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CHAPTER SIX

GEARING AND THE COST OF CAPITAL

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Learning OutcomesOn successful completion of this Chapter, students should normally be able to:

• Identify the principal interest rates in the UK financial markets

• Explain the term structure of interest rates• Define and calculate weighted average cost of capital

for companies with simple capital structures• Explain the traditional view of the relationship

between cost of capital and capital structure• Explain the view expounded by Modigliani and Miller

of the relationship between cost of capital and capital structure

• Perform arbitrage calculations that support the view of Modigliani and Miller

• Identify and discuss critically the assumptions underpinning the pre-tax version of the Modigliani and Miller model

• Discuss the possible impact of incorporating taxation in the Modigliani and Miller model

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The Weighted Average Cost of Capital

Example:The following information relates to the long term funding of Thompson plc:

Component of Capital Cost

Market Value£000

Ordinary Shares 15% 980

Preference Shares 12% 550

Debentures 8%   350

1,880

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The Weighted Average Cost of Capital

Example:The following information relates to the long term funding of Thompson plc:

Component of Capital Cost

Market Value£000

Cost x MV£000

Ordinary Shares 15% 980 147

Preference Shares 12% 550 66

Debentures 8%   350  28

1,880 241

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The weighted average cost of capital is the sum of the products(£241,000 in this case)divided by the sum of the weightings(£1,880,000 in this case),i.e. £241,000/£1,880,000= 0.12819..., say 13%.

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The Traditional View of the WACC‑Gearing Relationship

Historically, fixed interest investors have not demanded as high a return as equity investors.This is because they experience a lower level of risk.Hence, it is argued, the introduction of debt into a previously all-equity company will lower the WACC at low levels of gearing.As gearing increases, equity holders will require higher returns in order to compensate them for the increase in risk.At very high levels of gearing the fixed-interest investors will themselves demand a higher return for higher risk.

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The Traditional View of the WACC‑Gearing Relationship

Thus, WACC will decrease at low levels of gearing and increase at higher levels.The WACC profile against gearing will be saucer-shaped at low and medium levels of gearing, indicating that for a particular company there is an optimum mix of debt and equity.This is shown in Exhibit 1 below, where f(x) is the WACC, expressed as a percentage, and x is the level of gearing, expressed as the ratio of debt to total funding:

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0 0.2 0.4 0.6 0.8 10

10

20

30

40

f( )x

x

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If the traditional view is an accurate representation of how WACC varies with changes in gearing,then it should be possible to create wealth by optimising the firm’s capital structure.The next section shows how this would happen.

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Creating Wealth in a Firm by Changing its Capital Structure

The following two assumptions are made:

• Investors prefer more wealth to less• The wealth associated with a project

may be measured by calculating its net present value, as in the example below:

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Leverage Ltd. is an all-equity financed company that has a cost of capital of 12%. The net present value of Project X is calculated as follows:

Year

CashFlow

(£000)

12%DiscountFactor

PresentValue(£000)

0 (1,000) 1 (1,000)

1 400 0.893 357

2 500 0.797 399

3 600 0.712 427

183 = NPV

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Clearly, the amount of wealth (the NPV) is critically dependent on the discount factors and hence on the choice of discount rate.

Now, suppose that the traditional view is reliable, and that the following additional information is available.Leverage Ltd. is a company in which the cost of equity capital is 12% at low levels of gearing.The cost of debentures at low levels of gearing is 7%.The company moves from being all equity financed to being funded partly by debentures, and the ratio of the market values of debt to equity is 2:3.Despite this change in the company’s gearing, the costs of both equity and debt are unaltered.The weighted average cost of capital (WACC) of Leverage Ltd. is calculated as follows:

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2 x 7% + 3 x 12%WACC= 10%

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Year Cash Flow (£000)

10% Discount Factor

Present Value (£000)

0 (1,000) 1 (1,000)

