### Seeing is believing!

Before you order, simply sign up for a free user account and in seconds you'll be experiencing the best in CFA exam preparation.

### Subject 2. Cost of Debt and Preferred Stock

Capital components are the types of capital used by firms to raise fund. They include the items on the right side of a firm's balance sheet (debt, preferred stock, and common equity). Any increase in the firm's total assets must be financed by one or more of these capital components.

The cost of debt is defined as the cost to the firm in terms of the interest rate that it pays for ordinary debt (rd) less the tax savings that are achieved. Interest on debt is tax-deductible and therefore to calculate the cost of debt the tax benefit is deducted.

Two methods to estimate the before-tax cost of debt (rd) are discussed.

#### Yield-to-Maturity Approach

This approach uses the familiar bond valuation equation. Assuming semi-annual coupon payments, the equation is:

The six-month yield (rd/2) is derived and then annualized to arrive at the before-tax cost of debt, rd.

#### Debt-Rating Approach

This approach can be used if there isn't a reliable market price for a firm's debt. Based on the company's debt rating, the before-tax cost of debt is estimated by using the yield on comparably rated bonds for maturities that are a close match to those of the firm's existing debt.

For example, assume that:

• A firm's debt has an average maturity of 5 years.
• Its credit rating is AAA.
• The yield on debt with the same debt rating and similar maturity is 6%.
• The marginal tax rate is 30%.

Then the company's after-tax cost of debt is 6% x (1 - 30%) = 4.2%.

Other factors, such as debt seniority and security, may complicate the calculation, so analysts must take care when determining the comparable debt rating and yield.

#### Issues in Estimating the Cost of Debt

• Fixed-rate debt versus floating-rate debt

Estimating the cost of floating-rate debt is difficult because the cost depends not only on the current yield but also on the future yields. The term structure of interest rates may be used to calculate an average rate.

• Debt with option-like features

Be aware that some debt can have call or put options. (Valuing such debts is a topic for Level II candidates.)

• Non-rated debt

The yields of a firm's debt may not be available, or a firm may not have rated bonds.

• Leases

If a company uses leasing as a source of capital, the cost of these leases should be included in the cost of capital (long-term debt).

#### Cost of Preferred Stock

The cost of preferred stock is calculated by dividing the dollar amount of the dividend (which is normally paid on an annual basis) by the preferred stock current price.

It is important to note that tax does not affect the calculation of the cost of preferred stock, since preferred dividends are not tax deductible.

#### Practice Question 1

The before-tax cost of debt to a corporation at any point in time is ______.

A. the current market borrowing rate
B. greater than the risk-free rate if the bond beta is negative
C. equal to the coupon payment
D. the stated interest on the debt instrument

#### Practice Question 2

Which of the following is NOT true regarding a firm's before-tax cost of debt?

A. The before-tax cost of debt is the return the firm's creditors demand on new borrowing.
B. The firm's before-tax cost of debt based on past borrowing is known as embedded debt cost.
C. It is possible to determine the firm's before-tax cost of debt by observing yields on similar bonds that were recently issued.
D. The coupon rate on outstanding debt is not necessarily the firm's current before-tax cost of debt.
E. The firm's cost of equity is generally easier to calculate than the firm's before-tax cost of debt.

#### Practice Question 3

AC Ltd. has preferred stock that pays a \$1.25 dividend per share and sells for \$25 dollars a share. What is the cost of preferred stock?

A. 4.75%
B. 5%
C. 20%

The cost of preferred stock is kps = Dps / Pn. In this case, 1.25 / 25 = 0.05 or 5%.

#### Practice Question 4

True or False? The before-tax cost of debt capital for a firm can be observed directly even if the firm's bonds are not publicly traded.

#### Practice Question 5

A company is determining the cost of debt for use in its weighted average cost of capital. It has recently issued a 10-year, 6 percent semi-annual coupon bond for \$864. The bond has a maturity value of \$1,000. If the marginal tax rate is 35 percent, the cost of debt (%) the company should use in its calculation is closest to ______.

A. 2.6
B. 3.8
C. 5.2

The pre-tax cost of debt is the YTM of the bond. To calculate the YTM of the bond:
Using a financial calculator, enter N=20, PV=-864, PMT=30, and FV=1,000. Compute I/YR. The result (4%) is the semi-annual rate; double it to get the annual rate (8%). This is the pre-tax cost of debt. Multiplying the pre-tax cost of debt by 1 - tax rate gives the result: 5.2% (8 * 0.65 = 5.2).

Note: because the bond pays coupons semi-annually, there are 20 periods (10 years times two payments per year) and the periodic coupon payment is \$30 (6% of \$1,000 per year paid in two equal payments every six months).

