Business Finance

Business FinanceBA303 ♦ Fall 2012Michael Dimond

Michael DimondSchool of Business Administration

Risk and the costs of capital

• When considering common equity, preferred equity and debt, the owners of these securities each bear a different level of risk. The higher the risk, the higher the rate of return will be.

• Usually, this is what you expect: Rf < Kd < Kpfd < Ke

and… inflation < Rf

• What does this tell you about the return demanded by each type of investor?

• What does that imply about the risk borne by each?• Real Rates, Risk Premium, etc.• Market efficiency (the EMH)


More about risk and return

• Risk is uncertainty. Not just success or failure, but to what extent will something be as expected?

• It may be necessary to consider scenarios and weigh them based on their likelihood. For example:• The experts in your company predict the following results and probabilities:

• What is the expected rate of return?• The weighted average is 8.35%

Scenario Return Probability

Very poor 0.75% 0.05

Poor 1.25% 0.15

Average 8.5% 0.60

Good 14.75% 0.15

Very good 16.25% 0.05

0.75 x 0.05 = 0.0375

1.25 x 0.15 = 0.1875

8.5 x 0.60 = 5.1000

14.75 x 0.15 = 2.2125

16.25 x 0.05 = 0.8125

sum = 8.3500



• Variation or volatility is another form of uncertainty.• What is standard deviation? What does it represent?



• How do the following assets compare to Stock X?

• When making a decision, which should you consider first?• Risk?

• Return?

• Which has the lowest potential return?• Which has the highest potential return?• Which has the most uncertainty?• What would be the Coefficient of Variation for each?

• CoV = Std Deviation ÷ Return

• What is Diversification?• Can all risk be diversified away?

Stock X Stock A Stock B Stock CExpected Return 12% 12% 10% 14%Std Deviation 5% 7% 8% 6%


Determining Kd with YTM

• Remember from valuing bonds that the “i” in the TVM relationship is the yield on a bond.

• Yield is the rate of return demanded by investors in debt.• To find the Cost of Debt (Kd), solve for the yield of a bond.• Remember: Costs of capital are forward-looking numbers. It

is what an investor will demand from future performance.• What does this mean for the cost of debt (Kd)?


Determining Ke with the Dividend Growth Model• Ke is the required rate of return for equity investors

“Cost of Equity”• We can derive this from the dividend discount model:

P0 = D1/(r-g)

:. (r-g) = D1/P0

:. r = D1/P0 + g • Since r is the required rate of return, Ke = D1/P0 + g

• How do you test the answer you get?

• What if you wanted to solve for the expected growth rate?

• There is another way to find the cost of equity: CAPM


Determining Ke with CAPM

• Ke is the required rate of return for equity investors

“Cost of Equity”• The CAPM (Capital Asset Pricing Model) is a formula used to

compute Ke

Ke = Rf + β(Rm – Rf)

or

Ke = Rf + β(MRP)• MRP is the Market Risk Premium

MRP = Rm – Rf

• Remember: Costs of capital are forward-looking numbers. It is what an investor will demand from future performance.• What does this mean for the cost of equity (Ke)?


About beta

• Beta (β) represents how well an asset’s return correlates with the return on the market• Correlation, not Causality

• Beta measures sensitivity to economic inputs

• Beta is the slope of the line showing the relationship of the data

• What is the difference between Systematic and Unsystematic risk?

• Can beta be zero? Can beta be negative?

Mkt Return A Return2003 16% 28%2004 13% 22%2005 7% 14%2006 14% 18%2007 12% 20%2008 -5% -2%2009 -9% 2%2010 -12% -8%2011 4% 9%2012 8% 13%


Can beta really be negative?

What does a negative beta imply about the stock

performance?

What does a negative beta imply about Ke?


Determining Kpfd with the Dividend Discount Model• The value of a perpetuity is how we price preferred equity:

PVperp = CF/r:. Price = Dividend/Kpfd

:. Price x Kpfd = Dividend:. Kpfd = Dividend / Price

• So… If XYZ Company has 8% preferred stock with a $20.00 par value which is selling for $28.00, what would be the Cost of Preferred Equity?• 8% x 20.00 = 1.60

• 1.60 / 28.00 = 0.0571 = 5.71%


Market Value vs Book Value

• Investors have an opinion about the value of a company. A stockholder believes the price of stock is appropriate value, and this is different than what the balance sheet shows for the value of equity.