1 400  0.909 364 

2 500  0.826 413 

3 600  0.751 451 

228 

NPV at 10% DF

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Year Cash Flow (£000)

10% Discount Factor

Present Value (£000)

0 (1,000) 1 (1,000)

1 400  0.909 364 

2 500  0.826 413 

3 600  0.751 451 

228 

NPV at 10% DF

Year Cash Flow (£000)

12% Discount Factor

Present Value (£000)

0 (1,000) 1 (1,000)

1 400  0.893 357 

2 500  0.797 399 

3 600  0.712 427 

183 

NPV at 12% DF

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It appears that the introduction of debt into the company has resulted in an increase in wealth from £183,000 to £228,000.This conclusion relies on the assumption that the cost of equity will remain unchanged despite the introduction of debt.It is as if the holders of equity have not noticed that their risk position has worsened.The question arises as to whether this is likely— will the holders of equity really fall asleep and not notice that debt has been issued and their risk increased?

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If the cost of equity remains more or less unchanged(because enough of the ordinary shareholders fail to notice the introduction of debt)then there is an opportunity to make abnormally high returns for anyone who does notice.To put it another way,the ordinary shareholder who remains alert when the cost of equity remains unchanged despite the introduction of debt has access toa money making machine...

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A Money Making Machine(or Profiting through Arbitraging)

Ordinary Limited is a company that is identical to Leverage Ltd. except for funding.Both make an operating profit of £96,000 p.a.and both companies have a policy of paying out all residual profit as dividend.Further details are as follows:

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Leverage Ltd.Market Value

£000400,000 ordinary shares of £1 each 625£300,000 7% debentures 300

925

Ordinary LimitedMarket Value

£000400,000 ordinary shares of 50p each 800

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The pre-interest profit of £96,000 is apportioned as follows:

LeverageLtd.

OrdinaryLimited

£000 £000

Profit before Interest 96 96

Interest(7% x £300,000) 21 nilDividend 75 96

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Note that the return on equity in Leverage Ltd. is 100% x 75,000/625,000 = 12%,and that the cost of equity for Ordinary Limited is also 12%(100% x 96,000/800,000 = 12%).So, the market values of the two companies are in line with the traditional view that at low levels of gearing equity investors do not require increased return for low levels of financial risk.

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Note that the total market values of the two firms are different,even though the companies are identical in all respects except for their sources of funding.This is a result of the return on equity in both companies being the same, although one company also has debt.That the total market values of the two firms are different,even though the companies are operationally identical,is arguably anomalous...

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If an investor wanted to gain an annual income of £96,000 they could either

1. buy all the shares in Ordinary Limited and receive dividends totalling £96,000 each year, or

2. buy all the shares and all the debentures in Leverage Ltd. and receive interest on their debentures of £21,000 and dividends of £75,000.Either alternative would yield an annual income of £96,000, as required.However, to buy all the shares in Ordinary Limited would only cost £800,000compared with the cost of acquiring the shares and debentures in Leverage Ltd. of £925,000. (Recall that the companies are subject to the same level of business risk.)

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Roxy holds 4,000 ordinary shares in Leverage Ltd. with a market value of £6,250.The level of risk associated with this investment is exactly the level she wants, or to put it another way, the shareholding reflects her attitude towards risk.A strategy to increase her wealth without altering her risk position is as follows:

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1. Sell the shares for 1% x £625,000 = £6,250

2. Substitute personal borrowing for the corporate debt by borrowing 1% x £300,000 = £3,000 at 7% p.a.

3. Roxy has funds of £(6,250 + 3,000) = £9,250. She uses this to acquire 1% of the equity in Ordinary Limited, buying 4,000 shares at £2 each for £8,000. This realises a capital gain of £(9,250 – 8,000) = £1,250.

