Parte 2 Segundo Parcial

©2012, The McGraw-Hill Companies

Chapter 13

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Inputs are in BlueAnswers are in Red


Quiz 1

Micro Spinoffs, Inc., issued 20-year debt a year ago at par value with a couponrate of 8%, paid annually. Today, the debt is selling at $1,050. If the firm’s tax bracket is 35%,what is its after-tax cost of debt?

Time 20 yearsCoupon rate 8%Sales cost of debt $1,050.00 Tax bracket 35%

Solution:

Using a financial calculator:Interest rate on debt = 7.50%

After-tax cost of debt = 4.88%


Quiz 2

Micro Spinoffs has preferred stock outstanding. The stock pays a dividend of $4 per share, and the stock sells for $40. What is the cost of preferred stock?

Dividend $ 4.00 Stock price $ 40.00

Solution:

Cost of preferred stock = 10%


Quiz 3

Micro Spinoffs, Inc., issued 20-year debt a year ago at par value with a coupon rate of 8%, paid annually. Today, the debt is selling at $1,050. The firm’s tax bracket is 35%. Micro Spinoffs also has preferred stock outstanding. The stock pays a dividend of $4 per share,and the stock sells for $40. Suppose Micro Spinoffs’ cost of equity is 12%. What is its WACC if equity is 50%, preferred stock is 20%, and debt is 30% of total capital?

Time 20.00 yearsCoupon rate 8%Sales cost of debt $1,050.00 Tax bracket 35%Dividend $ 4.00 Stock price $ 40.00 Cost of equity 12%Equity 50%Preferred stock 20%Debt 30%

Solution:

After-tax cost of debt = 4.88%Cost of preferred stock = 10.00%Cost of equity = 12.00%

WACC = 9.46%

WACC=[DV ×rdebt×(1−TC )]+[ PV ×rpreferred ]+[ EV ×requity ]


Quiz 4

Reliable Electric is a regulated public utility, and it is expected to provide steady growth of dividends of 5% per year for the indefinite future. Its last dividend was $5 per share; the stock sold for $60 per share just after the dividend was paid. What is the company’s cost of equity?

Growth of dividends 5%Last dividend 5.00Stock price 60.00

Solution:

Cost of Equity = 13.75%


Quiz 5

Reactive Industries has the following capital structure. Its corporate tax rate is 35%. What is its WACC?

Security Market Value Required Rate of ReturnDebt $20 million 6%Preferred stock 10 million 8%Common stock 50 million 12%

Tax rate 35%

Solution:

Firm value = $80.00 million

WeightsDebt: = 25.00%Preferred: = 12.50%Common: = 62.50%

WACC = 9.475%

WACC=[DV ×rdebt×(1−TC )]+[ PV ×rpreferred ]+[ EV ×requity]


Quiz 6

Geothermal’s WACC is 11.4%. Executive Fruit’s WACC is 12.3%. NowExecutive Fruit is considering an investment in geothermal power production. Should it discount project cash flows at 12.3%? Why or why not?

Geothermal’s WACC 11.40%Executive Fruit’s WACC 12.30%

Solution:

The proper discount rate to discount the project cash flows is 11.40% .

Executive Fruit should use the WACC of Geothermal, not its own WACC, when evaluating an investment in geothermal power production. The risk of the project determines the discount rate, and in this case Geothermal’s WACC is more reflective of the risk of the project in question.


Quiz 7

Icarus Airlines is proposing to go public, and you have been given the task of estimating the value of its equity. Management plans to maintain debt at 30% of the company’s present value, and you believe that at this capital structure the company’s debtholders will demand a return of 6% and stockholders will require 11%. The company is forecasting that next year’s operating cash flow (depreciation plus profit after tax at 40%) will be $68 million and that investment expenditures will be $30 million. Thereafter, operating cash flows and investment expenditures are forecast to grow by 4% a year.

a. What is the total value of Icarus?

b. What is the value of the company’s equity?

