# Level 1 CFA® Exam:

Cost of Debt & Cost of Preferred Stock

Let's start with the cost of debt.

The cost of debt is the cost of financing the company by issuing bonds or taking out a loan or credit. The methods of calculating the cost of debt include:

- the yield to maturity approach, and
- the debt-rating approach.

### Yield to Maturity Approach

Yield to maturity is a return earned on a bond that an investor purchases today and holds until maturity. It is therefore a rate that discounts future cash flows of the bond by equating it with the market price of the bond. This is presented by the formula below:

\(P_{0}=\frac{PMT_{1}}{(1+\frac{r_{d}}{2})}+\ldots +\frac{PMT_{n}}{(1+\frac{r_{d}}{2})^{n}}+\frac{FV}{(1+\frac{r_{d}}{2})^{n}} =\\= (\Sigma^{n}_{t=1}\frac{PMT_{t}}{(1+\frac{r_{d}}{2})^{t}})+\frac{FV}{(1+\frac{r_{d}}{2})^{n}}\)

- \(P_{0}\) - current market price of the bond
- \(PMT_{t}\) - interest payment in period "t"
- \(r_{d}\) - yield to maturity
- \(n\) - number of periods remaining to maturity
- \(FV\) - maturity value of the bond

To use this method to calculate the cost of capital, you need to calculate the yield to maturity from the formula. Of course, you can do it using a financial calculator. To determine the yield to maturity (YTM), you can either use the TVM worksheet on a calculator or use the BOND or CASH FLOW sheet.

Note that the yield to maturity that equates the price of a bond with the present value of coupons and bond face value is nothing else than the IRR we discuss in one of the previous readings. Let's look at an example:

You have a 7-year bond with a face value of USD 1000 and a USD 80 coupon paid at the end of each year. The bond price is USD 950. What is the YTM of this bond?

(...)

The second method used for calculating the cost of debt is called the debt-rating approach. This method is also used to estimate the before-tax cost of debt. In the debt-rating approach we use the yield on comparably rated bonds with maturities that closely match the maturity of the company’s existing debt.

If a company took out a loan for a period of five years, the tax rate is 20% and the yield on bonds with similar debt rating and the same duration is 5%, then the after-tax cost of debt is closest to …?

(...)

The cost of preferred stock depends on the characteristics of preferred stock, for example, if they pay a dividend, if they include options, or if they are convertible into common stock, etc.

However, the cost of the preferred stock with no maturity date, which pays fixed dividends regularly and doesn’t have built-in options, can be determined using this formula:

\(P_{p} = \frac{D_{p}}{r_{p}}\)

- \(P_{p}\) - current preferred stock price per share
- \(D_{p}\) - preferred stock dividend per share
- \(r_{p}\) - cost of preferred stock

This is the formula for the present value of a perpetuity. A perpetuity is an annuity with cash flows continuing forever paid at regular intervals, e.g. annually. The preferred stock price which pays dividends indefinitely is equal to the present value of the future dividends. To determine the present value, you need to know the discount rate, that is the required rate of return on preferred stock, which is also the cost of capital for the company.

Knowing the preferred stock price and the amount of the preferred dividend, you can determine the cost of preferred stock for the company by rearranging the formula above.

A company issued preferred stock without embedded options at a price of USD 70 and USD 60 face value. The current market price of the stock is equal to USD 80. If the cost of debt is 8%, and the nominal yield is 12%, what is the cost of preferred stock?

(...)

- The cost of debt is the cost of financing the company by issuing bonds or taking out a loan or credit.
- The methods of calculating the cost of debt include the yield to maturity approach and the debt-rating approach.
- Yield to maturity is a return earned on a bond that an investor purchases today and holds until maturity.
- In the debt-rating approach we use the yield on comparably rated bonds with maturities that closely match the maturity of the company’s existing debt.
- The cost of preferred stock depends on the characteristics of preferred stock.
- The cost of the preferred stock with no maturity date, which pays fixed dividends regularly and doesn’t have built-in options, can be determined using the formula for the present value of a perpetuity.