 By Yuriy Smirnov Ph.D.

## Definition

The cost of common stock is common stockholders’ required rate of return. Companies can raise new common equity in two ways: by a new common stock issue or by retaining and reinvesting previous earnings. Three approaches are usually employed to assess the required rate of return:

1. Dividend discount model or DMM
2. Capital asset pricing model or CAPM
3. Bond yield plus risk premium approach

These techniques are not mutually exclusive and can be used simultaneously to get an average assessment.

## Dividend discount model – DMM

The price of a common stock can be determined as the present value of all future cash flows in the form of a dividend. In general, the equation can be written as

 P0 = D1 + D2 + … + Dn (1 + rs)1 (1 + rs)2 (1 + rs)n

where D1, D2 … Dn are expected dividends, P0 is the current market price of the stock, and rs is the required rate of return.

If a company pays dividends for the lifetime of a stock and dividends grow at a constant rate, the formula above may be modified as

 P0 = D0 × (1 + g) = D1 rs - g rs - g

where D0 is the last actual dividend paid, D1 is the expected dividend, and g is the dividend’s growth rate.

Knowing the current market price of a stock and the last dividend paid, we can calculate the required rate of return, which is equal to the cost of common stock.

To estimate a dividend’s growth rate, we can use the formula below

g = Retention Rate × ROE

where ROE is the return on equity ratio.

If a company is going to raise capital by issuing new stock, we should take into account the flotation costs when estimating the cost of common stock

where F is a flotation cost.

## Capital assets pricing model – CAPM

The cost of common stock can be estimated using the capital assets pricing model or CAPM

rs = rRF + β × (rM - rRF)

where rRF is the risk-free rate, β is the beta coefficient of a stock, and rM is the expected market return.

## Bond yield plus risk premium approach

For a rough estimate of the cost of common stock, a company’s own bond yield can be employed plus the risk premium (RP) approach:

rs = Bond Yield + RP

The key assumption is that the cost of equity is always higher than the cost of debt within the same company. This derives from the fact that equity investments are always riskier than investments in debt instruments of the same company.

The risk premium can be assessed as a historical spread between bond yield and stock yield. Empirical studies suggest that the risk premium is usually between 3% and 5%.

## Examples

### Example 1

Company A intends to carry out a new stock issue to raise financing for a new project. The current market price of a stock is \$13.65, the last dividends paid are \$1.5 per share, the historical dividends’ growth rate is 3%, and floatation costs are 5%.

To estimate the cost of common stock issue, we use the dividend discount model.

D1 = D0 × (1 + g) = \$1.5 × (1 + 0.03) = \$1.545

 rs = D1 + g = \$1.545 = 11.914% P0 × (1 – F) \$13.65 × (1 -0.05)

### Example 2

Three companies have a different beta coefficient:

• Company A has 0.89
• Company B has 1.2
• Company C has 1.67

To estimate their cost of common stock, we should employ the CAPM model. Assume that the risk-free rate is 2.75% and the expected market return rate is 14.7%.

rs of Company A = 2.75 + 0.89 × (14.7 - 2.75) = 13.386%

rs of Company B = 2.75 + 1.2 × (14.7 - 2.75) = 17.09%

rs of Company C = 2.75 + 1.67 × (14.7 - 2.75) = 22.707%

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