ACCA paper f9 financial management study materials F9FM session10 d08

1 DIVIDEND VALUATION MODEL 1.1 The general model Ü The dividend valuation model states that: “the market value of a share or other security is equal to the present value of the future e

OVERVIEW

Objective

Ü To develop a model for the valuation of shares and bonds

Ü To use this model to estimate the cost of equity and the cost of debt

Ü To consider further practical influences on the valuation of securities

EQUITY

ANALYSIS

SECURITY VALUATION AND THE COST OF CAPITAL

DEBT ANALYSIS

Ü Dividend Valuation Model

Ü Cost of equity Ü Ü Irredeemable debentures Redeemable debentures

Ü Semi-annual interest

Ü Convertible debentures

1 DIVIDEND VALUATION MODEL

1.1 The general model

Ü The dividend valuation model states that:

“the market value of a share or other security is equal to the present value of the future expected cash flows from the security discounted at the investor’s required rate of return”

Ü A security is any traded investment e.g shares and bonds

1.2 Constant Dividend

Ü The formula for share valuation can be developed as follows:

Ex-div market value at time 0 = Present value of the future dividends

discounted at the shareholders’

required rate of return

Ü Ex-div market value is the market value assuming that a dividend has just been paid

Ü Let:

Po = Current ex-div market value

Dn = Dividend at time n

ke = Shareholders’ required rate of return/company’s cost of equity

Ü The model then becomes:

Po =

ke)(1

Dke)

(1

Dke)(1

D

3

3 2

2 1

+

++

+

ke)(1

Dn

n

+

Ü If the dividend is assumed to be constant to infinity this becomes the present

value of a perpetuity which simplifies to:

keD

Ü This version of the model can be used to determine the theoretical value of a share which pays a constant dividend e.g a preference share or an ordinary share in a zero growth company

Ü If dividends are forecast to grow at a constant rate in perpetuity, where g = growth rate

Po =

gke

g)(1

D1

−where Do = most recent dividend

D1 = dividend in one year The formula is published in the exam in the following format:

1

DO

Where re= required return of equity investors = ke

1.4 Assumptions behind the dividend valuation model

Ü rational investors

Ü all investors have the same expectations and therefore the same required rate of return

Ü perfect capital market assumptions, e.g.,

̌ no transactions costs

̌ large number of buyers and sellers of shares

̌ no individual can affect the share price

̌ all investors have all available information

Ü dividends are paid just once a year and one year apart

Ü dividends are either constant or are growing at a constant rate

1.5 Uses of the dividend valuation model

Ü The model can be used to estimate the theoretical fair value of shares in unlisted

companies where a quoted market price is not known

Ü However if the company is listed, and the share price is therefore known, the model can

be used to estimate the required return of shareholders i.e the company’s cost of equity finance

Illustration 1

Suppose that a share has a current ex-div market value of 80 cents and

investors expect a dividend of 10 cents per share to be paid each year as has

been the case for the past few years

Using the dividend valuation model the required return of the investors for

this share can be determined:

keD 80c =

ke10c

80c10c

Investors will all require this return from the share as the model assumes they

all have the same information about the risk of this share and they are all

rational

If investors think that the dividend is due to increase to 15 cents each year then

at a price of 80 cents the share is giving a higher return than 12.5% Investors

will therefore buy the share and the price will increase until, according to the

model, the value will be:

0.12515c = 120 cents Alternatively suppose that the investors' perception is that the dividend will

remain at 10 cents per share but that the risk of the share has increased thereby

requiring a return of 15% If the share only gives a return of 12.5% (on an 80

cents share price) then investors will sell and the price will fall The fair value

of the share according to the model will be:

0.1510c = 66.7 cents

Ü The dividend valuation model gives a theoretical value, under the assumptions of the model, for any security

Ü In practice there will be many factors other than the present value of cash flows from a security that play a part in its valuation These are likely to include:

The dividend valuation model helps us to understand how a change in these

variables should affect the market value of the security

Ü Share prices change, often dramatically, on a daily basis The dividend valuation model will not predict this, but will give an estimate of the underlying fair value of the shares

2.1 Shareholders required rate of return

Ü The basic dividend valuation model is:

Ü Therefore the cost of equity for a company with a constant annual dividend can be

estimated as the dividend divided into the ex-div share price i.e the dividend yield

Ü The ex-div market value is the market value of the share assuming that the current dividend has just been paid A cum-div market value is one which includes the value of

Example 1

A company’s shares have a market value of $2.20 each The company is just

about to pay a dividend of 20c per share as it has every year for the last ten

years

What is the company’s cost of equity?

