EM4001Ch6 Gearing and Cost of Capital

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CHAPTER SIXGEARING AND THE COST OF CAPITAL

Preamble

In problems that we have considered so far, a discount rate has beenspecified. In practice, we shall have to choose an appropriate discount rate.It seems plausible that there will be a connection between a companys costof capital and the discount rate for project appraisal. Consequently, weexplore the concept of the weighted average cost of capital in this section.We also examine some views of the relationship between cost of capital andcapital structure. However, we begin with a review of interest rates.

Learning Outcomes

On successful completion of this Chapter, students should normally be ableto:

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

Interest Rates

Introduction

Interest rates are an important factor in the financial environment ofcompanies and, consequently, they have a significant impact on financialstrategists decision-making. Interest rates are of significance for a number ofreasons, including the following:

1. Interest rates measure the cost of borrowing. When interest rates rise,companies will pay more interest on those borrowings with a variable rateof interest (including on bank overdrafts),

2. Interest rates in a country influence the foreign exchange value of thatcountrys currency,

3. Interest rates can be used as a guide to the return that a companysshareholders will require,

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4. Changes in market interest rates will affect share prices.

In addition, as we have seen, there is a strong connection between interestrates and the discount rate to be used in investment appraisal.

Principal interest rates in the financial markets of the UK

The interest rates in the UK financial markets that are most commonly quotedare as follows.

1. Base rates of the clearing banks1. Banks lend money to small companiesand individual customers at certain margins above their base rate.Theoretically, each clearing bank sets its own base rate independently ofthe others; however, in practice, a change in the base rate of one clearingbank is followed by similar changes to the base rates of all the otherbanks,

2. LIBORis the most widely used reference rate for short-term interest rates.LIBOR stands for the London Interbank Offered Rate, and is the rate ofinterest at which banks borrow funds from other banks in the Londoninterbank market. It is compiled by the British Bankers Association andreleased to the market at about 11.00 a.m. each day. For large loans tolarge companies, banks set interest rates at a margin above LIBOR, ratherthan at a margin above base rate,

3. The Treasury bill rate is the rate payable by the Bank of England onTreasury bills it has sold to the discount market,

4. The yield on long-dated2 gilt-edged securities. Gilt-edged securities areinterest-bearing securities issued by the government,

5. The yield on bank deposit accounts or building society accounts,6. The bank overdraft rate for personal customers.

There are a number of reasons why interest rates are different in differentmarkets:

Risk lenders will require compensation for lending to borrowers at higherrisk of default.

The need to make a profit on re-lending financial intermediaries make profit

from lending at a higher rate of interest than the cost of their borrowing.

The length of the loan normally, long-term loans will earn a higher yieldthan short-term loans, this is known as the term structure of interest rates, andis discussed below.

The size of the loan deposits greater than a certain amount lodged with abank or building society may attract higher rates of interest than smallerdeposits.

1 A clearing bank is a member bank of a national cheque clearing system. In the UK, the

clearing banks include the main English high-street banks, their Scottish and Northern Irishequivalents, and several regional banks.2 Say, 20 years to maturity.

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International interest rates interest rates varies from country to country dueto differing rates of inflation from country to country and different governmentpolicies on interest rates and foreign currency exchange rates.

Different types of financial asset different types of financial asset attractdifferent rates of interest. This is mainly a result of the competition fordeposits between different types of financial institution. For example, buildingsocieties have to offer a high enough yield to depositors to attract enoughdeposits to meet the demand for mortgages. Since bank deposit accounts areseen as a competitor for individuals savings, building societies may offer aslightly higher rate of interest than bank deposits. Similarly, discount houses,banks, local authorities, and finance houses3 all compete to borrow money inthe money markets. To attract funds away from the discount houses, localauthority deposits will offer a slightly higher yield, and the interbank rate couldbe slightly higher than that. Finance houses, to attract one-month deposits,

could be obliged to offer a higher yield than the one-month interbank rate.

The term structure of interest rates

Suppose an investor decides to invest in some government securities. Sincethe securities represent borrowing by the government, and the investment istherefore risk-free, it might seem reasonable to expect that the nominal rate ofinterest paid would be the same, no matter what the type of security.However, this is not the case. One reason for this is that the governmentborrows by issuing new securities from time to time, and the rate of interestoffered on a new issue of securities will depend on conditions in the market atthe time. This explains why the nominal interest rate on new gilt-edgedsecurities might be 12% on one occasion, 9% on another, and 11% onanother.

Another important reason why interest rates on the same type of financialasset might vary is that interest rates depend on the term to maturity of theasset and, for example, Treasury Stock can be short-dated, medium-dated, orlong-dated. The term structureof interest rates refers to the way in which theyield on a security varies according to the term of the borrowing, i.e. thelength of time until the debt will be repaid. Normally, the longer the term of an

asset to maturity, the higher the rate of interest paid on the asset. There aretwo reasons for this, firstly, there is a greater risk in lending long-term than inlending short-term, simply because the borrower has more time in which toget into financial difficulties. To compensate investors for this risk, they willrequire a higher yield on longer dated investments. Secondly, an investor willrequire compensation for tying up his or her money in the asset for a longerperiod of time. To illustrate, if the government were to make two issues of12% Treasury Stock on the same date, one with a term of five years and onewith a term of 20 years (and if there were no expectations of changes ininterest rates in the future) then the liquidity preference of investors wouldmake them prefer the five year stock. The only way to overcome the liquidity

3 Finance houses, also known as finance companies, provide the financing for varioustransactions, particularly hire purchase.

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preference of investors is to compensate them for the loss of liquidity; that isto say, to offer a higher rate of interest on longer dated stock.

This leads us to expect that the yield curve will normally be upward sloping, sothat long-term financial assets offer a higher yield than short-term assets.

However, a yield curve can slope downwards, with short-term rates higherthan longer-term rates. The most likely causes are:

1. Expectations about the way that interest rates will move in the future.When interest rates are expected to fall, short-term rates might be higherthan long-term rates, and the yield curve would be downward sloping.Thus, the shape of the yield curve gives an indication to the financialstrategist about how interest rates are expected to move in the future.

2. Government policyon interest rates. If government influence over interestrates is directed mainly towards short-term interest rates, a policy of

keeping interest rates relatively high could have the effect of forcing short-term interest rates higher than long-term rates.

The Weighted Average Cost of Capital

Ideally, perhaps, to carry out investment appraisal using a discounted cashflow approach, a particular project should be associated with its specificfunding: however, it is often the case that this is not possible and, in thesecircumstances, it is arguable that the companys funding should be seen as apool of resources. Indeed, a number of commentators argue that the poolapproach ought to be adopted even where it is possible easily to identify aspecific source of funding for a given project. If the pool approach is taken,the appropriate discount rate for appraising a project would be the weightedaverage cost of capital (WACC).

Once the cost of individual sources of finance for a company have beenestablished, it is possible to calculate the weighted average cost of capital forthe company as a whole. The weighting is usually based on the marketvalues of the different types of capital, rather than on book amounts4.

