Chapter 5 Cost of capital Flashcards
1.1 The weighted average cost of capital
Rate of return a company achieves on its projects must be sufficient for it to satisfy the required returns of its investors, including:
- equity shareholders: return is in the form of constant or growing dividend stream. The return the company needs to achieve to pay sufficient dividends is known as: Ke (cost of equity)
- preference shareholders: return is in form of fixed dividend stream. Return the company needs to achieve to pay these dividends is known as Kp (cost of preference shares)
- debt holders: return is in form of fixed interest and repayment. The return the company needs to afford the interest/repayment is known as Kd (cost of debt)
The weighted average cost of capital is therefore an average of Ke, Kp and Kd. Therefore, the formula is:
(MVe x Ke) + (MVp x Kp) + (MVd x Kd) / (Mve + MVp + MVd),
Where Mve is the market value of equity and Ke is the cost of equity.
2.1 The cost of equity
A basic assumption in a perfect market is that the current share price is the present value of the expected future dividends discounted at the investor’s required return (Ke) and therefore the investors required rate of return (Ke) is the IRR achieved by investing the current price and receiving the future dividends.
As a formula if dividends are expected to grow at a rate of g%:
Price (P0) = D0 (1 + g) / Ke – g
For a listed company, since the share price is known and the future dividends normally predictable, the shareholders required return can be found by rearranging the formulae:
Required (Ke) return = (D0 (1 + g) / P0) + g
2.2 Cum and ex-div share prices
Cum div share price – dividend due = ex div share price
2.3 Estimating growth
There are two ways of estimating the likely growth rate of dividends:
- extrapolating based on past dividend patterns (historic method)
- assuming growth is dependent on the level of earnings retained in the business (earnings retention model)
Historic method
Where past dividend stream shows consistent growth, we assume the growth continues indefinitely.
Annual growth (g) = (n√D0 / dividend n yrs ago) – 1, or g = (D0 / dividends n yrs ago)^(1/n) - 1
This can also be calculated using the spreadsheet function: g = POWER (most recent value / oldest value, 1 / number of periods of growth) – 1
2.4 Earnings retention model (Gordon growth model)
The higher the level of retentions in a business, the higher the potential growth rate of dividends. Growth can be estimated as: g = r x b,
Where R is the accounting rate of return on the new investment and b is the earnings retention rate.
2.5 Historic growth and dealing with share issues
New issues and rights issues: these raise funds for the company, therefore although the number of shares has increased, so has the earnings potential of the company. As long as growth is calculated using dividend per share, then this will not be a problem.
Bonus issues: increase the shares in issue without adding funds to increase earnings potential, therefore although total dividends should remain consistent, dividends per share is reduced. The approach is still to calculate g using dividend per share, but the earlier DPS must be calculated by adjusting the number of shares for subsequent bonus issues.
3.1 The cost of preference shares (Kp)
For Ke the basic assumption in a perfect market is that the current share price equals present value of the expected future dividends discounted at the investor’s required return (Kp), and therefore the investors’ required rate of return (Kp) is the IRR achieved by investing the current price and receiving the future dividends. Given that preference dividends do not grow over time, then as a formula:
Price (P0) = D/Kp and rearranging Kp = D/P0
4.1 The cost of debt (Kd)
Basic assumption is that the current price is the present value of the expected future income discounted at the investor’s required return. This holds true for debt and equity, but the income stream from the investment depends on whether the debt is irredeemable or redeemable.
Irredeemable debentures
Price of a debenture is the present value of the future interest steam received in perpetuity discounted at the investor’s required return. And therefore, the investors required rate of return is the IRR achieved by investing the current price and receiving the future interest. The formula for valuing a debenture is therefore: Price (P0) = i / r and rearranging required return = i / P0, where:
- i = annual interest starting in one year’s time
- r = debt holders’ required return (known as the yield)
4.2 Problem of tax
Debt interest attracts tax relief, the required return of debt holders (the yield) does not equal company’s cost of debt (Kd). The company gets 25% tax relief for the amount of interest required by the investor. Therefore, providing interest of i will only cost the company ‘i x 75%’. Adjusting for tax, the formula becomes:
Price (P0) = i(1 – T) / Kd and rearranging Kd = i(1 – T) / P0, where T is the corporation tax rate.
4.3 Redeemable debentures
Price of debenture is the present value of the future interest received up to redemption plus the redeemed amount all discounted at the investors’ required return, therefore the investors’ required rate of return is achieved by investing the current price and receiving the future interest and redemption payment.
Given the cash flows are not a simple perpetuity there is no formula to calculate the NPV or the IRR
A market price or issue price of a debenture can be calculated using the spreadsheet function: =PV (investor’s required return, number of time periods, interest value, redemption value).
A yield is the return that is given back to investors (pre-tax). For irredeemable debt, as the company achieves tax relief on the debt finance, Kd is calculated as the yield x (1 – tax). To calculate the yield on the debt, we use the spreadsheet function: =RATE (number of time periods, interest payment, market value, redemption value) or =IRR (cash flows).
4.4 Semi-annual coupon payments
Interest paid at set intervals. We use spreadsheet functions as above, making sure the number of time periods is equal to the number of interest payments made over the life of the loan.
4.5 Convertible debentures
Treated as redeemable debt with the following adjustment:
- compare the redemption value with the value of the conversion option
- select the higher of the two values as the amount to be received at tn
- find the internal rate of return of the cash flows
4.6 non-tradable debt
Bank and other non-tradable fixed interest loans simply need to be adjusted for tax relief. Cost = interest rate x (1 – T).
5.1 Discursive elements of WACC
When is it appropriate to use WACC as a discount rate for a project:
- if proportions of debt and equity (gearing) are not going to change over project life.
- If the level of risk is not going to change
- If the finance is not project-specific
Assumptions using the dividend valuation model:
- A perfect market is operating to ensure the share price is the PV of future dividends discounted at Ke
- Dividends are paid once a year and dividend growth is expected to be constant and predictable
- If using historic dividends to assume growth, we assume the past is a good guide to the future
- If using earnings retention model to predict growth, we assume the rate of return and retention rate will remain constant over time