Solution

2.2 Dividend with constant growth

Ü The model can also deal with a dividend that is growing at a constant annual rate of g

Ü The formula for valuing the share is as seen earlier:

Po =

gke

g)(1

D0

−

+ =

gke

D1

−where Do = most recent dividend

D1 = dividend in one year

Ü Rearranged this becomes

Po

g)(1

D0

+

+

where g = growth rate (assumed constant in perpetuity)

where Po = ex div market value

Ü Therefore the cost of equity = dividend yield + estimated growth rate

2.3 Growth from past dividends

Ü Look at historical growth and use this to predict future growth If you have specific information about future growth, use that

̌ If dividends have grown at 5% in each of the last 20 years, predicted future growth

= 5%

̌ Uneven but steady growth – take an average overall growth rate

̌ Discontinuity in growth rate – take the most recent evidence

̌ New company with very high growth rates – take care! It is unlikely to produce such high growth in perpetuity

̌ No pattern – do not use this method (i.e dividends up one year, down the next)

Example 2

A company has paid the following dividends over the last five years

Cents per share

Estimate the growth rate and the cost of equity if the current (19X4) ex div

market value is $10.50 per share

Solution

2.4 Gordon’s growth model

Ü Gordon’s growth model states that growth is achieved by retention and reinvestment of profits

taxafterProfit

=

assetsNet

taxafterProfit

b =

taxafterProfit

profitRetained

Ü These figures can be obtained from the statement of financial position and income statement

Example 3

A company has 300,000 ordinary shares in issue with an ex-div market value of

$2.70 per share A dividend of $40,000 has just been paid out of post-tax profits

of $100,000

Net assets at the year end were valued at $1.06m

Estimate the cost of equity

Solution

Illustration 3

A plc is all equity financed and has 1m shares quoted at $2 each ex div It pays

constant annual dividends of 30c per share

It is considering adopting a project which will cost $500,000 and which is of the

same risk as its existing activities The cost will be met by a rights issue The

project will produce inflows of $90,000 pa in perpetuity All inflows will be

distributed as dividends

What is the new value of the equity in A plc and what is the gain to the

shareholders? Ignore tax

Ü ke = 20..0030 = 15%

Ü New dividend

$

Value of equity =

15.0

000,390

= $2,600,000 Shareholders’ gain = $(2,600,000 – 2,000,000) – $500,000

= $100,000 Project NPV = ($500,000) +

15.0

000,

90 = $100,000

Therefore, new value of equity = Existing value + Equity outlay + NPV

= Existing value + Present value of additional dividends

Ü Therefore the NPV of a project serves to increase the value of the company’s shares i.e the NPV of a project shows the increase in shareholders’ wealth

Ü This proves that NPV is the correct method of project appraisal – it is the only method consistent with the assumed objective of maximising shareholders’ wealth

Ü By definition preference shares have a constant dividend

Ü Ke =

PoD

Ü where D = constant annual dividend

Ü Preference dividends are normally quoted as a percentage, e.g 10% preference shares

This means that the annual dividend will be 10% of the nominal value, not the market

value

Example 4

A company has 100,000 12% preference shares in issue (nominal value $1)

The current ex-div market value is $1.15 per share

What is the cost of the preference shares?

Ü The coupon rate is the interest rate printed on the debenture certificate

Annual interest = coupon rate × nominal value

Ü Nominal value is also known as par or face value In the exam the nominal value of one

debenture is usually $100

Ü Market value (MV) is normally quoted as the MV of a block of $100 nominal value

e.g 10% debentures quoted at $95 means that a $100 block is selling for $95 and annual interest is $10 per $100 block

Ü Irredeemable debentures are a type of debt finance where the company will never repay

the principal but will pay interest each year until infinity They are also referred to as

undated debentures

Ü The market value of undated debt can be calculated using the same logic as the

Dividend Valuation Model:

MV (ex interest) = present value of future interest payments discounted at the holder’s required rate of return

debenture-Ü For irredeemable debentures the interest is a perpetuity

Ü MV (ex int) =

r

I

where I = annual interest

r = return required by debenture holder

Ü r =

int)(exMV

I = Interest yield

Ü The company gets tax relief on the debenture interest it pays, which reduces the cost of debentures to the company – known as the “tax shield” on debt