Example:

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

Component of Capital CostMarket Value

000Ordinary Shares 15% 980Preference Shares 12% 550Debentures 8% 350

1,880

4 The book amounts can get out of line with market values so quickly they will often have noeconomic significance.

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Using the market value as the weighting, we can generate a fourth column bymultiplying the cost of capital by the market value as follows:


000Cost x MV

000

Ordinary Shares 15% 980 147Preference Shares 12% 550 66Debentures 8% 350 28

1,880 241

The weighted average cost of capital is the sum of the products (241,000 inthis 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%.

In general, if there are n sources of long-term funding with individual costs ofcapital K1, K2, K3, ... Kn and market values V1, V2, V3, ... Vn, then the weighted

average cost of capital (WACC) is given by:

1 1 2 2 3 3

1 2 3

WACC n n

n

K V K V K V K V

V V V V

+ + + +=

+ + + +

K

K

Obviously, the value of the company as a whole is simply the sum of the

values of the individual sources of funding. Thus, 1 2 3 nV V V V + + + +K is the

total market value of the company, MV, and we may write:

1 1 2 2 3 3

WACCn n

K V K V K V K V

MV

+ + + +

=

K

Question 6.1

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


000Ordinary Shares 14% 980Preference Shares 11% 45

Debentures 5% 360

Estimate the weighted average cost of capital of Snowy plc.

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The Traditional View of the WACC-Gearing Relationship

Historically, fixed interest investors have not demanded as high a return asequity 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 theincrease in risk. At very high levels of gearing the fixed-interest investors willthemselves demand a higher return for higher risk. Thus, WACC willdecrease at low levels of gearing and increase at higher levels. The WACCprofile against gearing will be saucer-shaped at low and medium levels ofgearing, indicating that for a particular company there is an optimum mix ofdebt 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 theratio of debt to total funding:

0 0.2 0.4 0.6 0.8 10

10

20

30

40

f( )x

x

Exhibit 1: WACC as a Function of Gearing

Ifthe traditional view is an accurate representation of how WACC varies withchanges in gearing, then it should be possible to create wealth by optimisingthe firms capital structure. The next section shows how this would happen.

Creating Wealth in a Firm by Changing its Capital Structure

The following two assumptions are made:

1. Investors prefer more wealth to less

2. The wealth associated with a project may be measured by calculatingits net present value, as in the example below:

Leverage Ltd. has the opportunity to engage in a three-year project (known asProject X) that is expected to have the following cash flows associated with it:

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YearCash Flow

(000)0 (1,000)1 400

2 5003 600

Leverage Ltd. is an all-equity financed company that has a cost of capital of12%. The net present value of Project X is calculated as follows:

YearCash Flow

(000)12% Discount

FactorPresent Value

(000)0 (1,000) 1 (1,000)1 400 0.893 3572 500 0.797 399

3 600 0.712 427183 = Net Present Value

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

Now, suppose that the traditional view is reliable, and that the followingadditional information is available. Leverage Ltd. is a company in which thecost of equity capital is 12% at low levels of gearing. The cost of debenturesat low levels of gearing is 7%. The company moves from being all equityfinanced to being funded partly by debentures, and the ratio of the marketvalues of debt to equity is 2:3. Despite this change in the companys gearing,the cost of both equity and debt is unaltered. The weighted average cost ofcapital (WACC) of Leverage Ltd. is calculated as follows:

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

5=

Our earlier calculation of the NPV of Project X now needs to be amendedbecause of the change in the discount rate, the earlier calculation of NPV at12% is also shown to aid comparison:

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YearCash Flow

(000)12% Discount

FactorPresent Value

(000)0 (1,000) 1 (1,000)1 400 0.893 357

2 500 0.797 3993 600 0.712 427

183NPV at 12% DF

YearCash Flow

(000)10% Discount

FactorPresent Value

(000)0 (1,000) 1 (1,000)1 400 0.909 3642 500 0.826 4133 600 0.751 451

228NPV at 10% DF

It appears that the introduction of debt into the company has resulted in anincrease in wealth from 183,000 to 228,000.

This conclusion relies on the assumption that the cost of equity will remainunchanged despite the introduction of debt. It is as if the holders of equityhave not noticed that their risk position has worsened. The question arises asto whether this is likely will the holders of equity really fall asleep and notnotice that debt has been issued and their risk increased? Ifthe cost of equityremains more or less unchanged (because enough of the ordinaryshareholders fail to notice the introduction of debt) then there is an opportunityto make abnormally high returns for anyone who does notice. To put itanother way, the ordinary shareholder who remains alert when the cost ofequity remains unchanged despite the introduction of debt has access to amoney 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 forfunding. Both make an operating profit of 96,000 p.a. and both companieshave a policy of paying out all residual profit as dividend. Further details are

as follows:

Leverage Ltd.Market Value

000400,000 ordinary shares of 1 each 625300,000 7% debentures 300

925

Ordinary LimitedMarket Value

000

400,000 ordinary shares of 50p each 800

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

Leverage Ltd. Ordinary Limited000 000

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

We 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% x96,000/800,000 = 12%). So, the market values of the two companies are inline with the traditional view that at low levels of gearing equity investors donot require increased return for low levels of financial risk.

Note that the total market values of the two firms are different, even thoughthe 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 twofirms are different, even though the companies are operationally identical, is

arguably anomalous. For example, if an investor wanted to gain an annualincome of 96,000 they could buy all the shares in Ordinary Limited andreceive dividends totalling 96,000 each year, or the investor could buy all theshares and all the debentures in Leverage Ltd. and receive interest on theirdebentures of 21,000 and dividends of 75,000: both alternatives would yieldan annual income of 96,000, as required. However, to buy all the shares inOrdinary Limited would only cost 800,000 compared with the cost ofacquiring the shares and debentures in Leverage Ltd. of 925,000. Given thechoice of acquiring something for either 0.8m or 0.925m the rational personwould opt for the former. (Remember that the two companies are identical,except for their capital structure, so they are subject to the same level of

business risk.)

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Now, it may be said, quite rightly, that people with 0.925m (or even 0.8m) tospare are fairly rare creatures: however, the differential pricing of the twocompanies provides an opportunity for even small investors to increase theirwealth, as we shall (eventually) see:

Roxy holds 4,000 ordinary shares in Leverage Ltd. This is an investment witha modest market value of 6,250. The level of risk associated with thisinvestment is exactly the level she wants, or to put it another way, theshareholding reflects her attitude towards risk.

As a 1% investor in Leverage Ltd., any sales of shares that Roxy chooses tomake will have no material affect on the market price of the shares. Inaddition, she will not materially alter her current level of investment inLeverage Ltd. It follows that any share dealings in Leverage Ltd. that Roxyhas will not materially alter the market price. To put it another way, Roxy is aprice-taker. Her current annual return is:

1% x (96,000 - 7%.300,000) = 750.

A check on this calculation would be to argue that since Roxy is a 1%investor, she will receive a 1% share of the total shareholders dividend. Thistotal dividend was calculated above as 75,000, so Roxys share would be 1%x 75,000 = 750.

A simple-minded approach would be for Roxy to sell her shares in LeverageLtd. and invest the proceeds in Ordinary Limited equity, as follows:

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

2 Invest 6,250 in shares in Ordinary Limited. These shares have amarket value of 800,000/400,000 = 2 each, so she can buy6,250/2 = 3,125 shares, ignoring trading costs such as commission.

