Chapter 17 - The Cost Of Capital

Question 1

Dividend Valuation Model (DVM)

Answer 1

Assuming constant dividends:-

P(0) = D/ r(e)

D = constant dividend from year 1 to infinity
P(0) = share price now (year 0)
r(e) = shareholders required return, in decimals

Hence, r(e) = D/ P(0)

Question 2

DVM assuming dividend growth at a fixed rate

Answer 2

P(0) = D(0)(1+g)/ (r(e) - g) = D(1)/ (r(e) - g)

g = constant rate of growth in dividends expressed as a decimal
D(1) = dividend to be received in one year i.e. T(1)
D(0)(1+g) = dividend just paid, adjusted for one year's growth

Therefore, to find the cost of equity,

r(e) = D(0)(1+g)/ P(0) + g = D(1)/ P(0) + g

Note r(e) (the shareholder’s required return) and k(e) (the cost of equity) can be used interchangeably.

Question 3

The ex-div share price

Answer 3

Cum div share price - Dividend due = Ex div share price

P(0) represents the ex div share price

Question 4

Calculating returns

Answer 4

Market value of investment = The present value of the expected future returns discounted at the investors’ required return.

The investors’ required rate of return = The IRR achieved by investing the current price and receiving the future expected returns.

Question 5

Estimating growth

Answer 5

1. Past dividends

g = [(D(0)/ Dividend n years ago)^1/n] -1

n = number of years of dividend growth

2. The earnings retention model

g = br(e)

r(e) = accounting rate of return
b = earnings retention rate

Question 6

Weaknesses of the DVM

Answer 6

1. Current market price
   P(0) - This can be subject to other short term influences which distort the estimate of the cost of equity.
2. Future dividends
   We assume no growth or constant growth but these are unlikely growth patterns.
   Growth estimates based on the past are not always useful, market trends, economic conditions, inflation etc.
3. Relevance of earnings in the DVM
   Should be an indicator of the company’s long term ability to pay dividends and estimating the rate of growth of future dividends.
   The rate of underlying profits must also be considered.

Question 7

Estimating the cost of preference shares

Answer 7

K(p) = D/ P(0) and P(0) = D/ K(p)

D = the constant annual preference dividend
P(0) = ex div MV of the share
K(p) = cost of the preference share

Question 8

Estimating the cost of debt

Answer 8

Key points

1. Debt is always quoted in $100 nominal value books
2. Interest paid on debt is stated as a percentage of nominal value (coupon rate)
3. The terms ex-interest and cum-interest are used in much the same way as ex-div and cum-div for the cost of equity calculations.

Question 9

Cost of debt

Answer 9

K(d) - the required return of the debt holder (pre-tax)

K(d)(1-T) - the cost of the debt to the company (post tax)

Question 10

Irredeemable debt

Answer 10

Market Price (MV) = Future expected income stream from the debenture discounted at the investor’s required return.

MV = I/ K(d)

I = annual interest starting in one year's time
MV = market price of the loan note now (year 0)
K(d) = debt holders' required return (pre-tax cost of debt) as a decimal.

The required return (pre-tax cost of debt) can be found by rearranging the formula.

K(d) = I/ MV

The post-tax cost of debt to the company is found by adjusting the formula to take account of the tax relief on the interest:

K(d)(1-T) = I(1-T)/ MV

Question 11

Redeemable debt

Answer 11

1. Market price = Future expected income stream from the loan notes discounted at the investor’s required return (pre-tax cost of debt)
2. Expected income stream
   - interest paid to redemption
   - the repayment of the principal
3. Hence the market value of redeem ale loan notes is the sum of the PVs of the interest and the redemption payment.
4. The return an investor required can be found by calculating the IRR of the investment flows:

T(0) MV (x)
T(1-n) Interest payments x
T(n) Capital repayment x

Note:- For post-tax cost of debt to the company, the interest payments are tax deductible and x(1-T).

Question 12

Convertible debt

Answer 12

To calculate the cost of convertible debt:

1. Calculate the value of conversion option using available data.
2. Compare the conversion option with the cash option. Assume all investors choose the higher option value.
3. Calculate the IRR of the flows as for redeemable debt.

Note: No tax effect at the conversion date.

Question 13

Non-tradeable debt

Answer 13

Cost to company = Interest rate x (1-T)

Question 14

Estimating the cost of capital

Answer 14

Calculating weights:-

When using Market values to weight the sources of finance,

Equity = Market value of each share x Number of shares in issue

Debt = Total nominal value/ 100 x current market value

Question 15

Calculating the WACC

Answer 15

Step 1: Calculate the weights for each source of capital.

Step 2: Estimate cost of each source of capital.

Step 3: Multiply proportion of total of each source of capital by cost of that source of capital.

Step 4: sum the results of Step 3 to give the WACC.

Question 16

Return on risky investments - equities

Answer 16

Equity shareholders are paid only after all other commitments have been met.

The order of priority is:-

1. Secured lenders
2. Legally protected creditors such as tax authorities
3. Unsecured creditors
4. Preference shareholders
5. Ordinary shareholders

Required return = Risk-free return + Risk premium

Question 17

Systematic and unsystematic risk

Answer 17

The risk a shareholder faces is in large part due to the volatility of the company’s earnings.

Systematic risk - Market wide factors such as the state of the economy
Unsystematic risk - Company/ industry specific factors

Question 18

The CAPM

Answer 18

Required return = Risk-free return + Risk premium

Risk premium = Relative level of systematic risk x Market risk premium for a specific investment

Question 19

Assumptions underpinning CAPM

Answer 19

1. Investors hold diversified portfolios.
   - Known as market portfolio.
   - Investors will only require a return for the systematic risk of their portfolios since the unsystematic risk has been removed.
   - Even a limited diversification will produce a portfolio which approximates its behaviour so it is a workable assumption.
2. Perfect capital market.
   - All securities are valued correctly and their returns will plot on to the SML.

• A perfect capital market requires:
  1. No taxes
  2. No transaction costs
  3. Perfect information that is freely available to all investors
  4. All investors to be risk averse and rational
  5. A large number of buyers and sellers in the market

3. Unrestricted borrowing or lending at the risk free rate of interest.
   - Provides a minimum level of return required by investors.
   - In reality this is not possible because the risk associated with individual investors is much higher than that associated with the Government.
   - The SML is shallower in practice than in theory.
4. Single-period transaction horizon.
   - A holding period of one year is usually used in order to make comparable returns on different securities e.g. A return over 6 months cannot be compared to a return over 12.

Question 20

Advantages of CAPM

Answer 20

1. Provides a market-based relationship between risk and return and assessment of security risk and rates of return given that risk.
2. Shows why only systematic risk is important in this relationship.
3. One of the best methods of estimating a quoted company’s cost of equity capital.
4. Provides a basis for establishing risk-adjusted discount rates for capital investment projects.

Question 21

Disadvantages of CAPM

Answer 21

1. Less useful if investors are undiversified.
2. Ignores tax situation of investors.
3. Actual data inputs are estimates and may be hard to explain.