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As an investor in Ordinary Limited, Roxy’s annual return is now calculated as follows:

£

Gross annual return from Ordinary Limited of: £96,000/0.4m = 24p per share: 24p x 4,000 shares = 960 in total

Less: interest on borrowings of 7% x £3,000 =

  210

Receive a net return of £750

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Exercise:

Calculate the WACC of:

1. Leverage Ltd.

2. Ordinary Limited

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The view of Franco Modigliani and Merton H Miller is that the state of affairs outlined above would result in investors selling shares in Leverage Ltd. and buying shares in Ordinary Limited.This would result in the price of shares in Leverage Ltd. fallingand the price of shares in Ordinary Limited increasinguntil an equilibrium position was reachedat which point there would be no benefit in adopting the arbitrage strategy.That view is discussed further in the next section.

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The Modigliani and Miller View

The essence of this view is that firms of identical sizeexperiencing identical operating risksare identical in all material economic aspectsand will therefore have the same value— and hence the same WACC —irrespective of their gearing. Hence, the WACC profile is a straight line parallel to the x-axis. Thus, the MM view is that the capital structure of a firm is irrelevant to its value.

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The value of a firm stems from expectations about the future cash flows that the firm will generate.Investors are effectively buying future cash inflows,if a particular set of cash flows is available from a choice of two investments (of identical risk) then the cash flows should cost the same.If they have different prices,rational investors will switch from the more expensive to the cheaper company

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There are two arguments that are fundamental to the Modigliani and Miller view:-

• The issue of debt increases the risk for holders of equity.These holders therefore demand an increase in return which will exactly offset the effect on WACC of the use of the cheaper debt financing

• At high levels of gearing,risk-seeking investors will buy equity for the first time.

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The Equilibrium Position

For ease of calculating the equilibrium share price for the geared company:assume that the market value of the debt in the geared company is correctly priced,deduce the value of the equity,divide the market value of the equity by the number of ordinary shares in issue.

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Abandoning the Heroic Assumption

(by Incorporating Taxation)Interest on corporate debt is tax allowable (deductible) in the UK and USA,whereas dividend payments(being an appropriation of profit, rather than an expense)are not.There is therefore an advantage associated with debt financing.

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Consider an example in a world in which corporate taxes are charged at 25%:

G Ltd.£

E Ltd.£

Profit before interest and tax 1,000 1,000

Interest 160 nil

Profit before tax 840 1,000

Taxation 210 250

Profit after tax 630 750

Income to Financiers:

Equity 630 750

Debt 160 nil

Total 790 750

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The total income available to the people who finance G Ltd. is greater than the income available to the people who finance E Ltd.Some of the income has been ‘shielded’because the interest paid to service debt is tax allowable.This benefit is known as the interest tax shield: G Ltd. E Ltd.

Interest Tax Shield Value £40 Nil

Note that the value of the tax shield is25% x Interest = 25% x £160 = £40

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The interest tax shield is an asset.It can be valued as a perpetuity using a discounted cash flow approach.The appropriate discount for the tax shield depends on the relative riskiness of the tax shield itself.One assumption is that the risk attached to the tax shield is identical with the risk of the interest payments that give rise to the shield.The interest payment of £160 in the above example arose from interest of 4% on £4,000 debentures:the discount rate used would therefore be 4%.The Present Value (PV) of the tax shield is computed as £40/0.04 = £1,000.Effectively, the government is taking on the servicing of 25% of the loan of £4,000.

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Adopting the assumptions above there is a clear shortcut to calculating the PV of the tax shield.It is the product of the corporation tax rate and the amount of the debt, DT,where D is the amount borrowed andT is the rate of corporation tax.This is because the tax saving is TrDwhere r is the interest rate,and the PV of the tax shield is the tax saving divided by the interest rate, r; thus, the PV of the tax shield isTrD/r = DT.

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The Modigliani & Miller (Post-Tax) Assumptions

• Investors are rational;• There are no transaction costs;• Capital markets are efficient ;• There are equivalent firms;• Individuals can achieve corporate gearing;• Interest rates are independent of the level

of gearing;• There are no costs associated with

financial distress.

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