Transcript Costs of Capital
Business Finance
BA303 ♦ Fall 2012 Michael Dimond
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: R f < K d < K pfd < K e and… inflation < R f • 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) Michael Dimond School of Business Administration
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:
Scenario
Very poor Poor Average Good Very good
Return
0.75% 1.25% 8.5% 14.75% 16.25% • What is the expected rate of return?
• The weighted average is 8.35%
Probability
0.05
0.15
0.60
0.15
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
Michael Dimond School of Business Administration
More about risk and return
• Variation or volatility is another form of uncertainty.
• What is standard deviation? What does it represent?
Michael Dimond School of Business Administration
More about risk and return
• How do the following assets compare to Stock X?
Expected Return Stock X 12% Stock A 12% Stock B 10% Stock C 14% Std Deviation 5% 7% 8% • When making a decision, which should you consider first?
6% • 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?
Michael Dimond School of Business Administration
Determining K
d
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 (K d ), 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 (K d )?
Michael Dimond School of Business Administration
Determining K
e
with the Dividend Growth Model
• K e is the required rate of return for equity investors “Cost of Equity” • We can derive this from the dividend discount model: P 0 = D 1 /(r-g)
:.
(r-g) = D 1 /P 0
:.
r = D 1 /P 0 + g • Since r is the required rate of return, K e = D 1 /P 0 • How do you test the answer you get? • What if you wanted to solve for the expected growth rate?
+ g • There is another way to find the cost of equity: CAPM Michael Dimond School of Business Administration
Determining K
e
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 K e K e = Rf + β(Rm – Rf) or K e = 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 (K e )?
Michael Dimond School of Business Administration
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 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 Mkt Return 16% 13% 7% 14% 12% -5% -9% -12% 4% 8% A Return 28% 22% 14% 18% 20% -2% 2% -8% 9% 13% -20% -10% 30% 25% 20% 15% 10% 5% 0% -5% 0% -10% 10% 20% A Return Линейная (A y = 1,0893x + 0,0637 • What is the difference between Systematic and Unsystematic risk?
• Can beta be zero? Can beta be negative?
Michael Dimond School of Business Administration
Can beta really be negative?
What does a negative beta imply about the stock performance?
What does a negative beta imply about Ke?
Michael Dimond School of Business Administration
Determining K
pfd
with the Dividend Discount Model
• The value of a perpetuity is how we price preferred equity: PV perp = CF/r
:.
Price = Dividend/K pfd
:.
Price x K pfd = Dividend
:.
K pfd = 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% Michael Dimond School of Business Administration
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 Michael Dimond School of Business Administration
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 = w e x K e + w d x K d (1-t) • If there is preferred stock, we just expand the formula: WACC = w pfd x K pfd + w e x K e + w d x K d (1-t) Michael Dimond School of Business Administration
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 • W e = E/TC = 600/1,000 = 0.60
• W d = D/TC = 300/1,000 = 0.30
• W pfd = Pfd/TC = 100/1,000 = 0.10
• Note: the sum of the weights always equals 1.00
Michael Dimond School of Business Administration
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?
Michael Dimond School of Business Administration
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 • MV e = $27.50 x 1MM = $27.5MM
• MV d = 10MM ÷ 1,000 (assumed FV) x $1,125 = $11.25MM
• MV pfd = $125 x 10,000 = $1.25MM
• TC = $27.5MM + $11.25MM + $1.25MM = $40.0MM
• Find the weights & tax shield • W e = 27.5 ÷ 40.0 = 0.6875
• W d = 11.25 ÷ 40.0 = 0.2813
• W pfd = 1.25 ÷ 40.0 = 0.0313
• (1-t) = (1 - 0.34) = 0.66
Michael Dimond School of Business Administration
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 • K d : Solve for the yield find i, where: n=10x2, PV=-1125, FV=1000, PMT=0.085x1000
÷2 [i=3.3800]
:.
K d = 2x3.38% = 6.76% • K e : Use the Dividend Discount Model or the CAPM (based on data available) K K e e = r = D 1 /P 0 + g = [(1.80 x 1.07) / 27.50] + 0.07 = 0.1400
:.
K e = 14.00% • K pfd K pfd : Find the return on a non-growing perpetuity = r = D 1 /P 0 = (0.09 x 100)/125 = 0.0720
:.
K pfd = 7.20% Michael Dimond School of Business Administration
Determining the WACC
• 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
0.0446 is the
After-Tax Cost of Debt
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
Michael Dimond School of Business Administration
Determining the WACC
• 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 • MV e = $18,750,000 w e • MV pfd • MV d = $ 880,000 w pfd = $10,890,000 w d = 0.7095
• Tax Shield = (1 – t) = (1 - 0.35) = 0.65
Michael Dimond School of Business Administration
Determining the WACC
• 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 • K e = Rf + β(Rm – Rf) = 0.0315 +1.25(0.1038-0.0315) = 0.1219 = 12.19% • K pfd = Dividend / Price = 9.25/110 = 0.0841 = 8.41% • K d = Find YTM where i is semiannual and… n = 24 semiannual, PV = -1,100, FV = 1,000, PMT = 41.25 semiannual i = 3.5021 :. YTM = 7.0043%
or
0.0700
Michael Dimond School of Business Administration
Determining the WACC
• 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% Michael Dimond School of Business Administration
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.
Michael Dimond School of Business Administration
K
d
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 K d .
• 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% • K d = 11.03% • K d (After-tax) = 11.03% x (1-0.40) = 6.62% Michael Dimond School of Business Administration
K
pfd
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
• K pfd = 9.60 / 122.40 = 0.0784 = 7.84% Michael Dimond School of Business Administration
K
e
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 • 2009 • 2010 • 2011 • 2012 2.12
2.30
2.60
2.92
3.10
• What is their Cost of Equity for the SEO?
• K e = D 1 / P 0 + g… but what is g?
Michael Dimond School of Business Administration
K
e
with flotation cost – finding the growth rate
• Historic annual DPS for the last 5 years are: • 2008 • 2009 • 2010 • 2011 • 2012 2.12
2.30
2.60
2.92
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% Michael Dimond School of Business Administration
K
e
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 • 2009 • 2010 • 2011 • 2012 2.12
2.30
2.60
2.92
3.10
• What is their Cost of Equity for the SEO?
• K e = D 1 / P 0 + g • K e = 1.45 / P 0 + 0.0997 … what should we use for P 0 ?
Michael Dimond School of Business Administration
K
e
with flotation cost
• 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?
• K e = D 1 / P 0 + g • K e = 1.45 / 44.36 + 0.0997 = 0.1324 = 13.24% • What if they used Retained Earnings instead of issuing new stock?
• K e = 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?
Michael Dimond School of Business Administration