(162)---THE DIVIDEND GROWTH MODEL: NORMAL GROWTH

The Dividend Growth Model: Normal Growth

The dividend valuation model for a firm whose dividends are expected to grow at a consistent rate of growth (g) is as follows:

Po = DIV 1 / (Ke-g)

Where DIV1 = DIVo (1+g)
Equation can be solved for calculating the cost of equity Ke as follows:

Ke = (DIV 1 / Po) + g

The cost of equity is, thus, equal to the expected dividend yield (DIV1 /Po) plus capital gains as reflected by expected growth in dividends (g). It may be noted that equation is based on following assumptions.

• The market price of the ordinary share, Po, is a function of expected dividends.
• The dividend, DIV 1, is positive
• The dividends grow at a consistent growth rate g, and the growth rate is equal to the return on equity, ROE, times the retention ration, b (g = ROE x b)
• The dividend payout ration is consistent.

The cost of retained earnings determined by the dividend valuation model implies that if the firm would have distributed earnings to shareholders, they could have invested it in the shares of the firm or in the shares of other firms of similar risk at the market price (Po) to earn a rate of return equal to Ke. Thus, the firm should earn a return on retained funds equal to Ke to ensure growth of dividends and share price. If a return less than Ke is earned on returned earnings, the market price of the firm’s share will fall. It may be emphasized again that the cost of returned earnings will be equal to the shareholders’ required rate of return since no flotation costs are involved.

(161)---COST OF CAPITAL: THE DIVIDEND GROWTH MODEL

Cost of Capital: The Dividend Growth Model

A firm’s internal equity consists of its retained earnings. The opportunity cost of the retained earnings is the rate of return foregone by equity shareholders. The shareholders generally expect dividend and capital gain from their investment. The required rate of return of shareholders can be determined from the dividend valuation model.

There are two main costs are there

1. Internal cost of equity (reserves)
2. External cost of equity (new share issues)

So we can use three types of models for calculating cost of equity using dividend growth model.

1. Normal growth
2. Super normal growth
3. Zero growth

(160)---COST OF EQUITY

Cost of Equity

Is equity capital free of cost?

It is sometimes argued that the equity capital is free of cost. The reason for such argument is that it is not legally binding for firms to pay dividends to ordinary shareholders. Further, unlike the interest rate or preference dividend rate, the equity dividend rate is not fixed. It is fallacious to assume equity capital to be free of cost. As we have discussed earlier, equity capital involves an opportunity cost; ordinary shareholders supply funds to the firm in the expectation of dividends and capital gains commensurate with their risk of investment. The market value of the shares determined by the demand and supply forces in a well functioning capital market reflects the return required by ordinary shareholders. Thus, the shareholders’ required rate of return, which equates the present value of the expected dividends with the market value of the share, is the cost of equity. The cost of external equity would, however, be more than the shareholders’ required rate of return if the issue prize where difference from the market price of the shares.

In practice, it is a formidable task to measure the cost of equity. The difficulty bribes from two factors;

1. It is very difficult to estimate the expected dividends.
2. The future earnings and dividends are expected to grow overtime.

Growth in dividends should be estimated and incorporated in the computation of the cost of equity. The estimation of growth is not an easy task. Keeping these difficulties in mind, the methods of computation the cost of internal and external equity are discussed next posts.

(159)---COST OF EQUITY CAPITAL

Cost of Equity Capital

Firms may raise equity capital internally by retaining earnings. Alternatively, they could distribute the entire earnings to equity shareholders and raise equity capital externally by issuing new shares. In both cases, shareholders are providing funds to the firms to finance their capital expenditures. Therefore, the equity shareholders’ required rate of return would be the same whether they supply funds by purchasing new shares or by foregoing dividends, which could have been distributed to them. There is, however, a difference between retained earnings and issue of equity shares from the firm’s point of view. The firm may have to issue new shares at a price lower than the current market price. Also, it may have to incur flotation costs. Thus, external equity will cost more to the firm than the internal equity.

(158)---COST OF PREFERENCE SHARE CAPITAL

Cost of Preference Share Capital

Irredeemable Preference Share

The preference share may be treated as a perpetual security if it is irredeemable. Thus, its cost is given by the following equation:

Kp = PDIV/P0

Where Kp is the cost of preference share, PDIV is the expected preference dividend, and P0 is the issue price of preference share.

Redeemable Preference Share

Redeemable preference share (that is preference shares with finite maturity) are also issued in practice. A formula similar to above equation can be used to compute the cost of redeemable preference share:

Kp =(PDIV1 /(1+Kp)1) + (PDIV2 /(1+Kp)2) + ----------- + (PDIVn /(1+Kp)n) + (Pn/ (1+Kp)n)

The cost of preference share is not adjusted for taxes because preference dividend is paid after the corporate taxes have been paid. Preference dividends do not save any taxes. Thus, the cost of preference share is automatically computed on an after tax basis. Since interest is tax deductible and preference dividend is not, the after tax cost of preference is substantially higher than the after tax cost of debt.