As an investor in Ordinary Limited, Roxys annual return is calculated asfollows: annual return from Ordinary Limited is 96,000/0.4m = 24p per shareand 24p x 3,125 shares = 750. This is the same return as she received fromLeverage Ltd. However, her risk position has improved, in that her returns

from Ordinary Limited are less volatile than they were from Leverage Ltd.Suppose, for example, that the operating profit in both companies fell by 5%to 91,200. Then a 1% investor in Leverage Ltd. would see their returndecrease to 1% x (91,200 - 7%.300,000) = 702. However, Roxysinvestment in Ordinary Limited would yield:91,200 x 3,125/400,000 = 712.50.

Thus, this simple-minded strategy would allow Roxy to maintain her expectedreturn but decrease her risk. Since Roxy was happy with her risk in LeverageLtd., this suggests that she could improve her expected return whilst leavingher risk position as it was when she held shares in Leverage Ltd.

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A strategy to increase her wealth without altering her risk position is asfollows:


2 Substitute personal borrowing for the corporate debt by borrowing 1% x300,000 = 3,000 at 7% p.a.

3 Roxy has funds of (6,250 + 3,000) = 9,250. She uses this to acquire1% of the equity in Ordinary Limited, buying 4,000 shares at 2 eachfor 8,000. This realises a capital gain of (9,250 8,000) = 1,250.

As an investor in Ordinary Limited, Roxys annual return is now calculated asfollows:

Gross annual return from Ordinary Limited of:

96,000/0.4m = 24p per share: 24p x 4,000 shares = 960 in totalLess: interest on borrowings of 7% x 3,000 = 210Receive a net return of 750

We see that Roxy has the same return as before but has realised a gain of1,250.

The second stage of Roxys strategy (borrowing money) is intended tomaintain her risk position. We were told that The level of risk associated with[her original] holding [in Leverage Ltd.] is exactly the level she wants..., andhence her strategy must maintain that level of risk. However, if she simplysold shares in the geared company and bought shares in the ungearedcompany then she would change the riskiness of her investment, as we sawabove: there was financial risk associated with the debt in Leverage Ltd.whereas there is no financial risk associated with shares in Ordinary Limited.Hence, to maintain her risk position, she needs to reintroduce the financialrisk associated with the debt in Leverage Ltd. To effect this reintroduction,Roxy borrows money personally. The ratio of her debt to her equityinvestment in Ordinary Limited is the same as the ratio of debt to equity inLeverage Ltd. This ensures that the level of risk associated with her newinvestment is identical with that of the original investment.

We show that her risk position has been maintained, in that her returns fromOrdinary Limited are just as volatile as they were from Leverage Ltd.Suppose, for example, that the operating profit in both companies fell by 5%to 91,200. Then a 1% investor in Leverage Ltd. (as Roxy used to be) wouldsee their return decrease to 1% x (91,200 - 7%.300,000) = 702. Roxysinvestment in Ordinary Limited would yield 91,200 x 4,000/400,000 = 912,gross and the interest payments would reduce this to 702 net, the same asyielded by the equivalent investment in Leverage Ltd. It follows that thedegree of volatility in return and hence risk has been maintained.

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You may be wondering what the position would be if, instead of taking thecapital gain, Roxy invested all her available funds in Ordinary Limited. Herstrategy would then be as follows:


2 Substitute personal borrowing for the corporate debt by borrowing 1% x300,000 = 3,000 at 7% p.a.

3 Invest (6,250 + 3,000) = 9,250 in shares in Ordinary Limited. Theseshares have a market value of 800,000/400,000 = 2 each, so shecan buy 9,250/2 = 4,625 shares, ignoring trading costs such ascommission.

As an investor in Ordinary Limited, Roxys annual return is calculated asfollows:

Gross annual return from Ordinary Limited:96,000/0.4m = 24p per share and 24p x 4,625 shares = 1,110 in totalLess: interest on borrowings of 7% x 3,000 = 210Net annual return of 900

Roxy is now receiving an annual income of 900 instead of 750, so she isbetter off by 150 each year.

Note that Roxy had been a 1% equity investor in Leverage Ltd., but now holdsmore than 1% of the ordinary shares in Ordinary Limited (4,625/0.4m =1.15625%, to be exact). Hence, as a shareholder, she is entitled to a largershare of the same cake. The reduction in her return due to interestpayments is the same in both cases.

When Roxy was a 1% equity investor in Leverage Ltd. she was entitled to 1%of the profit after interest, this was 750 [1% of (96,000 less the interest of21,000)]5. However, now she is entitled to 1.15625% of 96,000, and is stillonly paying 210 to service debt (which she has now taken on personally).Hence, she is better off by the difference between 1.15625% of 96,000 and1% of 96,000 = 0.15625% x 96,000 = 150, as shown earlier.

A further effect of the change in her holding from 1% to slightly more than 1%is that she has slightly decreased her risk. Suppose, for example, that theoperating profit in both companies fell by 5% to 91,200. Then a 1% investorin Leverage Ltd. would see their return decrease to 1% x (91,200 - 7%.300,000) = 702, a decrease of 6.4%. Roxys investment in OrdinaryLimited would yield 91,200 x 4,625/400,000 = 1,054.5 gross, and theinterest payments would reduce this to 844.5 net, a decrease from 900 of

just under 6.2%. So, Roxy has both increased her income and reduced her

5 Another way of looking at this is to consider that she was entitled to 1% of 96,000 (i.e. 960),

and that the company was paying directly to the lenders her share of the associated debtfinancing (i.e. 1% of 21,000 = 210). So her net entitlement was 960 less 210, i.e. the 750we calculated earlier in a different way.

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risk. This has arisen because Roxy borrowed only 1% of the debt in LeverageLtd, although she bought 1.15625% of the equity in Ordinary Limited.Suppose that she borrows 1.15625% of the debt in Leverage Ltd.:

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

2 Substitute personal borrowing for the corporate debt by borrowing1.15625% x 300,000 = 3,468.75 at 7% p.a. Total funds = (6,250 +3,468.75) = 9,718.75.

3 Buy 1.15625% of the shares in Ordinary Limited at a cost of 9,250,i.e. 4,625 shares, ignoring trading costs such as commission. Thisrealises a capital gain of 468.75.


Gross annual return from Ordinary Limited:96,000/0.4m = 24p per share and 24p x 4,625 shares = 1,110.00Less: interest on borrowings of 7% x 3,468.75= 242.81Net annual return of 867.19

Roxy is now receiving an annual income of 867.19 instead of the 750 shereceived from Leverage Ltd., so she has increased both her annual incomeand realised a capital gain. We now consider her risk position. Suppose, forexample, that the operating profit in both companies fell by 5% to 91,200.Then a 1% investor in Leverage Ltd. would see their return decrease to 1% x(91,200 - 7%.300,000) = 702, a decrease of 6.4%. Roxys investment inOrdinary Limited would yield 91,200 x 4,625/400,000 = 1,054.5, gross andthe interest payments of 242.81 would reduce this to 811.69 net, adecrease from 867.19 of 6.4%. Thus, she has the same risk as she hadoriginally.