Debt ratio 30%Debt cost 6%Equity cost 11%Tax rate 40%Operating cash flow $ 68.00 millionInvestment expenditures $ 30.00 millionGrowth rate 4%

Solution:

a.

WACC = 8.78%Total value of Icarus = $ 795.00 million

b. Value of Equity = $ 556.50 million

WACC=[DV ×rdebt×(1−TC )]+[ EV ×requity]


Practice Problem 8

The common stock of Buildwell Conservation & Construction, Inc., has a beta of .90.The Treasury bill rate is 4%, and the market risk premium is estimated at 8%. BCCI’s capitalstructure is 30% debt, paying a 5% interest rate, and 70% equity. What is BCCI’s cost of equitycapital? Its WACC? Buildwell pays tax at 40%.

Beta 0.90 Treasury bill rate 4%Market risk premium 8%Debt 30%Interest rate 5%Equity 70%Tax rate 40%

Solution:

Cost of equity capital = 11.20%

WACC = 8.74%



Practice Problem 9

The common stock of Buildwell Conservation & Construction, Inc., has a beta of .90.The Treasury bill rate is 4%, and the market risk premium is estimated at 8%. BCCI’s capitalstructure is 30% debt, paying a 5% interest rate, and 70% equity. Buildwell pays tax at 40%.

BCCI is evaluating a project with an internal rate of return of 12%. Should it accept the project?If the project will generate a cash flow of $100,000 a year for 8 years, what is the most BCCI should be willing to pay to initiate the project?

Beta 0.90 Treasury bill rate 4%Market risk premium 8%Debt 30%Interest rate 5%Equity 70%Tax 40%Internal rate 12%Cash flow 100,000.00Time 8.00 years

Solution:

Cost of equity capital = 11.20%

WACC = 8.74%

Present value cash flows = $558,870.94



Practice Problem 10

The common stock of Buildwell Conservation & Construction, Inc., has a beta of .90.The Treasury bill rate is 4%, and the market risk premium is estimated at 8%. BCCI’s capitalstructure is 30% debt, paying a 5% interest rate, and 70% equity. What is BCCI’s cost of equitycapital? Its WACC? Buildwell pays tax at 40%.

You need to estimate the value of Buildwell Conservation. You have the following forecasts (in millions of dollars) of Buildwell’s profits and of its future investments in new plant and working capital:

Year1 2 3 4…

Earnings before interest, taxes, depreciation,and amortization (EBITDA) 80 100 115 120Depreciation 20 30 35 40Pretax profit 60 70 80 80Investment 12 15 18 20

From year 5 onward, EBITDA, depreciation, and investment are expected to remain unchangedat year-4 levels. Estimate the company’s total value and the separate values of its debt andequity.

Beta 0.90 Treasury bill rate 4%Market risk premium 8%Debt 30%Interest Rate 5%Equity 70%Tax 40%

Solution:

Year1 2 3 4

3. EBITDA 80 100 115 1204. Depreciation 20 30 35 405. Profit before tax = 3 – 4 60 70 80 806. Tax at 40% 24 28 32 327. Profit after tax = 5 – 6 36 42 48 488. Operating cash flow = 4 + 7 56 72 83 889. Investment 12 15 18 2010. Free cash flow = 8 – 9 44 57 65 68

WACC 8.74%Horizon value at year 4 is: $778.03 million

The company’s total value is: $744.33 million

Value of the firm’s debt $223.30 million

Value of the firm’s equity $521.03 million


From year 5 onward, EBITDA, depreciation, and investment are expected to remain unchanged


Practice Problem 11

Find the WACC of William Tell Computers. The total book value of the firm’s equity is $10 million; book value per share is $20. The stock sells for a price of $30 per share, and the cost of equity is 15%. The firm’s bonds have a face value of $5 million and sell at a price of 110% of face value. The yield to maturity on the bonds is 9%, and the firm’s tax rate is 40%.

