The company is financed entirely by equity and there are 1 000 000 shares in issue, each with a market value of $3.35 ex div.
Required
(a) What is the cost of equity?
(b) What implications does dividend growth appear to have for earnings retentions?
Solution
The dividend growth model will be used. The dividend per share in the current year is $262 350/1 000 000
= $0.26235.
(a) Growth in past dividends
Dividends have risen from $150 000 in 20X1 to $262 350 in 20X5. The increase represents four years growth. (Check that you are aware that there are four years' growth, and not five years' growth, in the table.)
The average growth rate, g, may be calculated as follows:
Dividend in 20X1 ×(1 g)+ 4 = Dividend in 20X5
The growth rate over the last four years is assumed to be expected by shareholders into the indefinite future, so the cost of equity, Ke, is:
P g
Retained profits will earn a certain rate of return and so growth in dividends will come from the yield on the retained funds.
It might be assumed that g = bR where b is the yield on new investments and R is the proportion of profits retained for reinvestment.
In our example, if dividends continue to grow at the same rate as previously the future annual growth rate would be 15 per cent.
If this is due to the retention and reinvestment policy, then g = 0.15 = bR
If we assume that the rate of return on new investments averages 24% (which is the cost of equity and hence the return shareholders require from projects) and if the proportion of earnings retained is 62.5% (which it has been, approximately, in the period 20X1 – 20X5) then
g = bR = 24% × 62.5% = 15%.
A change in the level of earnings retained or the return on reinvested earnings would result in a different future growth rate.
Question 2: Cost of equity with dividend growth
The current market price of Conrad Co's shares is $3.50. It has just paid a dividend of 35c.
Conrad has consistently applied a dividend payout policy of 1/3 earnings. It makes an average return on investment of 15%. Estimate Conrad’s cost of equity.
(The answer is at the end of the chapter)
2.5 Weaknesses of the dividend growth model
(a) The model does not incorporate risk.
(b) Dividends do not grow smoothly in reality, so g is only an approximation.
(c) The model fails to take capital gains into account, however it is argued that a change of share ownership does not affect the present value of the dividend stream.
(d) No allowance is made for the effects of taxation although the model can be modified to incorporate tax.
(e) It assumes there are no issue costs for new shares.
2.6 Private companies and the cost of equity
The cost of capital cannot be calculated from market values for private companies in the way that has been described so far, because the shares in a private company do not have a quoted market price. Since private companies do not have a cost of equity that can be readily estimated, it follows that a big problem for private companies which want to use DCF for evaluating investment projects is how to select a cost of capital for a discount rate.
Suitable approaches might be: to estimate the cost of capital for similar public companies, but then add a further premium for additional business and financial risk; or to build up a cost of capital by adding estimated premiums for business risk and financial risk to the risk-free rate of return.
3 The cost of preference share capital
Section overview
• The cost of preference share capital is the return an enterprise must pay to the investors.
• For preference shares, this is the annual dividend as a percentage of the ex-div market value of the shares.
For preference shares the future cash flows are the dividend payments in perpetuity so that:
P0 = 3
where: P0 is the current market price of preference share capital after payment of the current dividend d is the dividend received.
kpref is the cost of preference share capital.
3....
This can be rearranged to find the cost of preference share capital:
Formula to learn
The cost of preference shares can be calculated as kpref = P
4 The cost of debt capital
Section overview
• The cost of debt is the return an enterprise must pay to its lenders. Debt is cheaper than equity or preference share capital because the interest payments attract tax relief. So actual the cost to the company is the after-tax cost.
• For irredeemable debt (or preference shares), this is the (post-tax) interest as a percentage of the ex int/div market value of the loan stock.
• For redeemable debt, the cost is given by the internal rate of return of the cash flows involved.
The same technique is used to calculate either the pre-tax or the post-tax cost of redeemable debt.
Only the interest payments attract tax relief.
4.1 Cost of irredeemable debt
Estimating the cost of fixed interest or fixed dividend capital is much easier than estimating the cost of ordinary share capital, because the amount received by the holder of the security in the form of interest or dividends is fixed by contract and will not fluctuate.
The cost of debt capital already issued is the rate of interest (the internal rate of return) which equates the current market price with the discounted future cash receipts from the security.
Ignoring taxation for the moment, in the case of irredeemable debt the future cash flows are the interest payments in perpetuity so that:
Formula to learn
P0 I
=Kb where:
P0 is the current market price of debt capital after payment of the current interest.
I is the annual interest.
Kb is the required return of the providers of debt capital.
This formula can be re-arranged:
0
b P
K = I
4.2 Cost of redeemable debt or redeemable preference shares
If the debt is redeemable, then in the year of redemption the interest payment will be received by the investor/lender as well as the amount payable on redemption, so:
Formula to learn
where Pn = the amount payable on redemption in year n.
The above equation cannot be simplified so 'Kb' will have to be calculated by trial and error, as an internal return of return (IRR) for the cash flows (using the method introduced in Chapter 2).
LO
The best trial and error figure to start with in calculating the cost of redeemable debt is to take the cost of debt capital as if it were irredeemable and then add the annualised capital profit that will be made from the present time to the time of redemption.