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Cost of Debt, Preferred Stock, and Common Stock

Site: Saylor Academy
Course: BUS601: Financial Management
Book: Cost of Debt, Preferred Stock, and Common Stock
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Date: Friday, 4 April 2025, 12:24 AM

Description

A critical component in developing the firm's capital plan is determining what the cost of debt and equity is. When you have completed reading these sections, you will be able to calculate the cost of debt and the cost of equity.

Table of contents

Cost of Debt

Learning Objectives
  1. Understand the components of the cost of debt.
  2. Identify the tax implications of debt.
  3. Explain how debt plays into the weighted average cost of capital.

The cost of long-term debt, r{d}, is the after-tax cost of raising long-term funds through borrowing. The important cost is our marginal debt cost which is the next dollar of debt. If we were to issue another dollar (an additional dollar) of debt, how much would it cost us? The cost of new issuance of debt will probably not be the same as other debt we have issued in the past (our historical debt cost), as we will need to satisfy the current market demand.

 

How to Calculate the Cost of Debt

There are a few methods to calculate the cost of debt. We are looking for the yield to maturity (YTM), since this is the most accurate gauge of market demand. How do we figure out the yield to maturity? If we have outstanding debt of an appropriate maturity, we can assume the YTM on this debt to be our cost.

If our company, however, has no publicly traded debt, we could look to the market to see what the yield is for other publicly traded debt of similar companies. Or, if we are completely using bank financing, we can simply ask the bank to provide us with an estimated rate.

Equation 12.1 Pre-Tax Cost of Debt

Component Cost of Debt = r_{d}

Since interest payments made on debt (the coupon payments paid) are tax deductible by the firm, the interest expense paid on debt reduces the overall tax liability for the company, effectively lowering our cost. To calculate the real cost of debt we take out the tax liability.

Equation 12.2 After-Tax Cost of Debt

After-Tax Component Cost of Debt = r_{d}-\left(r_{d} \times T\right)=r_{d} \times(1-T)

Here, r_{d} is the before tax return and T is the corporate tax rate.

 

Worked Example: Falcons Footwear

Falcons Footwear is a company that produces sneakers for children. Each sneaker has a black and red falcon head on it. Their marginal tax rate is 40%, and they have $100 million notional, 30-year bonds with a 7% coupon. The bonds currently sell for par. What's the after-tax cost of debt?

Since the bonds are selling for par, we know that the YTM equals the coupon rate of 7%.

After-Tax Cost of Debt for Falcon Footwear  =0.07 \times(1-0.4)
=0.042 or 4.2 \%

Key Takeaways

The debt component has important considerations.

  • Tax considerations are important as interest payments are tax deductible.
  • We can estimate the cost of debt either by looking at the market or by looking at our historical debt issuances.


Exercises
  1. What's the cost of debt if the company has $20 million in 20-year debt that pays 11% and they are in the 40% tax bracket?
  2. What's the cost of debt if the company has $50 million in 10-year debt that pays 6% and they are in the 40% tax bracket?

Source: https://2012books.lardbucket.org/books/finance-for-managers/s12-02-cost-of-debt.html
Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.

Cost of Preferred Stock

Learning Objectives
  1. Understand the components of preferred stock.
  2. Explain how preferred stock is a part of the weighted average cost of capital.

Preferred stock dividends are not tax deductible to the company who issues them. Preferred stock dividends are paid out of after-tax cash flows so there is no tax adjustment for the issuing company.

When investors buy preferred stock they expect to earn a certain return. The return they expect to earn on preferred stock is denoted r_{ps}.

D_{ps} is the dividend from preferred stock, P_{ps} is the price of preferred stock.


Worked Example: Falcons Footwear

Falcons Footwear has 2 million shares of preferred stock selling for $85/share. Its annual dividend is $7.50. What's the r_{ps}?

Typically the cost of preferred stock is higher than the after-tax cost of debt. This is because of both the tax deductibility of interest and the fact that preferred stock is riskier than debt.

Key Takeaways
  • Preferred stock is a hybrid security - it's both debt and equity.
  • Preferred stock return is calculated as its dividend divided by its price.

Exercises
  1. Calculate the component cost of preferred stock given the following: Company A has $10 million in preferred stock selling for $100 each and pays a dividend of $7.80. What's the r_{ps}?
  2. Why is there no tax-adjustment made to our calculation of preferred stock?

Cost of Common Stock

Learning Objectives
  1. Understand the components of common stock.
  2. Explain how common stock is a part of the weighted average cost of capital.