Book value firm’s equity $ 10.00 millionBook value per share $ 20.00 Stock sells for a price of $ 30.00 Cost of equity 15%Bonds total face value $ 5.00 millionSelling price of bond 110%Yield to maturity of bonds 9%Firm’s tax rate 40%Bonds face value $1,000.00

Solution:

Security Market Value

Debt $5.50 millionEquity 15.00 millionTotal $20.50

WACC = 12.42%

WACC=[DV ×rdebt×(1−TC )]+[ EV ×requity ]


Practice Problem 12

Nodebt, Inc., is a firm with all-equity financing. Its equity beta is .80. The Treasury bill rate is 4%, and the market risk premium is expected to be 10%. What is Nodebt’s asset beta?What is Nodebt’s weighted-average cost of capital? The firm is exempt from paying taxes.

Beta 0.80 Treasury bill rate 4%Market risk premium 10%

Solution:

Since the firm is all-equity financed, asset beta = equity beta = 0.80

The WACC is the same as the cost of equity, which can be calculated using the CAPM:

= 12%requity

requity= rf +β (rm - r f )


Practice Problem 14

Bunkhouse Electronics is a recently incorporated firm that makes electronic entertainment systems. Its earnings and dividends have been growing at a rate of 30%, and the current dividend yield is 2%. Its beta is 1.2, the market risk premium is 8%, and the risk-free rate is 4%.

Growth Rate 30%Current dividend yield 2%Beta 1.20 Market risk premium 8%Risk-free rate 4%

a. Calculate two estimates of the firm’s cost of equity.

b. Which estimate seems more reasonable to you? Why?

Solution:

a. Using the recent growth rate of 30% and the dividend yield of 2%, one estimate would be: 32%

Another estimate, based on the CAPM, would be:

= 13.6%

b. The estimate of 32% seems far less reasonable. It is based on a historic growth rate

per share must be viewed as highly stable over the foreseeable future. In other words, it requires the use of the sustainable growth rate.

requity

that is impossible to sustain. The DIV1/P0 + g rule requires that the growth rate of dividends



Practice Problem 15

Olympic Sports has two issues of debt outstanding. One is a 9% coupon bond with a face value of $20 million, a maturity of 10 years, and a yield to maturity of 10%. The coupons are paid annually. The other bond issue has a maturity of 15 years, with coupons also paid annually, anda coupon rate of 10%. The face value of the issue is $25 million, and the issue sells for 94% of par value. The firm’s tax rate is 35%.

Bond 1:Coupon Rate 9%Total face Value 20 millionMaturity 10.00 yearsYield to maturity 10%

Bond 2:Coupon Rate 10%Total face Value 25 millionMaturity 15.00 yearsIssue sells for 94%Tax rate 35%Face Value 1,000.00

a. What is the before-tax cost of debt for Olympic?

b. What is Olympic’s after-tax cost of debt?

Solution:

a. The 9% coupon bond has a yield to maturity of 10% and sells for 93.86% of face value, as shown below:Present Value $938.55 or 93.86%Therefore, the market value of the issue $18.77 million.

The 10% coupon bond sells for 94% of par value and has a yield to maturity of: 10.83%

The market value of the issue is $23.50 million.Weighted-average before-tax cost of d = 10.46%

b. After-tax cost of debt = 6.80%


Practice Problem 16

Examine the following book-value balance sheet for University Products, Inc. What is the capitalstructure of the firm on the basis of market values? The preferred stock currently sells for $15 per share

BOOK VALUE BALANCE SHEET(all values in millions)

Assets Liabilities and Net Worth

Cash and short-term securities $ 1.00 Bonds, coupon = 8%, paid annually(maturity = 10 years, current yieldto maturity = 9%) $ 10.00

Accounts receivable 3.00 Preferred stock (par value $20 pershare) 2.00

Inventories 7.00 Common stock (par value $.10) 0.10 Plant and equipment 21.00 Additional paid-in stockholders’

equity 9.90 Retained earnings 10.00

Total $ 32.00 Total $ 32.00

Preferred stock current price $ 15.00 Common stock current price $ 20.00 Bond Coupon 8%Bond par value $1,000.00 Maturity 10.00 yearsCurrent yield to maturity 9%Preferred stock par value $ 20.00 Common stock par value $ 0.10 Common shares outstanding 1.00 million

Solution:

Capital structure :

Security PercentBonds $ 9.36 30.3%Preferred Stock 1.50 4.9%Common Stock 20.00 64.8%Total $ 30.86 100.0%

and the common stock for $20 per share. There are 1 million common shares outstanding.

