Introduction
When a company uses the NPV method in relation to investment appraisal it needs to discount the expected cash flows of the project at its cost of capital. This chapter considers how the company can determine the cost of its various sources of equity and debt finance and whether the resulting weighted average cost of capital is an appropriate discount rate for investment appraisal purposes.
Before you begin
If you have studied these topics before, you may wonder whether you need to study this chapter in full. If this is the case, please attempt the questions below, which cover some of the key subjects in the area.
If you answer all these questions successfully, you probably have a reasonably detailed knowledge of the subject matter, but you should still skim through the chapter to ensure that you are familiar with everything covered.
There are references in brackets indicating where in the chapter you can find the information, and you will also find a commentary at the back of the Study Manual.
1 What is an investor’s required return based on? (Section 1)
2 What does the dividend valuation model (DVM) state? (Section 2.2)
3 Name two methods of estimating dividend growth. (Section 2.4)
4 A company's share price is $1.50. It has just paid a dividend of 20c. Dividends (Section 2.3) are expected to grow at 6 per cent per annum. Calculate the company’s cost
of equity.
5 What is the difference between the required return of a debenture holder and
the cost of that debenture to the company? (Section 4.3)
6 How would you calculate the cost of debt for a redeemable debenture? (Section 4.3.2) 7 What assumptions are made when Weighted Average Cost of Capital (WACC) (Section 5.1)
is used as a discount rate?
8 What is the general formula for calculating the WACC? (Section 5.2)
1 What is the cost of capital?
Section overview
• The cost of capital is the rate of return that a business must pay to satisfy the providers of funds, and it reflects the riskiness of the funding transaction.
• The cost of capital can be measured by studying the returns required by investors, and then used to derive a discount rate for DCF analysis and investment appraisal.
• The investor’s required return from a particular company will reflect the risk free rate of return plus an additional premium for both business and financial risk. Therefore, the cost of capital applied to one company may differ radically from the cost of capital of another.
When a company evaluates an investment, and possibly decides how the investment should be financed if it goes ahead, it might carry out a DCF analysis and estimate the NPV of the project. Calculating an NPV involves discounting future cash flows at a cost of capital (see Chapter 2).
To do this, the company must first of all establish what its cost of capital is.
Definition
The cost of capital has two aspects to it:
(a) It is the cost of funds that a company raises and uses.
(b) It is also the return that investors expect to be paid for putting funds into the company. It is therefore the minimum return that a company should make on its own investments, to earn the cash flows out of which investors can be paid their return.
The cost of capital can therefore be measured by studying the returns required by investors, and then used to derive a discount rate for DCF analysis and investment appraisal.
1.1 The cost of capital as an opportunity cost of finance
The cost of capital, however it is measured, is an opportunity cost of finance, because it is the minimum return that investors require. If they do not get this return, they will transfer some or all of their investment somewhere else. Here are two examples:
(a) If a bank offers to lend money to a company, the interest rate it charges is the yield that the bank wants to receive from investing in the company, because it can get just as good a return from lending the money to someone else. In other words, the interest rate is the opportunity cost of lending for the bank.
(b) When shareholders invest in a company, the returns that they can expect must be sufficient to persuade them not to sell some or all of their shares and invest the money somewhere else. The yield on the shares is therefore the opportunity cost to the shareholders of not investing
somewhere else.
1.2 The cost of capital and risk
The cost of capital has three elements. It consists of a premium over a risk-free rate to compensate the investor for the business risk and for the finance risk in the investment.
(c) The premium for financial risk relates to the danger of high debt levels (high gearing). For ordinary shareholders, financial risk is evident in the variability of earnings after deducting payments to holders of debt capital. The higher the gearing of a company's capital structure, the greater will be the financial risk to ordinary shareholders, and this should be reflected in a higher risk premium and therefore a higher cost of capital.
Because different companies are in different types of business (varying business risk) and have different capital structures (varying financial risk) the cost of capital applied to one company may differ radically from the cost of capital of another.
1.3 The costs of different sources of finance
Where a company uses a mix of equity and debt capital, its overall cost of capital might be taken to be the weighted average of the cost of each type of capital. The weighted average cost of capital, and whether it is the appropriate cost of capital to use, is considered later. First of all, we must look at the cost of each separate source of capital: equity, preference shares and forms of debt capital.
2 The cost of equity capital
Section overview
• The 'fundamental theory of share values' states that the market price of a share is the present value of the expected future revenue cash flows from the share, discounted at the cost of equity capital.
• The dividend valuation model can be used to estimate a cost of equity, on the assumption that the market value of shares is directly related to the expected future dividends on the shares.
• Expected growth in dividends can be allowed for in calculating a cost of equity, using Gordon's growth model.