• The balance sheet shows the book value. The market price determines the market value.• Example: Book Value

• Example: Market Value (“Market Cap” or Market Capitalization)

• P/B ratio


WACC

• Investors care about market value more than book value.• Costs of capital are used in making investing decisions.• :. If we wanted to know the overall cost of capital for a

company (the cost of equity and the cost of debt combined), we would use a weighted average of the percentages, and weight them based on the market values.

• The Weighted Average Cost of Capital is called the WACC.

WACC = we x Ke + wd x Kd (1-t)• If there is preferred stock, we just expand the formula:

WACC = wpfd x Kpfd + we x Ke + wd x Kd (1-t)


Weights of Equity & Debt

• The weight is the proportion of that type of capital compared with the total capital in the firm.

• What is the weight of each type of capital below?• Equity = E = $600MM

• Debt = D = $300MM

• Preferred Stock = Pfd = $100MM

• Total Capital = TC = 600+300+100 = 1,000• We = E/TC = 600/1,000 = 0.60• Wd = D/TC = 300/1,000 = 0.30• Wpfd = Pfd/TC = 100/1,000 = 0.10

• Note: the sum of the weights always equals 1.00


Determining the WACC

• You may need to compute the WACC from information presented like this:• ABC Company needs to know their WACC. They have $10MM in 8.5% bonds

payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125.

• What is the best approach to solving this problem?


Break a complicated problem into smaller pieces

• ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125.

• Find the market values• MVe = $27.50 x 1MM = $27.5MM

• MVd = 10MM ÷ 1,000 (assumed FV) x $1,125 = $11.25MM

• MVpfd = $125 x 10,000 = $1.25MM

• TC = $27.5MM + $11.25MM + $1.25MM = $40.0MM

• Find the weights & tax shield• We = 27.5 ÷ 40.0 = 0.6875

• Wd = 11.25 ÷ 40.0 = 0.2813

• Wpfd = 1.25 ÷ 40.0 = 0.0313

• (1-t) = (1 - 0.34) = 0.66


Break a complicated problem into smaller pieces

• ABC Company needs to know their WACC. They have $10MM in 8.5% bonds payable, which sell for $1,125, have semiannual payments and mature in ten years. Their tax rate is 34%. They have 1 million shares of stock which paid $1.80 in dividends last year. The dividends are expected to grow 7% per year forever and the stock currently sells for $27.50. They also have 10,000 shares of 9% preferred stock with a $100 par value which sells for $125.

• Find the different costs of capital• Kd : Solve for the yield

find i, where: n=10x2, PV=-1125, FV=1000, PMT=0.085x1000÷2 [i=3.3800]:. Kd = 2x3.38% = 6.76%

• Ke : Use the Dividend Discount Model or the CAPM (based on data available)Ke = r = D1/P0 + gKe = [(1.80 x 1.07) / 27.50] + 0.07 = 0.1400:. Ke = 14.00%

• Kpfd : Find the return on a non-growing perpetuityKpfd = r = D1/P0 = (0.09 x 100)/125 = 0.0720 :. Kpfd = 7.20%


• From there, put the pieces of the formula in place, then work through the formula in steps• WACC = wpfd x Kpfd + we x Ke + wd x Kd x (1-t)

• WACC = 0.0313 x 0.072 + 0.6875 x 0.14 + 0.2813 x 0.0676 x 0.66

• WACC = 0.0023 + 0.0963 + 0.2813 x 0.0446

• WACC = 0.0023 + 0.0963 + 0.0126

WACC = 0.1112 = 11.12%

• By parsing the problem, you avoid errors• Try another example:

• XYZ Company needs to know their WACC. They have $9.9MM in 8.25% bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25


0.0446 is the After-Tax

Cost of Debt


• Try another example:• XYZ Company needs to know their WACC. They have $9.9MM in 8.25%

bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25

• Market Values & Weights• MVe = $18,750,000 we = 0.7095

• MVpfd = $ 880,000 wpfd = 0.0217

• MVd = $10,890,000 wd = 0.2688

• TC = $40,520,000 1.0000

• Tax Shield = (1 – t) = (1 - 0.35) = 0.65



• Try another example:• XYZ Company needs to know their WACC. They have $9.9MM in 8.25%

bonds payable, which sell for $1,100, have semiannual payments and mature in twelve years. Their tax rate is 35%. They have 1 million shares of stock which currently sell for $28.75. They also have 8,000 shares of 9.25% preferred stock with a $100 par value which sells for $110. U.S. government bonds currently yield 3.15% and the expected return on the market is 10.38%. XYZ has a beta of 1.25