We have seen strategies that have resulted in:

maintenance of income with a reduction in risk maintenance of both risk and income with a capital gain

an increase in income and a capital gain with a reduction in risk

The remaining outcome that a rational investor might wish to see ismaintenance of risk with an increase in income but no capital gain. Considerthe following:

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

2 Borrow 3,750. Total funds available for investment = (6,250 + 3,750)= 10,000.

3 Buy 5,000 shares in Ordinary Limited at a cost of 10,000, ignoringtrading costs such as commission.

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Gross annual return from Ordinary Limited:

96,000/0.4m = 24p per share and 24p x 5,000 shares = 1,200.00Less: interest on borrowings of 7% x 3,750= 262.50Net annual return of 937.50

Roxy is now receiving an annual income of 937.50 instead of the 750 shereceived from Leverage Ltd., so she has increased her annual income. Wenow consider her risk position. Suppose, for example, that the operating profitin both companies fell by 5% to 91,200. Then a 1% investor in LeverageLtd. would see their return decrease to 1% x (91,200 - 7%.300,000) = 702,a decrease of 6.4%. Roxys investment in Ordinary Limited would yield91,200 x 5,000/400,000 = 1,140, gross and the interest payments of

262.50 would reduce this to 877.50 net, a decrease from 937.50 of 6.4%.Thus, she has the same risk as she had originally.

Question 6.2

Calculate the WACC in both Leverage Ltd. and Ordinary Limited before andafter the various strategies outlined above.

Question 6.3

Mixed Ltd and Pure Ltd are companies that are identical except for funding.Both make an operating profit of 2.5m p.a. and both companies have apolicy of paying out all residual profit as dividend. Further details are asfollows:

Mixed LtdMarket Value

0004m ordinary shares of 1 each 8,0004m 5% debentures 5,000

13,000

Pure LtdMarket Value

00050m ordinary shares of 50p each 12,500

Your client, Valentina, holds 40,000 ordinary shares in Mixed Ltd. Thisreflects her attitude towards risk.

Required:

1. Devise a strategy to increase Valentinas wealth whilst maintaining her riskposition.

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2. Calculate the WACC for Mixed Ltd. and Pure Ltd.

Where Nominal and Market Values of Debt are Different

In the Question of Mixed Ltd. and Pure Ltd., the 5% debentures in Mixed Ltd.

had a market value that was 25% higher than their nominal value. Someonewith 125 to invest would be able to acquire debentures with a nominal valueof only 100. Interest receivable on those debentures would be 5% x 100 =5 p.a. So the investor would receive 5 interest from an investment that cost125: this implies a market rate of interest of (5/125) x 100% = 4%. Thereason for the difference between the market rate and nominal rate of thesedebentures could be that 5% was the market rate of interest for thosedebentures when they were issued, but that the current market rate is 4%.

It is possible to approach the question by assuming that an investor couldborrow in the same way as Mixed Ltd., that is, by assuming that the investor

could borrow 50,000 and pay interest at 5% on 40,000 (= 2,000).However, it is more realistic to assume that she would be able to borrow50,000 at the prevailing rate of interest, 4%, leading to interest payable of4% x 50,000 = 2,000.

The strategy is given below:

As a 1% investor in Mixed Ltd., Valentinas current annual return is:1% x (2.5m - 5%.4m) = 23,000.

1 Sell the shares for 1% x 8m = 80,000

2 Pay the same amount of interest as her earlier share of the corporateinterest, 2,000 p.a.. The prevailing rate of interest is 4% p.a. so shecan borrow 50,000 (the quickest way of calculating this amount issimply to take 1% of the market value of the corporate debt).

3 Invest 125,000 in 500,000 shares to become a 1% investor in PureLtd., realising a gain of (80,000 + 50,000) - 125,000 = 5,000.

Receive an annual return from Pure Ltd of: 2.5m/50m =5p per share; 5p x 500,000 shares = 25,000Less: interest on borrowings of 4% x 50,000 = 2,000Receive a net return of 23,000

We conclude that our investor is maintaining both her income and riskexposure, but has realised a capital gain of 5,000.

Note that the interest calculation can be checked as follows: interest paid bythe company at 4% on 5m debentures = 4% x 5m = 200,000, Valentinas1% share of this = 2,000: Checks.

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We now identify the anomaly implicit in the traditional view, in relation to theprevious illustration:

WACC of Pure Ltd.: An ordinary shareholder in Pure Ltd receives2.5m/50m = 5p per share. The market value of a share in Pure Ltd is

12.5m/50m = 25p. So, the cost of capital is 5/25 = 20%.

WACC of Mixed Ltd.: The 4m shares in Mixed Ltd. have a market value of8m so each share is worth 2. The total return to the shareholders is2,300,000 or 57.5p per share, hence the return on equity is 57.5/200 =28.75%. The return on 100 nominal value debentures is 5%x100 = 5 andthe market value of such a holding is 100x5/4 = 125. Thus, the return onthe debentures is 5/125 = 4%. So, the WACC in Mixed Ltd. is:

(8m.28.75% + 5m.4%)/(8m + 5m) 19.23%.

These calculations demonstrate the anomaly of ostensibly identical (exceptfor funding) companies having different WACCs.

The view of Franco Modigliani and Merton Miller is that the state of affairsoutlined above would result in investors selling shares in Mixed Ltd. andbuying shares in Pure Ltd. This would result in the price of shares in MixedLtd. falling and the price of shares in Pure Ltd. increasing until an equilibriumposition was reached at which there would be no benefit in adopting thearbitrage strategy. That view is discussed further in the next section.

The Modigliani and Miller View

The essence of this view is that firms of identical size experiencing identicaloperating risks are identical in all material economic aspects and will thereforehave the same value and hence the same WACC6 irrespective of theirgearing. Hence, the WACC profile is a straight line parallel to thex-axis.

Thus, the MM view is that the capital structure of a firm is irrelevant to itsvalue. The value of the firm stems from expectations about the future cashflows that the firm will generate. Investors are effectively buying future cashinflows, 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. Ifthey have different prices, rational investors will switch from the moreexpensive to the cheaper company (as we saw with the earlier examples ofLeverage Ltd. and Ordinary Limited, and Mixed Ltd. and Pure Ltd.), andsupply and demand will mean that the cheaper company will become moreexpensive and the more expensive company will become cheaper until suchtime as their prices will no longer lead to a gain on switching. At that stage,the prices are said to be in equilibrium and those prices will be such thatthe total market value of the companies are the same.

6 If the firms have the same total income and the same market value, then they have the sameWACC.

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

1. The issue of debt increases the risk for holders of equity. Theseholders therefore demand an increase in return which will exactly offset

the effect on WACC of the use of the cheaper debt financing2. At high levels of gearing, risk-seeking investors will buy equity for the

first time.

