OM FINAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

CHAPTER THREE: COST OF CAPITAL

Yi Zhou

Associate Professor Department of Finance

College of Business San Francisco State University

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

MOTIVATION

MOTIVATION

Suppose you have just become the president of a large company and the first decision you face is whether to go ahead with a plan to renovate the company’s warehouse distribution system. The plan will cost the company $50 million, and it is expected to save $12 million per year after taxes over the next six years. To address it, you would determine the relevant cash flows, discount them, and, if the net present value is positive, take on the project; if the NPV is negative, you would scrap it. So far, so good; but what should you use as the discount rate?

The new project will have a positive NPV only if its return exceeds what the financial markets offer on investments of similar risk. We called this minimum required return the cost of capital associated with the project. We use the terms required return, discount rate, and cost of capital interchangeably.

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

YIELD-TO-MATURITY APPROACH DEBT-RATING APPROACH

YIELD-TO-MATURITY APPROACH

Consider a company whose yield-to-maturity is 5.26%. What is the after-tax cost of debt if the marginal tax rate is 40%? The after-tax cost of debt is rd(1 − t) = 5.26% × (1 − 40%) = 3.16%.

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

YIELD-TO-MATURITY APPROACH DEBT-RATING APPROACH

DEBT-RATING APPROACH

Use yields on comparably rated bonds with maturities similar to what the company has outstanding. Example: Consider a company whose debt rating is AA. The yield on AA debt is currently 6.2%. What is the after-tax cost of debt if the marginal tax rate is 40%? The after-tax cost of debt is rd(1 − t) = 6.2% × (1 − 40%) = 3.72%

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

COST OF PREFERRED STOCK

The cost of preferred stock that is noncallable and nonconvertible:

rpreferred = Dpreferred

P

Suppose a company has a preferred stock outstanding that has a dividend of $1.25 per share and a price of $ 20. What is the company’s cost of preferred equity?

rpreferred = 1.25 20

= 0.0625 = 6.25%

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

CAPITAL ASSET PRICING MODEL (CAPM) DIVIDEND GROWTH MODEL (DGM) BOND YIELD PLUS RISK PREMIUM

CAPITAL ASSET PRICING MODEL (CAPM)

Suppose stock in Alpha Air Freight has a beta of 1.2. The market risk premium is 8 percent, and the risk-free rate is 6 percent. What is Alpha’s cost of equity capital?

re = rf + βe × (rM − rf ) = 6% + 1.2 × 8% = 15.6%

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

CAPITAL ASSET PRICING MODEL (CAPM) DIVIDEND GROWTH MODEL (DGM) BOND YIELD PLUS RISK PREMIUM

DIVIDEND GROWTH MODEL (DGM)

Alpha’s last dividend was $2 per share, and the dividend is expected to grow at 8 percent indefinitely. The stock currently sells for $30. What is Alpha’s cost of equity capital?

re = D1 P0

+ g = D0(1 + g)

P0 + g =

2 × (1 + 0.08) 30

+ 0.08 = 15.2%

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

CAPITAL ASSET PRICING MODEL (CAPM) DIVIDEND GROWTH MODEL (DGM) BOND YIELD PLUS RISK PREMIUM

BOND YIELD PLUS RISK PREMIUM

The bond yield plus risk premium approach requires adding a premium to a company’s yield on its debt:

re = rd + risk premium

Citigroup, as of early January 2006, the yield to maturity of the Citigroup bonds maturing in 2016 was approximately 4.95%. Adding an arbitrary risk premium of 3.5% produces an estimate of the cost of equity of 4.95 + 3.5 = 8.45%.

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

WACC = wd rd(1 − t) + wprp + were

wd is the proportion of debt.

rd is the before-tax marginal cost of debt.

t is the company’s marginal tax rate.

wp is the proportion of preferred stock.

rp is the marginal cost of preferred stock.

we is the proportion of equity.

re is the marginal cost of equity.

wd + wp + we = 1

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

WACC EXAMPLE 1

Assume that ABC Corporation has the following capital structure: 30 percent debt, 10 percent preferred stock, and 60 percent equity. ABC Corporation wishes to maintain these proportions as it raises new funds. Its before-tax cost of debt is 8 percent, its cost of preferred stock is 10 percent, and its cost of equity is 15 percent. If the company’s marginal tax rate is 40 percent, what is ABC’s weighted average cost of capital?

wd = 0.3, wp = 0.1, we = 0.6, rd = 0.08, rp = 0.10, re = 0.15, t = 0.40

WACC = 0.3 × 0.08 × (1 − 0.40) + 0.1 × 0.1 + 0.6 × 0.15 = 11.44%

YI ZHOU CHAPTER THREE: COST OF CAPITAL

MOTIVATION COST OF DEBT

COST OF PREFERRED STOCK COST OF EQUITY

WEIGHTED AVERAGE COST OF CAPITAL (WACC)

WACC EXAMPLE 2

Suppose the Widget Company has a capital structure composed of the following, in billions: Debt $10, Common equity $40. If the before-tax cost of debt is 9%, the required rate of return on equity is 15%, and the marginal tax rate is 30%, what is Widget’s weighted average cost of capital?

WACC = 10

10 + 40 × 0.09 × (1 − 0.30) + 0 +

40 10 + 40

× 0.15 (1)

= 0.0126 + 0.120 = 0.1326

YI ZHOU CHAPTER THREE: COST OF CAPITAL