• Costs of Capital• Ke = Rf + β(Rm – Rf) = 0.0315 +1.25(0.1038-0.0315) = 0.1219 = 12.19%

• Kpfd = Dividend / Price = 9.25/110 = 0.0841 = 8.41%

• Kd = Find YTM where i is semiannual and…n = 24 semiannual, PV = -1,100, FV = 1,000, PMT = 41.25 semiannuali = 3.5021 :. YTM = 7.0043% or 0.0700



• From there, put the pieces of the formula in place, then work through the formula in steps• WACC = wpfd x Kpfd + we x Ke + wd x Kd x (1-t)

• WACC = 0.0217 x 0.0841 + 0.7095 x 0.1219 + 0.2688 x 0.0700 x 0.65

• WACC = 0.0018 + 0.0865 + 0.2688 x 0.0455

• WACC = 0.0018 + 0.0865 + 0.0122

WACC = 0.1005 = 10.05%



Real life is more complicated

• Equity can come from retained earnings or from new investment.

• New issues of stocks and bonds come with flotation costs, price adjustments, etc. which must be factored in.

• Growth rates are rarely stated, so they must be computed.


Kd with flotation cost

• ABC Company is in the 40% tax bracket and can sell 15-year bonds ($1,000 par) paying annual interest of 12%. Market rates are slightly below that for bonds of this rating, so the bonds will sell for $1,100. To issue the bonds, ABC will have flotation costs of $30 per bond. Find Kd.• n = 15 years (annual)

• i = ?? Solve for YTM (annual)

• PMT = 12% x 1,000 (annual) outflow

• PV = 1,100 – 30 (expected proceeds less flotation costs) inflow

• FV = 1,000 outflow

• i = 11.0252

• YTM = 11.03%

• Kd = 11.03%

• Kd (After-tax) = 11.03% x (1-0.40) = 6.62%


Kpfd with flotation cost

• XYZ Company is issuing preferred stock with an 8% dividend and a $120 par value. The shares will sell for $129.60 and have flotation costs of $7.20 per share. What is the cost of preferred equity?• Par = 120.00

• Dividend = 8% x 120 = 9.60

• Selling price = 129.60

• Flotation costs = 7.20

• Net proceeds = 129.60 – 7.20 = 122.40

• Kpfd = 9.60 / 122.40 = 0.0784 = 7.84%


Ke with flotation cost

• ABC Company is considering a SEO (Seasoned Equity Offering). Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. The planned dividend per share is $1.45 for the coming year, and they expect the growth of dividends to follow the same average growth it has for the past 5 years. Historic annual DPS are:• 2008 2.12

• 2009 2.30

• 2010 2.60

• 2011 2.92

• 2012 3.10

• What is their Cost of Equity for the SEO?• Ke = D1 / P0 + g… but what is g?


Ke with flotation cost – finding the growth rate• Historic annual DPS for the last 5 years are:

• 2008 2.12

• 2009 2.30

• 2010 2.60

• 2011 2.92

• 2012 3.10

• Growth can be found by solving for the CAGR (Compound Annual Growth Rate)• (3.10/2.12) = 1.46

• 1.46 ^ (1/4) = 1.0997 (a 5-year sample means we see 4 years of compounding)

• CAGR = 1.0997 – 1 = 0.0997 – 9.97%

• g = 9.97%



• ABC Company is considering a SEO (Seasoned Equity Offering). Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. The planned dividend per share is $1.45 for the coming year, and they expect the growth of dividends to follow the same average growth it has for the past 5 years. Historic annual DPS are:• 2008 2.12

• 2009 2.30

• 2010 2.60

• 2011 2.92

• 2012 3.10

• What is their Cost of Equity for the SEO?• Ke = D1 / P0 + g

• Ke = 1.45 / P0 + 0.0997 … what should we use for P0?



• Their stock currently sells for $48.22, but the new shares will be underpriced by $1.00 and have $2.86 per share in flotation costs. • Net Proceeds will be 48.22 – 1.00 – 2.86 = 44.36

• What is their Cost of Equity for the SEO?• Ke = D1 / P0 + g

• Ke = 1.45 / 44.36 + 0.0997 = 0.1324 = 13.24%

• What if they used Retained Earnings instead of issuing new stock?• Ke = 1.45 / 48.22 + 0.0997 = 0.1298 = 12.98%

• Why is the cost of equity higher for new stock than for retained earnings?

• What would happen if a company always issued new stock instead of funding growth from retained earnings?

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