Illustration 4

Consider two companies with the same earnings before interest and tax (EBIT)

The first company uses some debt finance, the second uses no debt

Effective cost of debt

$

debenture holders

Unless told otherwise, we assume that tax relief is instant (in practice, there will be a minimum time lag of nine months under the UK tax system)

Ü Note that if debt is irredeemable then:

Cost of debt to the company (also

known as the post tax cost of debt) =

=

Return required by the debenture holders × (1–Tc)

Interest yield × (1–Tc)

Where Tc = corporate tax rate as a decimal

Ü Kd can be used to denote the cost of debt – but care is needed as to whether it is stated pre-tax or post-tax

Example 5

12% undated debentures with a nominal value of $100 are quoted at $92 cum

interest The rate of corporation tax is 33%

Find

(a) the return required by the debenture-holders

(b) the cost to the company

Solution

Ü The cash flows are not a perpetuity because the principal will be repaid However from the dividend valuation model we can derive the following rule:

The cost of any source of funds is the IRR of the cash flows associated with that source

Ü If we are looking at the return from an investor’s point of view, interest payments are included gross

Ü If we are looking at the cost to the company, we take the interest payments net of

corporation tax Assume instant tax relief

Ü Assume that the final redemption payment does not have any tax effects

Ü To find the cost of debt for a company find the IRR of the following cash flows:

A company has in issue $200,000 7% debentures redeemable at a premium of

5% on 31 December 19X6 Interest is paid annually on the debentures on 31

December It is currently 1 January 19X3 and the debentures are trading at $98

ex interest Corporation tax is 33%

What is the cost of debt for this company?

Solution

the cost of debt of the company

Required return of the

redeemable debenture

holder

= IRR of pre-tax cash flows from the debenture

= Gross redemption yield

Ü Gross Redemption Yield is also referred to as the Yield To Maturity (YTM)

Ü The cost of debt of the company is then determined by finding the IRR of the market

value, net of tax interest payments and redemption value

MV (ex interest) = present value of future interest payments and redemption value

discounted at the debenture-holder’s required rate of return

Example 7

A company has 8% debentures redeemable at a 5% premium in ten years

Debenture-holders require a return of 10%

What is the cost to the company? Corporation tax is 33%

Solution

Ü In practice debenture interest is usually paid every six months rather than annually This practical aspect can be built into our calculations for the cost of debt

Ü If interest payments are being made every 6 months then when the IRR of the debenture cash flows is calculated it should be done on the basis of each time period being 6 months

Ü The IRR, or cost of debt, will then be a 6 monthly cost of debt and must be adjusted to determine the annual cost of debt

Ü Effective annual cost = (1+semi annual cost)2 -1

Example 8

A company has in issue 6% debentures the interest on which is paid on 30 June

and 31 December each year The debentures are redeemable at par on 31

December 19X9 It is now 1 January 19X7 and the debentures are quoted at

96% ex interest

What is the effective annual cost of debt for the company? Ignore corporation

tax

Solution

Ü Convertible debentures allow the investor to choose between redeeming the debentures

at some future date or converting them into a pre-determined number of ordinary shares in the company

Ü To estimate the market value it is first necessary to predict whether the investor will choose redemption or conversion The redemption value will be known with certainty but the future share price can only be estimated

MV (ex interest) = present value of future interest payments and the higher of (i)

redemption value (ii) forecast conversion value, discounted at the debenture-holder’s required rate of return

Ü You may also be required to calculate other data for convertibles:

− Floor value = the value assuming redemption

− Conversion premium = market value – current conversion value

Example 9

A company has in issue 9% bonds which are redeemable at their par value of $100 in five years’ time Alternatively, each bond may be converted on that date into 20 ordinary shares The current ordinary share price is $4.45 and this is expected to grow at a rate of 6.5% per year for the foreseeable future Bondholders’ required return is 7% per year

Required:

Calculate the following values for each $100 convertible bond:

(i) market value;

(ii) floor value;

(iii) conversion premium

Solution

A company has in issue some 8% convertible loan stock currently quoted at $85

ex interest The loan stock is redeemable at a 5% premium in five years time, or

can be converted into 40 ordinary shares at that date The current ex-div

market value of the shares is $2 per share and dividend growth is expected at

7% per annum Corporation tax is 33%

What is the cost to the company of the convertible loan stock?

Solution