• Growth can be estimated either by extrapolating past dividend growth or by considering the company’s retention and reinvestment policy.
2.1 Sources of equity finance
New funds from equity shareholders are obtained either from new issues of shares or from cash deriving from retained earnings (see Chapter 4). Both of these sources of funds have a cost. Shareholders will not be prepared to provide funds for a new issue of shares unless the return on their investment is sufficiently attractive. Retained earnings also have a cost. This is an opportunity cost of the dividend forgone by shareholders. This is discussed further in Chapter 8.
Shareholders put a value on their shares. In the case of shares traded on a stock market, this value is represented by the market price of the shares. The market price shows how much investors are currently willing to pay for the shares, in return for the future benefits they expect to obtain. Shareholders may measure their income stream in terms of a dividend payout ratio, which is simply the proportion of total post-tax profits that is paid out in total as a dividend (for example, if profits are $100 000 and $25 000 in total is paid out in dividends the dividend payout ratio is 25 per cent).
2.2 The dividend valuation model
Definition
The 'fundamental theory of share values' states that the market price of a share is the present value of the expected future revenue cash flows from the share, discounted at the cost of equity capital.
LO 4.4
The cost of equity, both for new issues and retained earnings, could be estimated by means of a dividend valuation model (DVM), on the assumption that the market value of shares is directly related to expected future dividends on the shares.
Formula to learn
If the future annual dividend per share (D1) is expected to be constant in amount 'in perpetuity', the share price (P0) can be calculated by the following formula:
P0
=
r D1
where ris the shareholders' required return (cost of equity), expressed as a proportion (e.g. 12% = 0.12).
The share price is 'ex dividend', which means that it excludes the value of any current dividend that has just been paid or is currently payable. The next annual dividend is receivable in one year's time.
The share price is the present value of a constant annual dividend forever, i.e. in perpetuity. The mathematical formula is quite simple because the PV of a constant annual cash flow $C in perpetuity, discounted at a cost of capital r, is $C/r.
Formula to learn
Re-arranging this formula, we get a formula for the cost of equity.
Ke =
0 1
P D
where:
Ke is the shareholders' cost of capital
D1 is the annual dividend per share, starting at year 1 and then continuing annually in perpetuity
2.2.1 DVM assumptions
The following assumptions are made in the dividend valuation model:
(a) The dividends from projects for which the funds are required will be of the same risk type or quality as dividends from existing operations.
(b) There would be no increase in the cost of capital, for any other reason besides (a) above, from a new issue of shares.
(c) All shareholders have perfect information about the company's future, there is no delay in obtaining this information and all shareholders interpret it in the same way.
(d) Taxation can be ignored.
(e) All shareholders have the same marginal cost of capital.
(f) There would be no issue expenses for new shares.
LO 4.7
LO 9.1
2.3 The dividend growth model
Shareholders will normally expect dividends to increase year by year and not to remain as a constant amount every year. Expected growth in dividends can be allowed for in calculating a cost of equity, using Gordon's growth model.
Given an expected constant annual growth in dividends, the share price formula would be:
Formula to learn
D0 is the current year's annual dividend (i.e. the year 0 dividend) or dividend just paid.
P0 is the current ex-dividend share price.
r is the shareholders’ required return, expressed as a proportion.
g constant growth rate of dividends, is the annual growth rate in dividends, expressed as a proportion (e.g. 4 per cent = 0.04).
This formula assumes a constant growth rate in dividends, but it can be adapted for uneven growth.
Re-arranging the formula, we get a formula for the ordinary shareholders' cost of capital, Ke
Formula to learn
This is equivalent to the following equation:
Ke = g
This dividend growth model is sometimes called Gordon's growth model.
Question 1: Cost of equity capital
A share has a current market value of 96c, and the last dividend was 12c. If the expected annual growth rate of dividends is 4%, calculate the cost of equity capital.
(The answer is at the end of the chapter)
2.4 Estimating growth rates
The value of g may be estimated in two ways.
LO 4.7 LO 9.1
2.4.1 Extrapolation of growth in past dividends Worked Example: Past dividend growth
A company’s dividend payments from 20X1 to 20X5 were as follows:
Year $ 000 20X1 2 200 20X2 2 578 20X3 3 108 20X4 3 560 20X5 4 236 Required
Estimate the dividend growth rate.
Solution
Dividend in 20X1 ×(1 + g) = Dividend in 20X5 4 (1 + g) = 4
20X1 in Dividend
20X5 in Dividend
(1 + g) = 4 4 236/2 200 = 1.925 1+ g = 41.925 = 1.18 g = 0.18 = 18%
2.4.2 Analysis of the future earnings rate and retention policy Formula to learn
g = bR where:
g is the annual growth rate in dividends b is the yield on new investments, and
R is the proportion of profits retained for reinvestment.