Market Value(in millions)


Practice Problem 17

Examine the following book-value balance sheet for University Products, Inc. The preferred stock currently sells for $15 per share and the common stock for $20 per share. There are 1 million common shares outstanding.

If the preferred stock pays a dividend of $2 per share, the beta of the common stock is .8, the market risk premium is 10%, the risk-free rate is 6%, and the firm’s tax rate is 40%, whatis University’s weighted-average cost of capital?


Assets Liabilities and Net Worth

Cash and short-term securities $ 1.00 Bonds, coupon = 8%, paid annually(maturity = 10 years, current yieldto maturity = 9%)

Accounts receivable 3.00 Preferred stock (par value $20 pershare)

Inventories 7.00 Common stock (par value $.10)Plant and equipment 21.00 Additional paid-in stockholders’

equityRetained earnings

Total $ 32.00 Total

Preferred stock current price $ 15.00 Common stock current price $ 20.00 Bond Coupon 8%Bond par value $1,000.00 Maturity 10.00 yearsCurrent yield to maturity 9%Preferred stock par value $ 20.00 Common stock par value $ 0.10 Common shares outstanding 1.00 millionPreferred stock dividend $ 2.00 Common stock beta 0.80 Market risk premium 10%Risk-free rate 6%Tax Rate 40%

Solution:

Capital structure :

SecurityBonds $ 9.36 30.3% DeudaPreferred Stock 1.50 4.9%Common Stock 20.00 64.8%Total $ 30.86 100.0%

Para el WACC siempre utilizaremos el valor del mercado


% de deuda

bancaria


WACC = 11.36%

Checar ya que el resultado boto un 11.68%



Examine the following book-value balance sheet for University Products, Inc. The preferred stock


$ 10.00

2.00 0.10

9.90 10.00 $ 32.00

9%13.30%14.50%

Costo obligacion


Practice Problem 18

Following is the book-value balance sheet for University Products, Inc. The preferred stock currently sells for $15 per share and the common stock for $20 per share. There are 1 million common shares outstanding. Preferred stock pays a dividend of $2 per share, the beta of the common stock is.8, the market risk premium is 10%, the risk-free rate is 6%, and the firm’s tax rate is 40%.

University Products is evaluating a new venture into home computer systems. The internal rate of return on the new venture is estimated at 13.4%. WACCs of firms in the personal computer industry tend to average around 14%. Should the new project be pursued? Will University Products make the correct decision if it discounts cash flows on the proposed venture at the firm’s WACC?

BOOK VALUE BALANCE SHEET

(all values in millions)Assets Liabilities and Net Worth

Cash and short-term securities $ 1.00 Bonds, coupon = 8%, paid annually(maturity = 10 years, current yieldto maturity = 9%) $ 10.00

Accounts receivable 3.00 Preferred stock (par value $20 pershare) 2.00

Inventories 7.00 Common stock (par value $.10) 0.10 Plant and equipment 21.00 Additional paid-in stockholders’

equity 9.90 Retained earnings 10.00

Total $ 32.00 Total $ 32.00

Preferred stock current price $ 15.00 Common stock current price $ 20.00 Bond Coupon 8%Bond par value $1,000.00 Maturity 10.00 yearsCurrent yield to maturity 9%Preferred stock par value $ 20.00 Common stock par value $ 0.10 Common shares outstanding 1.00 millionPreferred stock dividend $ 2.00 Common stock beta 0.80 Market risk premium 10%Risk-free rate 6%Tax Rate 40%IRR on new venture 13.4%WACC (industry average) 14%


Solution:

Capital structure :

Security PercentBonds $ 9.36 30.3%Preferred Stock 1.50 4.9%Common Stock 20.00 64.8%Total $ 30.86 100.0%

WACC = 11.36%

The IRR on the computer project is less than the WACC of firms in the computer industry. Therefore, the project should be rejected. However, the WACC of the firm (based on its existing mix of projects) is only 11.36% . If the firm uses this figure as the hurdle rate, it will incorrectly go ahead with the venture in home computers.




