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what are the two methods that can be used to calculate the cost of equity?

Dividend valulation/growth model


What is the dividend valuation model and what is it based on

The dividend discount model (DDM) is a quantitative method used for predicting the price of a company's stock based on the theory that its present-day price is worth the sum of all of its future dividend payments when discounted back to their present value.

The cost of equity finance to the company is the return the investors expect to achieve on their shares. We will be able to determine the return investors expect to receive by looking at how much they are prepared to pay for a share.


What are the assumptions of DVM?

DVM states that:

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

Share price = Dividends paid in perpetuity discounted at the shareholder’s rate of return.


The formula for valuing a share is therefore?

P0= D ÷ re

P0=Share price now T0
D= Constant dividend from year 1 to infinity
re= shareholder's required return


Although in reality a firm’s dividends will vary year on year, a practical assumption is to assume a constant growth rate in perpetuity. The share valuation formula then becomes:

P0= [D0(1+g)] ÷ [re-g]

g = constant rate of growth in dividends, expressed as a decimal

D0(1+g) = dividend just paid, adjusted for one year’s growth (equivalent to D1)


What is the ex div share price and explain what the formula for P0 is?

P0 represents the ‘ex div’ share price.

The DVM model is based on the perpetuity formula, which assumes that the first payment will arise in one year’s time

If the first dividend is receivable immediately, then the share is termed cum div. In such a case the share price would have to be converted into an ex div share price, (ex div meaning 1st dividend is payable in a years time) so that we can use the DVM formula

Before dividend= Cum div share price
Dividend occurs
After dividned= Ex div share price

Ex Div share price= Cum div- dividend due


How do you calculate the g (growth rate) in the DVM formula?

name the specific terms used to describe the methods rather than the names of the method

Two ways of estimating the likely growth rate of dividends are:

extrapolating based on past dividend patterns
assuming growth is dependent on the level of earnings retained in the business


What is the historic method?

This method assumes that the past pattern of dividends is a fair indicator of the future.

the formula for extrapolating growth is

G=[ n√(D0÷ Dn) ] - 1

n = number of years of dividend growth.


what is the gordons growth model and the formula and the assumption

Assumption : The higher the level of retentions in a business, the higher the potential growth rate.

g= bre

b= earnings retention rate (Profit retained/ Profit after tax)

re= RETURNS ON EARNING retained. This is ROE (Return on equity)

(Profit after tax- preference dividend)
(Ordinary shares)


what is the weakness of the DVM

The model does not incorporate risk

 the input data used may be inaccurate:
– current market price of the share is subject to other short-term fluctuations due to influences, such as rumoured takeover bids affecting the price. This means that your answer too might keep changing

– It assumes dividends grow at a constant rate 'g' - for simplicity, we usually assume no growth or constant growth.

- future growth is predicted from past results- these are unlikely growth patterns. growth estimates based on the past are not always useful; market trends, economic conditions, economic events, inflation, etc. need to be considered


the growth in earnings is ignored.

-Earnings do not feature as such in the DVM. However, earnings should be an indicator of the company’s long-term ability to pay dividends and therefore in estimating the rate of growth of future dividends, the rate of growth of the underlying profits must also be considered. E.g. dividend growing 10% and earnings 5%= bad and vice versa


How do you estimate the cost of preference shares and the formula

Preference shares usually have a constant dividend. So the same approach can be used as we saw with estimating the cost of equity with no growth in dividends.

Kp= D÷ P0

D = the constant annual preference dividend
P0 = ex div MV of the share
Kp = cost of the preference share.


what's the difference between Kd and 'Kd (1 – T)

 'Kd' – the required return of the debt holder (pre-tax)
 'Kd (1 – T)' – the cost of the debt to the company (post-tax).

Care must be taken since it is not always possible to simply calculate 'Kd (1 – T)' by taking Kd and multiplying by (1 – T). You should therefore regard 'Kd (1 – T)' as a label for the post-tax cost of debt rather than as a mathematical formula.

Note also that Kd, the required return of the debt holder can also be referred to as the 'yield', the 'return on debt' and as the 'pre-tax cost of debt'.


what are irredeemable debt

Irredeemable debt – no repayment of principal – interest in perpetuity.


what is the formula for the lenders of irredeemable debt

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

 expected income stream will be the interest paid in perpetuity. The formula for valuing a loan note is therefore: MV = I÷ Kd

where: I = annual interest in $ starting in one year's time
P0/MV = market price in $ of the loan note now (year 0)
Kd = debt holders’ required return (pre-tax cost of debt), expressed as a decimal.