New stock issues (IPOs) gain many headlines, as such companies are usually growing fast and require a large influx of capital. Secondary issues don't get as much press, but are also a sign that companies are raising capital. But these are actually not the most common way of raising equity financing!

Because dividends are not required to be increased (or even paid!) when a company is doing well, the company can instead retain excess earnings and reinvest them (hence the item on the balance sheet). Most capital is raised through reinvesting earnings, instead of through issuing new stock, because issuing new stock incurs flotation costs. We will assume that the cost to the firm, r_{s}, is the same.

The cost of equity is the most difficult source of capital to value properly. We will present three basic methods to calculate r_{s}: the Dividend Discount Model (DDM), the Capital Asset Pricing Model (CAPM), and the Debt plus Risk Premium Model (D+RP).

 

Using the Dividend Discount Model (DDM)

In Chapter 10 "Stock Valuation", we explored the DDM model.

P{0} is the price of the share of stock now, D_{1} is our expected next dividend, r_{s} is the required return on common stock and g is the growth rate of the dividends of common stock. This model assumes that the value of a share of stock equals the present value of all future dividends (which grow at a constant rate). This equation states that the cost of stock equals the dividend expected at the end of year one divided by the current price (dividend yield) plus the growth rate of the dividend (capital gains yield).

 

Worked Example: Falcons FootwearConstant Growth to calculate r_{s}

Falcons Footwear has 12 million shares of common stock. The stock is currently selling for $60/share. It pays a dividend of $3 this year and the dividend is growing at 4%. What is r_{s}?

First, we must calculate D{1}. D{1} = D{0}*(1+g) = $3*(1+.04) = $3.12

If our stock isn't currently paying dividends, then the equation reduces to our capital gains yield, which should be proportional to our expected long term growth rate.

 

Using the Capital Asset Pricing Model (CAPM)

We learned that the Capital Asset Pricing Model (CAPM) was a relationship between the return for a given stock and the nondiversifiable risk for that stock using beta (β).

Required return on stock = risk free rate + (market risk premium)*(Beta of stock)

r_{s} = R{F} + [R{M} − R{F}] × β

Equation 12.6 Market Risk Premium

market risk premium = expected market return − risk free rate

Where RF is the risk free rate, RM is the market return or the return on the market portfolio and β is beta. If our company has yet to issue stock, then beta will need to be estimated (perhaps by looking at a public competitor's).

 

Worked Example: Falcons Footwear - CAPM to calculate r_{s}

Falcons Footwear wants to calculate rs using the CAPM. They estimate the risk free rate (RF) to be 4%. The firm's beta is 1.3 and the market return is 9%.

r_{s} = 0.04 + [0.09 − 0.04] * (1.3) = 0.105 = 10.5%

 

Using the Debt plus Risk Premium Model (D+RP)

If we know that, historically, our stock has traded at a particular premium to our cost of debt, we can use that relationship to estimate our cost of equity. If our stock isn't publically traded, we can estimate based upon competitors or industry averages.

r_{s} = r_{d} + \text{Risk Premium}

Worked Example: Falcons Footwear - D+RP to calculate r_{s}

We know that current Falcons Footwear bonds are yielding 7%. If we know that comparable companies have cost of equity about 4% higher than their cost of debt, what is a good estimate of Falcons Footwear's cost of equity?

r_{s} = 0.07 + 0.04 = 0.11 = 11%

 

Which Method Is Best?

Each method has its strengths and weaknesses, and all are subject to the quality of the inputs. DDM is very sensitive to the estimation of the growth rate. CAPM depends upon an accurate estimate of the firm's beta. D+RP assumes that the risk premium is accurate.

Often, the best method is to calculate all three results and make an informed judgment based on the results. If one result varies wildly from the other two, perhaps it is best omitted. Estimating the cost of equity is one of the most difficult tasks in finance, and it can end up being equal parts art and science.

 

Final Thoughts on r_{s}

  1. If a firm's only investors were common stockholders, then the cost of capital would be the required rate of return on equity.
  2. The cost of retained earnings is the same as r_{s}.
  3. Tax implications of common stock are also large. The dividends issued by the company are not tax deductible (just like preferred stock dividends), and the company bears the full cost.
Key Takeaways
  • The cost of common stock can be calculated either using the constant growth model or using CAPM.
  • The cost of using retained earnings is assumed to be the same as r_{s}.

Exercises

  1. Calculate r_{s} using CAPM given the following:

    R_{F} = 5%, R_{M} = 4%, b = 1.4

  2. Calculate r_{s} using Constant Growth Model given the following:

    D1 = $5, Selling price is $35, Dividend is growing at 2%.