The second argument is an assumption to which we shall return later, for thetime being we note that there is little experience in Western economies ofveryhigh levels of gearing. The first argument contradicts the traditional viewthat the ordinary shareholders do not require compensation for being exposedto low levels of financial risk, i.e. the Modigliani and Miller view is that ordinaryshareholders will always require compensation for increased financial risk even at comparatively low levels of gearing. Furthermore, it is argued that if

such compensation is not supplied the shareholders can themselves createthe compensation by switching their investment to an ungeared company ofidentical business risk and using personal borrowing to replace the corporatefinancial risk that was present in their original investment. This was illustratedabove by means of an arbitrage effect calculation. The following questiongives a further example of an arbitrage strategy.

Question 6.4

Geared Ltd. and All-Equity Ltd. are identical in every respect, except funding.The annual pre-interest profit for both firms is 1m, and, as a matter ofcompany policy, all profit is distributed as dividend.

Geared Ltd.Market Value

m6m ordinary shares of 1 each 8.44m 4% debentures 4.0

12.4

All-Equity Ltd. m10m ordinary shares of 1 each 10.0

Required:

Demonstrate an arbitrage opportunity open to a holder of 1% of the equity inGeared Ltd.

We now calculate the return available to an equity investor in Geared Ltd. andthen calculate the return available to an equity investor in All-Equity Ltd.

Cost of equity capital in Geared Ltd.

The annual pre-interest profit for both firms was 1m. The cost of servicingthe debt in Geared Ltd. is 4% x 4m, i.e. 160,000 leaving 1m - 160,000 =

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840,000 net profit for the holders of the 6m equity shares. Eachshareholders annual return is 14p per share. The market value of a share inGeared Ltd. is 8.4m/6m = 140p. The cost of equity capital in Geared Ltd. istherefore (14p/140p) x 100% = 10%.

Cost of equity capital in All-Equity Ltd:

The return for an equity investor in All-Equity Ltd. = (1m/10m) = 10p pershare, and the cost of equity capital in All-Equity Ltd. is therefore (10p/100p) x100% = 10%.

Supporters of the MM view claim that this state of affairs would beunacceptable to an investor in Geared Ltd. Such an investor is receiving onlythe same return as an investor in the equity of All-Equity Ltd., but is running ahigherrisk due to the presence of gearing.

Inter alia, the investor could:

sell shares in Geared Ltd. and buy shares in All-Equity Ltd. to earn thesame return at less risk, or

sell shares in Geared Ltd., substitute personal borrowing for corporatedebt, and buy shares in All-Equity Ltd. to yield a higher rate of return, or

sell shares in Geared Ltd., maintain the same level of risk by borrowingmoney, and buy enough shares in All-Equity Ltd. to yield the same returnas before this will leave some money left over, being a capital gain.

The course of action would depend on the amount of risk the investor wantedto run. The first option is covered by the following Question, a solution is setout below for the second, and the third is left as an exercise for the reader7.

Question 6.5

Required:

(a) Calculate the annual return to a holder of 30 shares in Geared Ltd.(b) Calculate the annual return available to a holder of 30 shares in

Geared Ltd. who sold the shareholding and invested the proceeds in

All-Equity Ltd.

7 Hint: To maximise income while maintaining risk, the investor has to use the money borrowedtogether with that realised by selling the shares in the geared company to buy shares in theungeared company such that the ratio of equity acquired in the ungeared company to the totalequity in that company is the same as the ratio of the amount borrowed to the corporate debt in

the geared company. Let the percentage of both equity and debenture be f:Sale proceeds + Borrowings = Investment in ungeared company and we have:1% x MV Geared Company + fx Debt = fMV Ungeared Company. Now solve forf.

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Option 2: Consider a 1% investor in the equity of Geared Ltd. The investorowns 60,000 shares worth 1.40 each, i.e. 84,000 worth of shares in total.The annual return is 14p per share, i.e. 8,400 in total. Our investor would:

1 Sell the shares for 84,000

2 Maintain the same effective gearing as before (4:8.4) by borrowing40,000

3 With the (84,000 + 40,000) = 124,000 available for investment buy124,000/1 = 124,000 shares in All-Equity Ltd.

Receive an annual return from All-Equity Ltd. of 10p per share = 12,400Pay interest on borrowings of 4% x 40,000 = 1,600Receive a net return of 10,800

The arbitrageur is now receiving an annual income of 10,800 instead of8,400.

Clearly, under these circumstances arbitrageurs will sell shares in Geared Ltd.and buy shares in All-Equity Ltd.: as they do so, the price of shares in GearedLtd. will fall and the price of shares in All-Equity Ltd. will rise. Arbitrageurs willstop switching from Geared to All-Equity when the return from All-Equity is thesame as that from Geared. This will occur when the total market values of thetwo firms are the same. The characteristics of this equilibrium position areexplored in the following section.

The Equilibrium Position

For ease of calculation let us assume that the market value of the debt inGeared Ltd. is correctly priced, and that the price of shares in All-Equity Ltd.remains constant whilst the price of shares in Geared Ltd. falls:

Market value of All-Equity Ltd. = 10m.

Put the market value of Geared Ltd. = 10m. The market value of the debt is

4m so that the equity component must be worth 6m. There are 6m ordinaryshares in issue so they are worth 1 each at equilibrium. If shares in All-Equity remain at their original value, arbitrageurs will stop switching fromGeared to All-Equity when shares in Geared fall to 1 each.

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Demonstration: Reconsider our investor in Geared Ltd. holding 60,000shares. The annual return is 14p per share, so our investor receives60,000x14p = 8,400 p.a. Consider the arbitrage steps:

1 The shares are worth 1 each, so 60,000 will be sold for (only) 60,000

2 Maintain the same effective gearing as before by borrowing 40,000

3 With the (60,000 + 40,000) = 100,000 available for investment, buy100,000/1 = 100,000 shares in All-Equity Ltd.

Receive an annual return from All-Equity Ltd. of 10p per share = 10,000Pay interest on borrowings of 4% x 40,000 = 1,600Receive a net return of 8,400

Thus the net return is exactly the same as was available from holding the60,000 shares in Geared Ltd., so there is no point in switching the investmentfrom the geared to the ungeared company.

We now calculate the WACC of the two companies at equilibrium.

WACC of Geared Ltd.: When shares in Geared Ltd. are worth 1 each, thecost of equity in Geared Ltd. is (14p/100p).100% = 14%. The cost of debt inGeared Ltd. is 4% and the WACC of Geared Ltd. is thus:

(6,000.14% + 4,000.4%)/(6,000 + 4,000) = 10%

WACC of All-Equity Ltd.: Since the company is funded exclusively by equity,the WACC for the company is simply the cost of equity which we have alreadycalculated above as 10%.

The WACC is the same for the two companies, lending weight to the view thatthe WACC is independent of gearing.

The next section proves that arbitraging will stop when the marketcapitalisations of the firms are equal.

