IFT Notes for Level I CFA^® Program

R33 Cost of Capital

Part 2

3. Costs of the Different Sources of Capital

Each source of capital has a different cost because of differences in seniority, contractual commitments, and potential value as a tax shield. Three primary sources of capital are:

Debt
Preferred equity
Common equity

3.1. Cost of Debt

Cost of debt is the cost of financing to a company using debt instruments such as taking a bank loan or issuing a bond. In simpler terms, it is the effective interest rate a company pays on its current debt. Two methods to estimate the before-tax cost of debt are:

The yield to maturity (YTM) approach
Debt-rating approach

Yield to Maturity Approach

YTM is the annual return an investor earns if the bond is purchased today and held until maturity. It is the rate at which the present value of all future cash flows equals the market price of the bond.

$P${}_{0\ }$= $\sum\limits_{t=1}^{n}[\frac{{PMT}_t}{{\left(1\ +\frac{r_d}{2}\right)}^t}]\ $+ $\frac{FV}{{\left(1\ +\ \frac{r_d}{2}\right)}^n}$$

where
$P_0$ = the current market price of the bond
$PMT_t$ = interest payment in period t
$r_d$${}_{\ }$ = the yield to maturity
n = number of periods remaining to maturity
FV = maturity value of the bond

Example

A company issues a 10-year, 8% semi-annual coupon bond. Upon issuance, the bond sells for $980. If the marginal tax rate is 30%, what is the after-tax cost of debt?

Solution:

First, calculate the before-tax cost of debt by entering the following values:

N = 20 because it is a semi-annual coupon bond, so there are 10 x 2 = 20 periods.

PV = -980; the price at which the bond is current selling

FV = 1000; the face value of the bond that will be repaid at maturity (the face value of the bond is not explicitly given but assume it is the nearest round figure.)

PMT = (0.08/2) * 1000 = 40 (Coupons are always paid on the face value)

Compute I/Y = 4.15 %

Annual I/Y = 4.15 x 2 = 8.30 = before-tax cost of debt

After-tax cost of debt = 8.30 (1 – 0.3) = 5.8%

Debt Rating Approach

This method is used when the company’s debt doesn’t have an YTM as it is not publicly traded. In such case, the approach is as follows:

Determine the current market rates for comparable bonds with similar ratings and maturities (using matrix pricing).
Analyze the company characteristics like covenants, seniority, etc. to get before-tax cost of debt.
Apply the marginal tax rate to arrive at the after-tax cost of debt.

3.2. Cost of Preferred Stock

The cost of preferred stock is the cost that a company has committed to pay to preferred stockholders in the form of preferred dividend. Preferred stock has the characteristics of both debt and equity. Unlike common dividend which is variable, preferred dividend is usually fixed and paid before common shareholders. The cost of preferred stock can be computed as:

$P_p=\frac{D_p}{r_p}$
where
$P_p=\$ the current preferred stock price per share
$D_p$ = the preferred stock dividend per share
$r_p$ = the cost of preferred stock

Example

A company issues preferred stock with par value $100 that is currently valued at $125 per share. The preferred dividend is $5 per share. The marginal tax rate is 33 percent. What is the cost of preferred stock?

Solution:

Cost of preferred stock = 5/125 = 4%

Note: We ignore taxes, because unlike interest payments, dividends are not tax deductible.

3.3. Cost of Common Equity

Cost of common equity, or cost of equity, is the rate of return required by a company’s common shareholders. It is the return expected by investors for the risk they undertake. Unlike debt and preferred stock, estimating the cost of equity is challenging because of the uncertain nature of future cash flows.

Three commonly used methods to estimate the cost of equity are:

Capital asset pricing model
Dividend discount model
Bond yield plus risk premium method

Capital Asset Pricing Model (CAPM) Approach

According to this method, the cost of equity is equal to the risk free rate plus a premium for bearing the security’s market risk. The premium is the beta for the security multiplied by the equity risk premium.

$r_e\ =\ RFR\ +\ \beta \ [E(R_{mkt})\ -\ RFR]$
where
$r_e$${}_{\ }$ = the cost of equity
RFR = risk-free rate of an asset
$\beta$ = the sensitivity of a stock’s return to changes in market return
$E\left(R_{mkt}\right)$ = expected return on the market
${$E\left(R_{mkt}\right)$ - RFR}$ is also called the equity risk premium because it is the premium that investors expect for investing in the market relative to the risk-free rate.