Practice Problem 19

The total market value of Okefenokee Real Estate Company is $6 million, and the total value of its debt is $4 million. The treasurer estimates that the beta of the stock currently is 1.2 and that the expected risk premium on the market is 10%. The Treasury bill rate is 4%.

a. What is the required rate of return on Okefenokee stock?

b. What is the beta of the company’s existing portfolio of assets? The debt is perceived to bevirtually risk-free.

c. Estimate the weighted-average cost of capital assuming a tax rate of 40%.

d. Estimate the discount rate for an expansion of the company’s present business.

e. Suppose the company wants to diversify into the manufacture of rose-colored glasses. Thebeta of optical manufacturers with no debt outstanding is 1.4. What is the required rate ofreturn on Okefenokee’s new venture? (You should assume that the risky project will notenable the firm to issue any additional debt.)

Total market value $ 6.00 millionTotal value of debt $ 4.00 millionBeta 1.20 Expected risk premium 10%Treasury bill rate 4%Tax Rate 40%Beta (e) 1.40

Solution:

a.

Required rate of return = 16%

b. Weighted-average beta = 0.72

c.

WACC = 10.56%

d. If the company plans to expand its present business, then the WACC is a reasonable estimate of the discount rate since the risk of the proposed project is similar to the risk of the existing projects. Use a discount rate of 10.56%

e. The WACC of optical projects should be based on the risk of those projects. Using a beta of 1.4, the discount rate for the new venture is: 18.00%




Practice Problem 20

With a tax rate of 35%, Big Oil had a WAAC of 10.5%. Suppose Big Oil is excused from paying taxes. How would its WACC change? Now suppose Big Oil makes a large stock issue and uses the proceeds to pay off all its debt. How would the cost of equity change?

Common stock beta 0.85 Risk-free interest rate 6%Debt Value 385.70Common stock 1,200.00 Debt interest rates 9%Cost of equity 12%

Solution:

New WACC = 11.27%

If Big Oil issues new equity and uses the proceeds to pay off all of its debt, the cost of equity will decrease. There is no longer any leverage, so the equity becomes safer and therefore commands a lower risk premium. In fact, with all-equity financing, the cost of equity would be the same as the firm’s WACC, which is 11.27%. This is less than the previous value of 12.0%. (We use the WACC derived in the absence of interest tax shields since, for the all-equity firm, there is no interest tax shield.)



Practice Problem 21

With a tax rate of 35%, Big Oil had a WAAC of 10.5%. Suppose Big Oil is excused from paying taxes.

TABLE 13.3

Security Type Capital Structure Required Rate of Return

Debt D = 385.7 D/V 0.243 9%

Common stock E = 1,200.00 E/V 0.757 12%Total V = 1,585.70

Suppose Big Oil starts from the financing mix in Table 13.3, and then borrows an additional $200 million from the bank. It then pays out a special $200 million dividend, leaving its assets and operations unchanged. What happens to Big Oil’s WACC, still assuming it pays no taxes? What happens to the cost of equity?

Common stock beta 0.85 Risk-free interest rate 6%Debt Value 385.70Common stock 1,200.00 Debt interest rates 9%Cost of equity 12%Borrowed 200.00 millionSpecial Dividend 200.00 million

Solution:

The net effect of Big Oil’s transaction is to leave the firm with $200 million moredebt (because of the borrowing) and $200 million less equity (because of the dividend payout). Total assets and business risk are unaffected. The WACC willremain unchanged because business risk is unchanged. However, the cost of equity will increase. With the now-higher leverage, the business risk is spread over a smaller equity base, so each share is now riskier.

New WACC = 11.27%

= 12.60%

rdebt

requity

We solve to find that requity


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Parte 2 Segundo Parcial