Proof That Arbitraging Stops When the Market Capitalisations of the Firmsare Equal

Let: Su = market value of the ungeared firmSg = market value of the equity of the geared firmLg = both the nominal and the market value of the geared firms loancapitali= interest rateX= (pre-interest) operating income of each firm

Both companies distribute all residual profit by way of dividend. Consider anindividual holding a proportion, a, of the equity in the geared firm. That

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individuals annual dividends would be a(X - iLg). The first arbitrage stagewould be to sell this holding foraSg. The second stage would be to substitutepersonal borrowing for corporate debt by borrowing money in the same ratioas in the geared firm, this amount will be aLg. With the funds now availablethe investor can invest aSg + aLg = a(Sg + Lg) in the equity of the ungeared

firm. This investment is a(Sg + Lg)/Su of the market value of the ungeared firm.The annual dividends from the new investment would be Xa(Sg + Lg)/Su.However, the investor would have to pay interest on the debt of iaLg. Hence,the net income from the new investment would be [Xa(Sg + Lg)/Su] - iaLg.Switching to the new investment is only worthwhile when the income from thenew investment, [Xa(Sg + Lg)/Su] - iaLg, exceeds the income from the originalinvestment, a(X- iLg). Switching ceases to be worthwhile and equilibrium isattained when [Xa(Sg + Lg)/Su] - iaLg is equal to a(X- iLg).

If [Xa(Sg + Lg)/Su] - iaLg = a(X- iLg)

Then [X(Sg + Lg)/Su] - iLg = (X- iLg)

and (Sg + Lg)/Su = 1

so (Sg + Lg) = Su

But (Sg + Lg) is the market value of the geared firm and Su is the market valueof the ungeared firm, so arbitraging will stop and equilibrium will be reachedwhen the market capitalisations of the two firms are equal.

Question 6.6

We saw in an earlier example that, given the arbitraging opportunities opento them, holders of equity in Mixed Ltd. would sell their shares and buyordinary shares in Pure Ltd. Assuming that this would result in the marketcapitalisation of Pure Ltd. at equilibrium being 12.75m and, assuming thatthe debt in Mixed Ltd. is already correctly priced, calculate the following:

the equilibrium market value of a share in Pure Ltd.the equilibrium market value of a share in Mixed Ltd.the WACC (to 2 decimal places) of Pure Ltd. at equilibriumthe WACC (to 2 decimal places) of Mixed Ltd. at equilibrium

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Question 6.7

It has been suggested that, if the equity and long-term capital of a companyare valued at market price, and if the rate of return on that capital is

calculated from earnings before loan interest, then that rate of return(ignoring taxation) will be identical for all companies having the same totalrisk.

The relevant data for two such companies are given below:

Lever Hume

Number of ordinary shares 90,000 150,000Market price per share 1.20 1.006% loan stock at par 60,000 nilEarnings before interest 18,000 18,000

All income after loan interest is distributed as dividend.

Required:

(i) explain and illustrate the process by which the market values of thecompanies might be brought into equilibrium;

(ii) list the assumptions implicit in your calculations;

(iii) comment on the likely effect of taxation on the market values of thetwo companies no calculations are required.

[15 marks]

So far, we have been very brave heroic, in fact by assuming that there isno taxation. It is now necessary to investigate the impact of taxation byabandoning the assumption of no corporate taxes.

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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 anexpense) are not. There is therefore an advantage associated with debt

financing. Reconsider the data in an earlier example in a world in whichcorporate taxes are charged at 25%:

Geared Ltd. All-Equity Ltd.

Profit before interest and tax 1,000 1,000Interest 160 nilProfit before tax 840 1,000Taxation 210 250Profit after tax 630 750

Income to Financiers:Equity 630 750Debt 160 nilTotal 790 750

The total income available to the people who finance Geared Ltd. is greaterthan the income available to the people who finance All-Equity Ltd. Some ofthe income has been shielded because the interest paid to service debt is taxallowable. This benefit is known as the interest tax shield:

Geared Ltd. All-Equity Ltd.Interest Tax Shield Value 40 Nil

Note that the value of the tax shield is 25% x Interest = 25% x 160 = 40.

The interest tax shield is an asset. It can be valued as a perpetuity using adiscounted cash flow approach. Of course there is a need to choose adiscount rate. The appropriate discount for the tax shield depends on therelative riskiness of the tax shield itself. One assumption that is commonlymade is that the risk attached to the tax shield is identical with the risk of theinterest payments that give rise to the shield. This seems plausible. The

interest payment of 160 in the above example arose from interest of 4% on4,000 debentures: the discount rate used would therefore be 4%. ThePresent 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 of4,000.

Adopting the assumptions above there is a clear shortcut to calculating the PVof the tax shield. It is the product of the corporation tax rate and the amountof the debt, DT, where D is the amount borrowed and T is the rate ofcorporation tax. This is because the tax saving is TrD where r is the interestrate, and the PV of the tax shield is the tax saving divided by the interest rate,

r; thus, the PV of the tax shield is TrD/r= DT.

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Let Vg be the market value of a geared company, and Su be the market valueof an ungeared company identical to the geared firm except for its financialstructure. Now, the value of a geared firm is the value it would have if all-equity financed plus the PV of the tax shield, so:

Vg = Su + DT

To return to the example introduced above:

A 1% investor in the geared firm will receive income of 6.30. S/he can sellthe holding for 84. S/he borrows:

1%.(1 - 25%).4,000 = 30.

To this is added only 70 from the 84 in order to buy 100 shares in theungeared company. The return from these shares is 7.50 from which

interest of 4%.30 = 1.20 is payable, giving net income of 6.30, as before.However, a capital gain of (84-70) = 14 has been made.

Using the same symbols as before:

The sale of shares in the geared firm yields aSg. The equity in the ungearedfirm costs aSu , of which a(1 - T)Lg is met by borrowing. The capital gain isthen:

aSg - [aSu - a(1 - T)Lg ], rearranging gives a[Sg - Su + (1 - T)Lg ].

Gains are available until Su = Sg + (1 - T)Lg.

Example: Consider two firms identical in all respects save funding:-

Caro plcMarket Value

0008m ordinary shares of 1 each 9,6002.8m 8% debentures 2,800

12,400

Orca plcMarket Value

0005m ordinary shares of 1 each 10,500

Pre-interest operating income is 5,000,000. Corporation tax is charged at25%. Calculate the capital gain available without loss of income to a 1%equity investor by switching from Caro plc to Orca plc.

Calculate the equilibrium share prices when the market value of Orca plc is

11,450,000.

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The gain is a[Sg - Su + (1 - T)Lg]

a = 1%Sg = 9.6mSu = 10.5m

T= 25%Lg = 2.8m

Substituting gives 12,000.

If the 5 million shares in Orca plc are worth 11,450,000 in total, then theprice per share is 2.29. In Caro plc the loan capital has a market value of2.8m; 75% of this is 2.1m leaving equity at (11.45m - 2.1m) = 9.35m.With 8m ordinary shares in issue this indicates a share price of about 1.17.

Even after abandoning the assumption of no corporate taxation, there are still

a number of assumptions inherent in the Modigliani and Miller hypothesis.These are briefly examined in the next section.