Example

In a developing market, the risk-free rate is 10% and the equity risk premium is 6%. The equity beta for a given company is 2. What is the cost of equity using the CAPM approach?

Solution:

r_e= 0.1 + 2 [0.06] = 22%

To estimate the risk-free rate, we use the yields on long-term government bonds. To estimate the equity risk premium we use historical returns. Historical equity risk premium is a good indicator of expected equity risk premium.

Dividend Discount Model (DDM) Approach

Before going deeper into DDM, let us understand a few basic concepts first.

Present value of a perpetuity: Assume an investment gives a cash flow of $10 at the end of each period forever. This is called a perpetuity, as the cash flow continues forever. If the discount rate is 5%, the present value of this infinite cash flow can be calculated as 10/0.05 = 200. That is, PV₀ = cash flow/interest rate.

Present value of a growing perpetuity: Now assume the cash flow for every successive period grows at a rate of 2%. $10 in period 1, $10.2 in period 2, $10.404 in period 3, and so on. The present value of a growing perpetuity can be computed as:

$PV${}_{0\ }$= $\frac{PMT_1}{r\ -\ g}$ = $\frac{10}{0.05\ -\ 0.02}$$ = 333.33

Note that the denominator for a growing perpetuity is smaller than a normal perpetuity as the cash flow is increasing every period. Consequently, the present value is greater in this case than a normal perpetuity. If the growth rate is higher, the present value is even higher.

Having understood these basic concepts, let us move to the DDM model. The dividend discount model states that the intrinsic value of a financial asset, such as a stock, is the present value of future cash flows (dividends). Gordon growth model is one example of a DCF model. It is also called the constant growth dividend discount model. If the dividends grow at a constant growth rate g, then the price of the stock can be written as:

$P${}_{0\ }$= $\frac{D_1}{r_e\ -\ g}$$
where
$D_1$ =dividend at end of each period
$P${}_{0}$$ = intrinsic price of stock
$r${}_{e\ }$$ = cost of equity

Therefore, rearranging the equation we get:

$r${}_{e\ }$= $\frac{D_1}{P_0}$$ + g

In the above equation, one needs to estimate , the dividend for the next period, and g, the constant growth rate of dividends. If the company has a stable dividend policy, then can be easily estimated. There are two ways to estimate the growth rate:

Use a forecasted growth rate from a published vendor.
Use the following relationship between the growth rate, the retention rate, and the return on equity:

g = b x ROE = $(1 -\frac{D}{EPS})$x$$ ROE
where:
g = sustainable growth rate
b = earnings retention rate
$\frac{D}{EPS}$ = dividend payout rate
ROE = return on equity

If you are given D_0, you can calculate D₁as D₀(1 + g).

Example

You have gathered the following information about a company and the market:

Current share price = 30
Most recent dividend paid = 2
Expected dividend payout rate = 40%
Expected ROE = 15%
Equity beta = 1.5
Expected return on market = 15%
Risk free rate = 8%

Using the DCF approach, what is the cost of retained earnings?

Solution:

Since the dividend payout rate is 40%, the retention ratio, b, is 1 – 0.4 = 0.6

g = b * ROE = 0.6 * 0.15 = 0.09

$r${}_{e\ }$= $\frac{D_1}{P_0}$ + g$

$r${}_{e}$ = $\frac{D_0\ *\ \left(1\ +\ g\right)}{P_0}$ + g = $\frac{2\ \times 1.09}{30}$ + 0.09 = 0.1627 = 16.27\%$

Bond Yield plus Risk Premium Method

In this method, we add a risk premium to the yield on the firm’s long-term debt. The assumption here is that the return on a company’s equity will be greater than the return on the company’s bond, as equity is riskier than the bond.

r_e= bond yield + risk premium

Example

A company’s interest rate on long-term debt is 8%. The risk premium of equity is estimated to be 5%. What is the cost of equity?

Solution:

$r_e=\ 8\%+\ 5\%\ =\ 13\ \%$