(157)---COST OF PREFERENCE CAPITAL

Cost of Preference Capital

The measurement of the cost of preference capital poses some conceptual difficulty. In the case of debt, there is a binding legal obligation on the firm to pay interest, and the interest constitutes the basis to calculate the cost of debt. However, in the case of preference capital, payment of dividends is not legally binding on the firm and even if the dividends are paid, it is not a charge on earnings; rather it is a distribution or appropriation of earnings to preference shareholders. One may, therefore, be tempted to conclude that the dividends on preference capital do not constitute cost. This is not true.

The cost of preference capital is a function of the dividend expected by investors. Preference capital is never issued with an intention not to pay dividends. Although it is not legally binding upon the firm to pay dividends on preference capital, yet it is generally paid when the firm makes sufficient profits. The failure to pay dividends, although does not case bankruptcy, yet it can be a serious matter from the ordinary shareholder’ point of view. The non payment of dividends on preference capital may result in voting rights and control to the preference shareholders. More than this, the firm’s credit standing may be damaged. The accumulation of preference dividend errors may adversely affect the prospects of ordinary shareholders for receiving any dividends, because dividends on preference capital represent a prior claim on profits. As a consequence, the firm may find difficulty in raising funds by issuing preference or equity shares. Also, the market value of the equity shares can be adversely affected if dividends are not paid to the preference shareholders and therefore, to the equity shareholders. For these reasons, dividends on preference capital should be paid regularly except when the firm does not make profits, or it is in a very tight cash position.

(156)---COST OF CAPITAL - COST OF EXISTING DEBT

Cost of Capital – Cost of Existing Debt

Sometime a firm may like to compute the “current” cost of its existing debt. In such a case, the cost of debt should be approximate by the current market yield of the debt.

Suppose that a firm has 11% debentures of 100000$ (100$ face value) outstanding at 31st December 20x1 to be matured on December 31st 20x6. If a new issue of debentures could be sold at a net realized price of 80$ in the beginning of 20x2, the cost of the existing debt, using short cut method, will be

Kd = (11 + 1/5 (100-80)) / (1/2 (100+80)) = 15/90 =0.167 = 16.7%

If tax rate (T) = 0.35, the after cost of debt will be:

Kd (1-T) = 0.167(1-0.35) = 0.109 = 10.9%

(155)---COST OF CAPITAL - COST OF DEBT TAX ADJUSTMENT

Cost of Capital – Cost of Debt Tax Adjustment

The Interest paid on debts is tax deductible. The higher the interest charges, the lower will be the amount of tax payable by the firm this implies that the government indirectly pays a part of the lender’s required rate of return. As a result of the interest tax shield, the after tax cost of debt to the firm will be substantially less than the investor’s required rate of return. The before tax cost of debt, Kd should, therefore be adjusted for the tax effect as followers:

After tax cost of debt = Kd (1-T)

Where T is corporate tax rate. If the before tax cost of bond in our example is 16.6%, and the corporate tax rate is 35% the after tax cost of bond will be:

Kd = 0.165 (1-0.35) =0.1073 = 10.73%

It should be noted that the tax benefit of interest deductible would be available only when the firm is profitable and is paying taxes. And unprofitable firm is not required to pay any taxes. It would not gain any tax benefit associated with the payment of interest, and its true cost of debt is the before tax cost.

It is important to remember that in the calculation of the average cost of capital, the after tax cost of debt must be used not the before tax cost of debt.

(154)---COST OF CAPITAL - DEBT ISSUED AT DISCOUNT OR PREMIUM

Cost of Capital – Debt Issued at Discount or Premium

Calculate the cost of capital using equation given below,

Bo = (INT1 /(1+Kd)1) + (INT2 / (1+Kd)2)----------------------------(INTn / (1+Kd)n) + (Bn / (1+Kd)n

Where Bn is repayment of debt on maturity and other variables as define earlier post.

Calculate the cost of capital of debt whether debt is issued at discount or premium the following equation can be used,

Kd = (INT + 1/n (F-Bo)) / (1/2 (F+Bo))

It should be clear from the preceding discussion that the before tax cost of bond to the firm is affected by the issue price. The lower the issue price, the higher will be the before tax cost of debt. The highly successful companies may sell bond or debentures at a premium, this will pull down the before tax cost of debt.

(153)---COST OF CAPITAL - DEBT ISSUED AT PAR

Cost of Capital - Debt Issued at Par

The before tax cost of debt is the rate of return required by lenders. It is easy to compute before tax cost of debt issued and to be redeemed at par,

It is simple equal to the conceptual of interest.

For example, a company decides to sell a new issue of 7 year 15% bonds of 100$ each at par. If the company realizes the full face value of 100$ bond and will pay 100$ principle to bondholders at maturity, the before tax cost of debt will simply be equal to the rate of interest of 15$. Thus:

Kd =i = Interest / Bo

Where Kd is the before tax cost of debt, i is the coupon rate of interest, Bo is the issue price of the bond and in equation it is assumed to be equal to the face value, and interest is the amount of interest. The amount of interest payable to the lender is always equal to:

Interest = Face value of debt X Interest rate

(152)---COST OF DEBT

Cost of Debt

A company may raise debt in a variety of ways, it may borrow funds from financial institutions or public either in the form of public deposits or debentures (bonds) for a specified period of time at a certain rate of interest. A debenture or bond may be issued at par or at a discount or premium as compared to its face value. The contractual rate of interest or the coupon rate forms the basis for calculating the cost of debt.