The Modigliani & Miller (Post-Tax) Assumptions

1. Investors are rational.

Task 1: Read the following three articles regarding share prices, and thenconsider whether the cases of Yahoo Japan (in 2000), John LawsCompagnie (in 1720), and Bre-X (in 1996) have anything in common witheach other:

In August 1717 [convicted murderer] John Law acquired a controllinginterest in the derelict Mississippi Company and renamed it the CompagniedOccident. This company had a monopoly on trade with French Louisianain North America (at the time thought to abound in precious metals) Bymid-1719 the Compagnie dOccident was re-organized as the Compagniedes Indes and had expanded to monopolize all French trade outsideEurope. In July 1719 the Compagnie purchased the right to mint newcoinage. In August 1719 the Compagnie bought the right to collect allFrench indirect taxes and in October 1719 the Compagnie took over the

collection of direct taxes. Finally, a plan was launched to restructure mostof the national debt, whereby the remainder of existing government debtwould be exchanged for Compagnie shares.

The activities of John Law were financed with share issues. TheCompagnie share price was around 500 livres in May 1719, rose to nearly10,000 livres in February 1720, and declined to 500 livres in September1721.

Erasmus Universiteit Rotterdam website:http://www.few.eur.nl/few/people/smant/m-economics/johnlaw.htm(Accessed 3 September 2004.)

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Yahoo Japan shares nudge $1m eachYahoo Japan is seen as a future money-spinner

Internet fever has helped create Japans first ever 100m yen share.

Following a 50-fold rise in its stock price in little more than two years, YahooJapans shares are worth more than 100m yen, or just under $1m each.The huge price tag is a result of scarcity of shares there are only 4,200shares on offer and continued internet fever.

Share split

In an effort to make the shares a little more affordable, there is to be a two-for-one share split but that will still leave each one costing hundreds ofthousands of dollars. Yahoo Japans current share price puts its price-to-earnings (PE) ratio the number of times the earnings per share must bemultiplied to reach the share price at 3,355. That compares with anaverage PE ratio of 80 for the Tokyo Stock Exchanges 1,900 companies,and a historical average across the world of about 10.

Potential remains

Shares in Yahoo Japan, the countrys most popular internet portal, brieflyrose by the daily limit to hit 101.4m yen ($959,600), on Wednesday [19January 2000]. The landmark followed a five-day rally partly inspired by theplanned two-for-one share split unveiled last week. The move the firms

third share split in the past year was aimed at feeding the demand forshares in Japans core internet stock, which has risen 30-fold in value in thepast year.

Kota Nakako, an analyst at Warburg Dillon Read, said: Probably, YahooJapans (PE) valuation is the highest in Japan, and, of course, much higherthan that of its US parent Yahoo Inc.

Despite the huge gap between its market valuation and actual performance,most analysts agree that Yahoo Japan has more upward potential becausethere is still a lot of money chasing relatively few shares in Japans youthful

internet industry.

Softbank investor

Another reason for the high price is the fact that there are just 4,200 YahooJapan shares offered for trading. Yahoo Japan is owned by Softbank Corp.,with 51% of the company, and Yahoo Inc. of the US which has 34%. BenWedmore of HSBC in Tokyo said that the small number of shares availablehad added scarcity value to them. He said: Average volume over the lastcouple of months was 23 shares a day. There are shares where you canonly buy a hundred or a thousand at a time. Yahoo is unusual in that the lot

size is one, but thats because the price is so high.

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Yahoo Japan shares were priced at two million yen when they went public inNovember 1997.

http://news.bbc.co.uk/1/hi/business/610317.stm Wednesday, 19 January,2000. (Accessed 3 September 2004.)

From end-1995 until early-1996 a Canadian mining company called Bre-XMinerals experienced a spectacular rise in its share price. The share pricewent from little more than a few C$ cents to more than C$ 25 per share.The reason was that the company had announced a large find of goldreserves in Indonesia (promising to be the largest new find of gold in the20th century). Estimates of the gold reserves increased over time andsubsequent reports of mining consultants and the Indonesian Mines Ministryindeed confirmed the existence of the gold reserves. Financial firms suchas Lehman Brothers and J.P. Morgan strongly recommended to buy theshares of Bre-X. The share price increased accordingly. Trouble startedwhen the chief geologist of Bre-X went missing and was presumed dead. Itturned out that the mining reports were based on salted samples and thegold reserves non-existent. The share price of Bre-X Minerals collapsed inthe early months of 1997.

Using the benefit of hindsight, some experts may label the Bre-X Mineralscase a typical example of irrational investor behavior in the stockmarket.However, the fact remains that ex ante, based on what appeared to bequalified and independent reports, rational stockmarket investors had validreasons to expect large future profits from this proposed mining operation.

They therefore increased the share price of Bre-X, which, according tofundamental finance theory, should currently reflect the expected discountedvalue of future cash flows.

Erasmus Universiteit Rotterdam website:http://www.few.eur.nl/few/people/smant/m-economics/southsea.htm(Accessed 3 September 2004.)

Task 2: Consider the following facts and consider whether investors could besaid to be behaving rationally in the light of the information available to themat the time (rather than considering the matter with the benefit of hindsight).

In 1929, Radio Corporation of Americas (RCA) price rose from $94 to$505, gaining 435 percent in just 18 months. By 1932, its price had fallen to

just $2. RCA was not an exceptional case The Dow Jones IndustrialAverage peaked in 1929 at 381, and, three years later, reached a low of 41.

Shares in the Australian nickel mining company, Poseidon, were trading forjust two or three A$ cents in 1966. In 1969/70, Poseidon shares rose fromA$1 to a peak of A$280, in less than four months, after news was reportedof a nickel discovery. In the mid-1970s, Poseidon went into receivership: itsfinal price zero.

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Do you think it is possible to learn how to avoid investing in shares that willlater collapse from these historical examples? Or do you think theunavoidable uncertainty about the future combined with human fallibilitymakes investment in shares a lottery?

2. There are no transaction costs.

This is unrealistic because of the existence of brokers commissions and otherdealing costs. This could prevent exploitation of minor mispricing of equity ingeared firms but would not invalidate the hypothesis where there wassignificant mispricing of equity in a geared firm relative to equity in anungeared one.

3. Capital markets are efficient.

It seems reasonable that investors are able to understand that an income

stream is an income stream irrespective of its packaging - an income streamdoes not change value when it is packaged differently. To this extent at leastit seems plausible that capital markets are efficient.

4. There are equivalent firms.

This is an assumption which is unlikely but also unnecessary, asdemonstrated by Stiglitz (1974).

5. Individuals can achieve corporate gearing.

There seems no reason why a few very wealthy individuals should not be ableto achieve corporate gearing. In addition, there is no reason why a companyshould not be an arbitrageur.

6. Interest rates are independent of the level of gearing.

At low levels of gearing lenders enjoy high asset to loan ratios. It seemsplausible that a lender would be indifferent between a ratio of 5:1 and 10:1.However, at high levels of gearing when the ratio approaches 1:1 then itseems likely that a price would be exacted for the erosion of the security.

7. There are no costs associated with financial distress.

In the event of bankruptcy, it is unlikely that assets could be sold for anamount that would return to the ordinary shareholders the market value oftheir shares immediately prior to liquidation. This is because of dealing costsand inefficiency in the market for real assets. Liquidation is most likely tooccur when gearing has been very high. In the UK, USA and continentalEurope gearing levels are modest so the assumption is arguablyunnecessary: indeed, it has been argued that the very existence ofbankruptcy costs is the cause of these modest levels of gearing (although it is

hard to reconcile this with the situation in Japan where gearing is

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tremendously high, except by seeing the providers of loan capital in thatcountry as de facto equity partners which is not unrealistic).

