Gordon Growth Model

 1.      Plover Plc and Lapwing Plc are two companies in the same business sector.   Plover Plc is entirely equity financed with 800,000 ordinary shares (par value 25p) with a current market price of £1.20.  Lapwing plc is a geared company with 500,000 ordinary shares (par value 25p), with a current market value of £1.00, and £600,000 of 8% irredeemable bonds currently quoted at par.   Both companies generate annual earnings before interest and tax of £120,000 and it is the policy of both companies to distribute all available earnings as a dividend.  It is envisaged that neither company will be liable to Corporation Tax in the foreseeable future.

Robin owns 5,000 shares in Lapwing Plc.   His friend has recommended he sells these shares and borrow £6,000, at a rate of 8%, and use the money to buy ordinary shares in Plover Plc.

Definition of ‘Gordon Growth Model’

A model for determining the intrinsic value of a stock, based on a future series of dividends that grow at a constant rate. Given a dividend per share that is payable in one year, and the assumption that the dividend grows at a constant rate in perpetuity, the model solves for the present value of the infinite series of future dividends.


Where:
D = Expected dividend per share one year from now
k = Required rate of return for equity investor
G = Growth rate in dividends (in perpetuity)

Required:

a)        Calculate the cost of equity and weighted average cost of capital for each company.

b)        Suggest reasons why these costs differ for each company.

c)         Advise Robin as to whether the proposed transaction is worthwhile.  You should consider both the risk and the return to Robin in your answer.

d)        Assuming all other prices remained constant calculate the price of the ordinary shares of Plover Plc that would eliminate any arbitrage profits.

current income from lapwing 5000 (number of shares he has) /500,000(number of shares total) x 72,000 = £720 income

 

Sell Shares:
5,000 shares @ £1 per share = 5,000

if he borrows in the same capital structure 5,000 equity 6,000 debt totaling £11,000

 

 

income of robin from plover = 720 after interest rate £1200

 

Plover =1200,000/800,000 = 15p

 

1,200 divided by dividend per share of 15
number of shares he should own to achieve 1200 = 8,000 shares to make 1,200

 

Income = 11,000 << money he has / 800,000 (which is the value of plover) x 1.2

e)        Calculate the cost of equity and weighted average cost of capital for each firm using the price of Plovers shares calculated above.

2. Partridge Plc and Pheasant Plc are two companies operating in the charter airline business.  Both companies shares are traded on the London Stock Exchange where they are generally assigned similar risk ratings.   Partridge, the larger of the two companies, has 3 million 75p ordinary shares in issue which currently stand at 180p (ex div.) in the market.  In addition, some years ago the company issued £10 million of 6% undated bonds to help finance a new holiday route and these are currently quoted at 75% (ex int.).  Their competitor, Pheasant Plc, operates on an all equity basis of 25 million 5p ordinary shares that have a current ex div. market value of 32p each.

 

Partridge Plc has annual earnings before interest and tax of £1.4 million, this level is generally expected to be maintained in the future.  Pheasant Plc has annual earnings before interest and tax of £1 million and this too is expected to remain stable.  Both companies follow a strict policy of not retaining any of their after tax earnings.

Required:

a)        Calculate the cost of equity capital and the weighted average cost of capital for both companies.  Suggest reasons why these costs of capital differ between the two companies.  Taxation is to be ignored.

Where:

Es
The expected return for a security
Rf
The expected risk-free return in that market (government bond yield)
βs
The sensitivity to market risk for the security
RM
The historical return of the stock market/ equity market
(RM-Rf)
The risk premium of market assets over risk free assets.

MV o Share = 3m * 1.8 = 5.4m
MV of Debt  = £10m * 75% = 7.5m

Ke = D1 / MV

 

Company A

Ke = 1.4 – (6% * 10m) / 5.4 = 1.4 -0.6/5.4 = 14.8%

Kd = 0.6/7.5 = 8%
WACC = 14.8% * 5.4 / 12.9 + 8% * 7.5 / 12.9 = 8.8%

 

Company B

Ke = 1m / 32 * 25 = 12.5%

b)        Explain what action you might take, if any, if you were a shareholder owning 10% of the share capital of Partridge and why.  Produce calculations to illustrate the effects of your actions stating any assumptions that you have made.  Comment on what the effect would be if other shareholder in Partridge took similar action.

 

c)         Comment briefly on what effect the presence of taxation and other capital market imperfections would be likely to make on your answer to part (b) above.

 

3)          There is a controversial debate in the literature about the dividends. Does the dividend policy affect the firm value? Discuss different empirical evidence which support relevance or irrelevance arguments.

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