6 Project Risk Characteristics and Financing


17/19


Skill: Analytical

4) The value of the gas and convenience store division is closest to:A) $4,500B) $6,000

C) $8,600D) $15,000Answer: DExplanation: D) ri= rrf+ (rm- rrf) = .03 + 0.8(.05) = .07 or 7.0%

V = = = $15,000


5) The overall value of Wyatt Oil (in $ millions) is closest to:

A) $25,000B) $18,846C) $31,250D) $15,000Answer: CExplanation: C) Oil Exploration Division:ri= rrf+ (rm- rrf) = .03 + 1.4(.05) = .10 or 10.0%

V = = = $7,500

Oil Refining:ri= rrf+ (rm- rrf) = .03 + 1.1(.05) = .085 or 8.5%

V = = = $8,750

Convenience Store;ri= rrf+ (rm- rrf) = .03 + 0.8(.05) = .07 or 7.0%

V = = = $15,000

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


18/19


6) The overall asset beta for Wyatt Oil is closest to:A) 0.95B) 1.05C) 1.15D) 1.25

Answer: BExplanation: B) Oil Exploration Division:ri= rrf+ (rm- rrf) = .03 + 1.4(.05) = .10 or 10.0%

V = = = $7,500


V = = = $8,750

Convenience Store:ri= rrf+ (rm- rrf) = .03 + 0.8(.05) = .07 or 7.0%

V = = = $15,000

Total Value = 7,500 + 8,750 + 15,000 = $31,250

WO= wOEOE+ wOROR+ wCSCS

= (1.4) + (1.1) + (0.8) = 1.028


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: AExplanation: A) Oil Exploration Division:ri= rrf+ (rm- rrf) = .03 + 1.4(.05) = .10 or 10.0%

V = = = $7,500


V = = = $8,750

Convenience Store:ri= rrf+ (rm- rrf) = .03 + 0.8(.05) = .07 or 7.0%

V = = = $15,000

Total Value = 7,500 + 8,750 + 15,000 = $31,250


19/19


rWO= wOErOE+ wORrOR+ wCSrCS

= (.10) + (.085) + (.07) = .0814

Diff: 3

Section: 12.6 Project Risk Characteristics and FinancingSkill: Analytical


Luther Industries has 25 million shares outstanding trading at $18 per share. In addition, Lutherhas $150 million in outstanding debt. Suppose Luther's equity cost of capital is 13%, its debt costof 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: AExplanation: A) Effective after-tax interest rate = r(1 - Tc) = .07(1 - .40) = .042 or 4.2%


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) rU= rE+ (1 - Tc)

= (13%) + (7%)(1 - .4) = 10.8%

Diff: 1

Section: 12.6 Project Risk Characteristics and FinancingSkill: Analytical

Documents

Problem Set_ Cost of Capital