The Cost of Capital

Question 1

What is the relationship between risk and return?

Answer 1

The basic relationship is that the higher the risk the higher the expected return. The total return demanded by investors will be dependant on two factors:

• The reward demanded by the investors for risk undertaken by advancing funds.
• The prevailing risk free rate of return.

Question 2

How can a business identify their overall cost of finance?

Answer 2

There are several steps to this process:

1. Identify sources of finance used - This may come from question narrative or the financial statements.
2. Equity Finance - Calculate cost of capital
3. Debt finance - identify type of debt, for each type calculate the cost of capital.
4. Using all costs find a weighted average cost (WACC)

The cost of Equity (K_e) or cost of Debt (K_d) can be equated with the return expected by the investor and is expressed as a percentage.

The underlaying assumption with this is that in a perfect market:

The PV of the expected future returns discounted at the investors required return = Market value of investment

or

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

Question 3

How is the cost of equity measured?

Answer 3

Cost of equity to the company = return expected on shares.

Under the base premise that investors required return = IRR the Dividend Valuation Model (DVM) determines expected return based on price paid for a share.

Underlaying assumptions are:

• Future income stream is dividends paid by company
• Dividends will be paid in perpetuity
• Dividends will be constant or growing at a fixed rate.

DVM - assuming constant dividends

P₀ = D/r_e

D = Constant dividend, P₀ = share price now, r_e = shareholders required rate of return (K_e and K_p) .

Where share price and dividend payment are known, rearrange the formula to give required rate of return:

r_e = D/P₀

The formula can also be used for estimating the cost of preference shares which usually have a constant dividend.

Question 4

How does the DVM change if constant growth is assumed?

Answer 4

Constant growth in dividends is assumed where dividend will vary year on year.

This changes the share valuation formula to:

P_{0 =} D₀(1 + g)/r_e-g = D₁/r_e-g

Where:

g = constant rate of growth in dividends as a decimal, D₁ = dividend to be received in 1 years time, D₀(1+g) = D₁

Cost of Equity can be found by rearranging the formula to:

r_e = (D₁/P₀)+ g

Question 5

In both versions of the DVM how do we know what price to use for P₀

Answer 5

DVM is based on perpetuity - so assumes that first payment will arise in 1 years time.

The share price in one years time would be referred to as Ex Div (after dividend)

If the question gives a Cum Div price the dividend to be paid must be deducted before the value is used in the DVM formula.

Question 6

In the DVM g = Growth, how do we identify the growth rate?

Answer 6

Growth can be identified based on the past pattern of dividends, this does assume that the pattern is a fair indicator of growth:

g = (D₀/D_n)^1/n-1

Where n = number of years of dividend growth.

Or

Using the earnings retention model (Gordons Growth model) which assumes that the higher the level of retentions in the business the higher the potential growth rate.

g = br_e

Where b = earnings retention rate (retained earnings^{see note}/profit after tax), r_e = required rate of return.

Note - Retained earnings are profit after tax less ordinary dividend paid.

Question 7

What are the weaknesses of the DVM?

Answer 7

• P₀ = Current share price may be subject to short term influences resulting in fluctuations which distort the value and the estimate based on it.
• The assumption that future dividends will grow based on past patterns does not take in to account market trends changing economic factors and other influence.
• Earnings do not feature in the DVM - growth in earnings will indicate a business ability to pay the dividends, watch out for dividend growth higher than earnings growth.

Question 8

When identifying the cost of debt what different types of debt may we need to deal with?

Answer 8

Note - the terms Loan notes, Bonds, loan stock and marketable debt are pretty much interchangeable. Gilts are debts issued by the Government.

Tradable Debt

• Irredeemable Debt - no repayment of capital, interest in perpetuity.
• Redeemable debt - interest paid until redemption of capital.
• Convertible debt - may later be converted to equity.

Non traded Debt - Bank loans.

Other key points:

• Debt is quoted in $100 nominal value blocks.
• Interest paid on debt is stated as a % of nominal value (coupon rate)
• Ex interest & Cum interest function in the same way as for dividends.
• The required return for investors (K_d) will differ from the cost of debt to the company (K_d(1-T)) due to the impact of tax relief.

Question 9

How is the cost of irredeemable debt calculated?

Answer 9

Remember - Irredeemable debt = pay interest in perpetuity (no capital repayment)

Assumptions:

• MV = future expected income stream from the debt discounted at the investors required return rate.
• Expected income stream will be the interest paid in perpetuity.

Pre tax cost of debt (K_d) = I/MV

Post tax cost of debt (K_d(1-T)) = I(1-T)/MV

Where:

MV = Market value of the loan note now, I = annual interest in $ in one years time

Question 10

How is the cost of Redeemable debt calculated?

Answer 10

Remember - Redeemable debt = interest and capital repayment.

Assumptions:

• Market price = future expected income from loan notes discounted at investors required rate of return.
• Expected income stream will be - interest paid to redemption & repayment of principle.

MV = PV of cash flows discounted at the investors required return rate.

Return required = IRR of the investment cash flows

If post tax cost of debt is required, when calculating IRR interest payment will be:

Interest payment x (1-T)

Question 11

What is convertible debt and how is the cost of it calculated?

Answer 11

Convertible debt - invest can take redemption proceeds or converting loan note to a pre set No. of shares.

Calculating the cost is approached in three steps:

1. Calculate value of conversion option
2. Compare conversion option to cash option. Assumption = investor will choose higher value.
3. calculate IRR of the flows (same as redeemable debt)

Question 12

How are all the different costs combined to give the overall cost of capital?

Answer 12

The costs must be combined to give a weighted average cost. WACC.

Formula for WACC is:

WACC = (V_e/Ve+Vd)Ke + (Vd/Ve+Vd)Kd(1-t)

If there are multiple sources of capital (debt or equity) then the formula will be longer.

It is appropriate to use WACC when:

• Historic proportions of Debt & equity are not to change.
• Operating risk of the firm will not change
• Finance is not project specific.

Question 13

What is the risk free rate of return?

Answer 13

Risk free rate of return = Rf

it may be stated in questions as:

• The return on treasury bills
• The return on Government gilts.

It is essentially an investment where returns are certain.

Question 14

What is meant by Systemic and Unsystemic risk?

Answer 14

Systemic Risk - market risk, factors that affect the market as a whole such as the state of the economy.

Un systemic risk - Risk factors that are specific to the company/industry.

To manage the impact of unsystemic risk a system called diversification is applied, where investors will spread their portfolio across different companies and industries.

Question 15

What is the Capital Asset model and how is it applied?

Answer 15

The CAPM builds on:

Required return = risk free return + risk premium

E( r )i =Rr + Bi(E(r_m)-Rr)

Where

E( r) i = expected return on investment

Rr = risk free rate of return

E(Rm) = the expected average return on the market

Bi = systemic risk of investment i compared to the market.

The Beta value is a measure of risk where

B > 1 riskier than average

B < 1 Less risky than average.

Question 16

What are the assumptions underpinning the CAPM?

Answer 16

• Investors hold a diversified portfolio - this assumption means that unsystemic risk has been removed so the required return is only for systemic risk.
• Perfect capital market - All securities are valued correctly and there are no
  
  • Taxes
  • Transaction costs
  • All investors are risk adverse and rational.
• Borrowing & lending at the risk free rate is unrestricted.
• There is a single period transaction horizon