#### Practice Question 6

If a company uses leasing as a source of capital, which of the statement is false?

A. The operating lease is not a form of borrowing. The capital lease is.
B. The cost of these leases should be included in the cost of capital.
C. The cost of leasing is similar to that of the company's other long-term borrowing.

#### Practice Question 7

In the debt-rating approach, the ______ is estimated by using the yield on comparably rated bonds for maturities that are closely aligned to the maturities of the existing debt of the company.

A. after-tax cost of debt
B. before-tax cost of debt
C. tax-shielded cost of debt

#### Practice Question 8

In general the cost of debt would be higher for companies:

I. that are unprofitable.
II. whose profit are not stable.
III. that are already using a lot of debt in their capital structure.

Correct Answer: I, II and III

The higher the investment risk, the higher the cost of debt. Factors that affect the level of investment risk include profitabilitym stability of profits, and the degree of financial leverage.

#### Practice Question 9

As an analyst you want to determine the cost of the bond of company ABC. The company's debt rating is A1. The yield on comparably rated, option-free bonds with similar maturity is 4.5%. ABC's bond has a put option, however. It allows the investor to sell the bond back to the issuer at a predetermined price. The before-tax cost of ABC's debt should be:

A. > 4.5%
B. = 4.5%
C. < 4.5%

Options affect the value of debt. The put option lowers the required yield on the bond.

#### Practice Question 10

The before-tax cost of debt capital for a firm ______

A. is the return that the firm's creditors demand on new borrowing.
B. can be estimated by finding the yield on recently issued, longer-maturity bonds with a lower bond rating.
C. can be calculated by looking at the coupon rates on existing bonds of similar risk.

#### Practice Question 11

A company is considering issuing a 10-year, option-free, semi-annual coupon bond with a 9 percent coupon rate. The bond is expected to sell at 95 percent of par value. If the company's marginal tax rate is 30 percent, then the after-tax cost of debt is closest to ______.

A. 6.20%
B. 6.86%
C. 7.38%

Using a financial calculator: N = 20, PMT = 45, PV = -950, FV = 1000; solve for I/Y = 4.90%. The annual yield is twice the semi-annual yield = 4.90% x 2 = 9.80%. The after-tax cost of debt = annual yield x (1 - t) = 9.80% x (1 - 0.30) = 6.86%.

#### Practice Question 12

A company plans to issue nonconvertible, noncallable, fixed-rate perpetual preferred stock with a \$6 annual dividend. The preferred stock is expected to sell for \$40. If the company's marginal tax rate is 30 percent, then the cost of preferred stock is closest to ______.

A. 9.8%
B. 12.7%
C. 15%

The cost of a perpetuity is the annual cash flow divided by the selling price. In this case, the cost of preferred stock = 6.00 / 40 = 15.0%. Because the preferred stock dividend is not tax deductible to the issuing company, there is no after-tax adjustment.

#### Practice Question 13

Suppose company A issues a new debt by offering a 20-year, \$100,000 face value, 10% semi-annual coupon bond. Upon issuance, the bond sells at \$105,000. What are company A's before-tax cost of debt and after-tax cost of debt if the marginal tax rate is 40%?

A. 9.44%
B. 5.66%
C. 4.89%

Given: PV = \$105,000, FV = \$100,000, PMT = (10% of \$100,000)/2 = \$5,000, N = 20 × 2 = 40, Using a financial calculator to solve for rd/2, the six-month yield, we get rd/2 = 4.72%.

Note PV = -\$105,000 when using the calculator instead of the formula.

The before-tax cost of debt is therefore rd = 4.72% × 2 = 9.44%, and the after-tax cost of debt = rd(1 – t) = 9.44% (1 – 0.40) = 5.66%.

#### Practice Question 14

Which of the following statements gives an accurate definition of yield-to-maturity?

A. The yield-to-maturity of a bond is the semi-annual return that an investor earns on a bond if they purchase the bond today and hold it until maturity.
B. The yield-to-maturity of a bond is the annual return that an investor earns on a bond if they purchase the bond today and hold it until maturity.
C. The yield-to-maturity of a bond is the return that an investor earns on a bond if they purchase the bond and sell it one year prior to maturity.

It is an annual return, and not a semi-annual return.

#### Practice Question 15

Company D issues fixed-rate, noncallable, nonconvertible preferred stock priced at \$102 and paying dividends of \$7.24. Company D's marginal tax rate is 35%. What is the estimate of company D's cost of preferred stock?

A. 4.61%
B. 7.10%
C. 7.24%