See our next post for calculating below points

• Debt issued at par
• Debt issued at discount or premium
• Tax adjustment for cost of debt
• Calculating cost of the existing debt

(151)---DETERMINING COMPONENT COSTS OF CAPITAL

Determining Component Costs of Capital

Generally, the component cost of a specific source of capital is equal to the investors’ required rate of return, and it can be determined by using equation present above post. But the investors’ required rate of return should be adjusted for taxes in practice for calculating the cost of a specific source of capital to the firm. In the investment analysis, net cash flows are computed on an after tax basis, therefore, the component costs, used to determine the discount rate, should also be expressed on an after tax basis.

In our next posts we covered,

• Cost of debt
• Cost of equity capital
• Cost of preference capital
• Weighted average cost of capital

(150)---FORMULA FOR THE OPPORTUNITY COST OF CAPITAL

Formula for the Opportunity Cost of Capital

The required rates of return are market-determined. They are established in the capital markets by the actions of competing investors. The influence of market is direct in the case of new issue of ordinary and preference shares and debt.


The market price of securities is a function of the return expected by investors. The demand and supply force in such a way that equilibrium rates are established for various securities. Thus opportunity cost of capital is given by the following formula,






Where Io is the capital supplied by investors in period 0 (it represents a net cash inflows to the firm) Ct are returns expected by investors (they represent cash outflows to the firm) and k is the required rate of return or the cost of capital.

(149)---RISK DIFFERENCES IN SHAREHOLDERS AND CREDITORS CLAIMS

Risk Differences in Shareholders’ and Creditors’ Claims

Investors will require different rates of return on various securities since they have risk differences. Higher the risk of a security, the higher the rate of return demanded by investors. Since ordinary share is most risky, investors will require highest rate of return on their investment in ordinary shares. Preference share is more risky than debt; therefore, its required rate of return will be higher than that debt. The risk return relationship for various securities is shown in above figure,

It may be observed in the figure that the required rate of any security is composed of two rates a risk free rate and risk premium. A risk free will require compensation for time value and its risk premium will be zero. Government securities, such as the treasury bills and bonds, are examples of the risk free securities. Investors expect higher rates of return on risky securities. The higher then risk of a security, the higher will be its risk premium, and therefore, a higher required rate of return.

Since the firm sells various securities to investors to raise capital for financing investment projects, it is necessary that investment projects to be undertaken by the firm should generate at least sufficient net cash flow to pay investors’ shareholders and debt holders their required rates of return. In fact, investment projects should yield more cash flows than to just satisfy the investors’ expectations in order to make a net contribution to the wealth of ordinary shareholders.

Viewed from all investor’s point of view, the firm’s cost of capital is the rate of return required by them for supplying capital for financing the firm’s investment projects by purchasing various securities. It may be emphasized that the rate of return required by all investors will be an overall rate of return a weighted rate of return. Thus, the firm’s cost of capital is the “average” of the opportunity costs of various securities, which have claims on the firm’s assets. This rate reflects both the business risk and financial risk resulting from debt capital. Recall that the cost of capital of an all equity financed firm is simply equal to the ordinary shareholders’ required rate of return, which reflects only the business risk.

(148)---CREDITORS CLAIMS AND OPPERTUNITIES

Creditors’ Claims and opportunities

In practice, both shareholders and creditors supply funds to finance a firm’s investment projects. Investors hold different claims on the firm’s assets and cash flows, and thus, they are exposed to different degrees of risk.

Creditors have a priority claim over the firm’s assets and cash flows. The firm is under a legal obligation to pay interest and repay principal. Debt holders are, however, exposed to the risk default. Since the firm’s cash flows are uncertain, there is a probability that it may default on its obligation to pay interest and principle.

Preference shareholders hold claim prior to ordinary shareholders but after debt holders. Preference dividend is fixed and known, and the firm will pay it after paying interest but before paying any ordinary dividend. Because preference dividend is subordinated to interest, preference capital is more risky than debt.

Ordinary shareholders supply capital either in the form of retained earnings or by purchasing new shares. Unlike creditors, they are owners of the firm and retain its control. They delegate powers to management to make investment decisions on their behalf in such a way that their wealth is maximized. However, ordinary shareholders have claim on the residual assets and cash flows. The payment of ordinary dividend is discretionary.

Ordinary shareholders may be paid dividends from cash remaining after interest and preference dividends have been paid. Also, the market price of ordinary share fluctuates more widely than that of the preference share and debt.

Thus, ordinary share is more risky than both preference share and debt. Various forms of corporate debt can also be distinguished in terms of their differential riskiness. If we compare corporate bonds and government bonds, the later are less risky since it is very unlikely that the government will default in its obligation to pay interest and principal.