Cost Of New Common Stock

This is "Cost of Common Stock", section 12.4 from the book Finance for Managers (v. 0.1). For details on it (including licensing), click here.

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12.4 Toll of Mutual Stock

Please Note: This book is currently in draft form; material is not final.

Learning Objectives

1. Understand the components of common stock.
2. Explain how common stock is a office of the weighted average cost of capital letter.

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

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

The cost of equity is the nigh difficult source of capital to value properly. We will present 3 bones methods to calculate r_south: the Dividend Discount Model (DDM), the Capital letter Asset Pricing Model (CAPM), and the Debt plus Risk Premium Model (D+RP).

Using the Dividend Disbelieve Model (DDM)

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

Equation 12.4 Toll of Common Stock

$$r_s=\frac{{\text{D}}_{\mathrm{ane}}}{{\text{P}}_0}+\text{ g}$$

P₀ is the price of the share of stock now, D_one 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 charge per unit). This equation states that the cost of stock equals the dividend expected at the stop of twelvemonth one divided by the electric current price (dividend yield) plus the growth rate of the dividend (capital gains yield).

Worked Example: Falcons Footwear—Constant Growth to calculate r_s

Falcons Footwear has 12 meg shares of common stock. The stock is currently selling for $60/share. Information technology pays a dividend of $three this year and the dividend is growing at four%. What is r_{due south}?

First nosotros must calculate D_i. D_i = D₀*(1+g) = $3*(1+.04) = $3.12

$$r_{\mathrm{due\; south}}=\frac{{\text{D}}_1}{{\text{P}}_0}+\text{ g}=\frac{\$3.12}{\$60}+0.04=0.52+0.04=0.092=\mathrm{ix.2}\%$$

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

Using the Capital Asset Pricing Model (CAPM)

Nosotros learned that the Capital Nugget Pricing Model (CAPM) was a relationship between the render for a given stock and the nondiversifiable risk for that stock using beta (β). The basic equation (from Chapter 11 "Assessing Adventure") is:

Equation 12.5 CAPM Equation

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

r _s = R_F + [R_Yard − R_F] × β

Equation 12.vi Market Risk Premium

market hazard premium = expected marketplace return − take a chance free rate

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

Worked Example: Falcons Footwear—CAPM to summate r_s

Falcons Footwear wants to calculate r_s using the CAPM. They estimate the hazard gratuitous charge per unit (R_F) to be 4%. The firm'due south beta is ane.three and the market return is 9%.

r _s = 0.04 + [0.09 − 0.04] * (1.3) = 0.105 = 10.5%

Using the Debt plus Take a chance 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 price of equity. If our stock isn't publically traded, nosotros tin can estimate based upon competitors or manufacture averages.

r _southward = r _d + Risk Premium

Worked Example: Falcons Footwear—D+RP to summate r_s

We know that current Falcons Footwear bonds are yielding vii%. If nosotros know that comperable companies have cost of equity well-nigh 4% higher than their price of debt, what is a good estimate of Falcons Footwear'southward cost of equity?

r _s = 0.07 + 0.04 = 0.11 = eleven%

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 authentic estimate of the firm'due south beta. D+RP assumes that the risk premium is accurate.

Frequently, the best method is to calculate all three results and make an informed judgment based on the results. If i event varies wildly from the other two, perhaps information technology is all-time omitted. Estimating the cost of equity is one of the most hard tasks in finance, and it tin end up being equal parts art and science.

Final Thoughts on r_s

1. If a business firm's only investors were common stockholders, then the price of capital would be the required rate of return on equity.
2. The price of retained earnings is the same as r_south.
3. Revenue enhancement implications of common stock are too big. The dividends issued by the company are not revenue enhancement deductible (just like preferred stock dividends), and the visitor bears the full toll.

Key Takeaways

• The toll of common stock can be calculated either using the abiding growth model or using CAPM.
• The cost of using retained earnings is assumed to be the same as r_s.

Exercises

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

   R_F = v%, R_M = iv%, b = 1.iv

2. Summate r_south using Abiding Growth Model given the following:

   D1 = $five, Selling price is $35, Dividend is growing at ii%.

Cost Of New Common Stock,

Source: https://2012books.lardbucket.org/books/finance-for-managers/s12-04-cost-of-common-stock.html

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