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

Kd= I / MV


what is the formula for the COMPANY of irredeemable debt

Kd (1-T)= I (1-t) / Mv


what are redeemable debt

what is it's market price

what is the expected income stream

Redeemable debt – interest paid until redemption of principal (sometimes at a premium or a discount to the original loan amount)

Market price = Future expected income stream from the loan notes discounted at the investor’s required return (pre-tax cost of debt).

Expected income stream will be:
– interest paid to redemption
– the repayment of the principal.

Hence the market value of redeemable loan notes is the sum of the PVs of the interest and the redemption payment.


What is the formula for redeemable debt?

Note that for the investor the purchase is effectively a zero NPV project, as the present value of the income they receive in the future is exactly equivalent to the amount they invest today.

The investor’s required return is therefore the internal rate of return (IRR) (breakeven discount rate) for the investment in the loan notes.


the return an investor requires is therefore found by calculating the IRR of the:

T0- MV (X)
T1..N- Interest payments X
Tn- Capital repayment X


the cost of debt for the company is therefore found by calculating the IRR of the:

T0- MV (X)
T1..N- Interest paymentsx(1-T) X
Tn- Capital repayment X


where the debt is redeemable at its current market price, the position of the investor is?

the same as a holder of irredeemable debt.

so both formulas will be the same


what is the convertible debt?

A form of loan note that allows the investor to choose between taking the redemption proceeds or converting the loan note into a pre-set number of shares.


how do you calculate the cost of convertible debt?

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

Note: There is no tax effect whichever option is chosen at the conversion date.


what is non tradeable debt cost to the company and whats the formula

Bank and other non-tradeable fixed interest loans simply need to be adjusted for tax relief:

Cost to company = Interest rate × (1 – T)


what is WACC- in terms of explaining why do we use it

if a question tells you that a project is to be financed by the raising of a particular loan or through an issue of shares, in practice, the funds raised will still be added to the firm’s pool of funds and it is from that pool that the project will be funded.

The general approach is to calculate the cost of each individual source of medium-long term finance and then weight it according to its importance in the financing mix.

A firm’s average cost of capital (ACC) is the average cost of the funds, normally represented by the WACC. The computed WACC represents the cost of the capital currently employed. This represents financial decisions taken in previous periods.


The formula for WACC is quite complicating (though given) so better to use the profoma: what is it?

Step 1 Calculate 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. All of the above can be summarised in the following formula, which is provided for you in the exam.


Which method is more optimal in deciding which weight to choose

Book value or MV
- mention which values are included in both
- which is better

Wherever possible MVs should be used.

The value of shareholders’ equity shown in a set of accounts will often reflect historic asset values, and will not reflect the future prospects of an organisation or the opportunity cost of equity entrusted by shareholders. Consequently, it is preferable to use MV weights for the equity.

Note that when using BVs, reserves such as share premium and retained profits are included in the BV of equity, in addition to the nominal value of share capital.

Note that when using MVs, reserves such as share premium and retained profits are ignored as they are in effect incorporated into the value of equity as designated by the share price.


What are the assumptions of WACC

1) the historic proportions of debt and equity will remain unchanged (assuming that gearing of the entity will remain constant in the long term)

2) Any new project will have the same risk as the existing activities of the company


The new project is assumed to be very small in relation to the existing activities of the company


The weighted average cost of capital (WACC) can be used as the discount rate in investment appraisal provided that some restrictive assumptions are met. These assumptions are as follows:

These assumptions are as follows:

- the investment project is small compared to the investing organisation

- the business activities of the investment project are similar to the business activities currently undertaken by the investing organisation

- the financing mix used to undertake the investment project is similar to the current financing mix (or capital structure) of the investing company

- existing finance providers of the investing company do not change their required rates of return as a result of the investment project being undertaken.

These assumptions are essentially saying that WACC can be used as the discount rate provided that the investment project does not change either the business risk or the financial risk of the investing organisation.


What is the impact of risk for DVM and WACC

Explain what is risk

When considering the return investors require, the trade-off with risk is of fundamental importance. Risk refers not to the possibility of total loss, but to the likelihood of actual returns varying from those forecast.

The DVM and WACC calculations above assume that an investor’s current required return will remain unchanged for future projects. For projects with different risk profiles, this assumption may not hold true.

DVM assumes that the return currently being paid to ordinary shareholders will continue to be their required return in the future. We have seen that the return required is a reflection of the risk the investor faces. Therefore, by using the DVM we are effectively assuming that all future investment projects will be subject to the same risk as those currently undertaken.

However, if the company is considering an investment project in a different business area, these assumptions may not be appropriate and an alternative approach to finding the cost of equity is needed


What is CAPM

It is alternative to measuring of determining the cost of equity. It is based on measuring the systemic risk of an investment.