Conclusion

The only serious weaknesses stem from assumptions 6. and 7. above.Furthermore, it appears that the weaknesses are only significant at high levelsof gearing. We might hypothesise that the tax advantages of loan capitalcause the cost of capital to fall steadily from low to moderate levels of gearing.

Above these moderate levels the increase in return to providers of debt capitalcaused by the erosion of their security, and the increase in return to holders ofequity occasioned by the increased risk of bankruptcy costs cause the cost ofcapital to increase. The problem then becomes the identification of amoderate level of gearing. Of course, there will not be a single pointrepresenting moderate gearing there will be a range, or, rather, there willbe a set of ranges, since the range will vary from industrial sector to industrial

sector.

Appendix

A Note on the Relationship between Weighted Average Cost of Capital andMarket Capitalisation in the Case of Identical Companies

Consider a company with two sources of funding, namely equity and a single

source of debt. Let the market value of the equity be eM , let the market value

of the debt be dM , and let the market value of the company be c d eM M M= + .

Let the cost of equity be eK and let the cost of debt be dK . Let k be thecoupon rate of the debt and P be the nominal value of the debt, then the

return to holders of debt will be kP. The cost of debt will be dd

kPK

M= .

Suppose the company has a policy of distributing all residual profit asdividend. Let the annual pre-interest profit be , then the return to equity

investors will be kP and the cost of equity will be ee

kPK

M

= . The

weighted average cost of capital, C, will be given by:

d d e e

d e

M K M K C

M M

+=

+

( )d e

d e

c

kPkPM M

M M

M

+

=

c c

kP kP

M M

+ = = .

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Suppose there is a second company with identical characteristics (includingannual profit), except for its capital structure (being funded exclusively byequity). The weighted average cost of capital in this company will be simply

the cost of equity, namelyEM

, where EM is the market value of the second

company, and it follows that the weighted average costs of capital for the firmswill be identical unless there is a difference in their market capitalisations.

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Tutorial Sheet

Question 6.8

The following information relates to two companies that are identical except

for their capital structure:

Dixon Ltd Market Value (000)Equity: 175,000 ordinary shares of 1 each 250Debt: 125,000 5% Debentures 100

350Morse Ltd Market Value (000)Equity: 250 000 ordinary shares of 1 each 300

The usual pre-interest profit for both companies is 100,000 per annum.

Required:

(a) Calculate the capital gain that can be realised by a holder of 1,750shares in Dixon Ltd., without altering their exposure to risk;

(35%)

(b) Identify and discuss the assumptions that you have made in answeringpart (a) above;

(30%)

(c) Comment on the likely effects of introducing corporation tax into themodel you have employed in answering parts (a) and (b);

(15%)

(d) If the market value of each of the companies at equilibrium is325,000, calculate for both companies, firstly, the equilibrium price ofan ordinary share, and, secondly, the WACC;

(30%)

(e) Demonstrate that the approach that you used in part (a) fails to yieldany benefit at the equilibrium position defined in part (d)

(30%)

[Total 140%]

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Question 6.9

The following information relates to two companies that are identical exceptfor their capital structure:

Allen Ltd Market Value (m)Equity: 15m ordinary shares of 1 each 60Debt: 20m 5% Debentures 20

80Campion Ltd Market Value (000)Equity: 80m ordinary shares of 1 each 60The usual pre-interest profit for both companies is 10m per annum.

Required:

(a) Demonstrate an opportunity open to a 1% investor in the equity of AllenLtd.

(35%)

(b) Identify and discuss the assumptions that you have made in answeringpart (a) above.

(30%)

(c) Calculate the equilibrium price of an ordinary share in each of thecompanies if their market value at equilibrium is 70m.

(20%)

(d) Comment on the likely effects on the post-tax model of Modigliani &Miller of a company operating at very high levels of gearing.

(15%)[Total 100%]

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Question 6.10


Curran plc Market Value (m)

Equity: 40m ordinary shares of 1 each 40

Debt: 25m 5% Debentures 25

65

Dowe plc Market Value (m)

Equity: 120m ordinary shares of 50p each 60

The usual pre-interest profit for both companies is 5m per annum.

Required:

(i) Demonstrate an opportunity open to a holder of 400,000 shares inCurran plc.

(60%)

(ii) Explain how your scheme in a) maintained the same level of risk for theinvestor as s/he originally enjoyed.

(30%)

(iii) Calculate the equilibrium price of an ordinary share in each of thecompanies if their market value at equilibrium is 62.5m.

(10%)

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Question 6.11


Uccello Ltd Market Value(000)

Equity: 100,000 ordinary shares of 1 each 300Debt: 95,000 5% Debentures 100

400Bellini Ltd Market Value

(000)Equity: 185 000 ordinary shares of 1 each 370The usual pre-interest profit for both companies is 150,000 per annum.

Required:

(a) Explain the ideas behind the traditional view of the relationshipbetween the weighted average cost of capital and gearing,

(25%)(b) Calculate the weighted average cost of capital for Uccello Ltd and

Bellini Ltd,(20%)

(c) Demonstrate an opportunity open to a holder of 1,000 shares inUccello Ltd.

(35%)(d) Calculate the equilibrium price of an ordinary share in each of the

companies if their market value at equilibrium is 385,000.(20%)

[Total 100%]

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Question 6.12

Bergen plc and Oslo plc are two companies operating in the aerospaceengineering industry. The companies enjoy the same business risk and areidentical in all material respects except for their capital structures. Both

companies anticipate earnings before interest and tax of 10m, and bothcompanies have a policy of paying out residual income by way of dividend.The companies capital structures are as follows:

Bergen plc000

Ordinary shares of 1 each 40,000Profit & Loss account 35,000

75,00010% Debentures 25,000

100,000

Oslo plc000

Ordinary shares of 50p each 40,000Profit & Loss account 60,000

100,000

Shares in Bergen plc and Oslo plc are currently trading at 200p and 150peach, respectively, whilst the debentures in Bergen plc are trading at 200%.Fredrik, an arbitrageur who holds 1% of the equity in Bergen plc, is intendingto realise a capital gain of 100,000 without changing his exposure to risk.

Required:

(i) Calculate Fredriks dividend income from Oslo plc if he proceeds withhis plan,

(30%)(ii) Calculate the weighted average cost of capital for each of Bergen plc

and Oslo plc,(40%)

(iii) Calculate the weighted average cost of capital for Bergen plc at

equilibrium, if, at equilibrium, the market capitalisation of Oslo plc is125 million.(30%)

[Total 100%]

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Question 6.13

Hare plc and Blake plc operate in the electronic engineering industry. Thecompanies enjoy the same business risk and are identical in all materialrespects except for their capital structures. Both companies anticipate annual

earnings before interest and tax of 30m, and both companies have a policyof paying out residual income by way of dividend. The companies capitalstructures are as follows:

Hare plc000


75,00010% Debentures 25,000

100,000

Blake plc000


100,000

Shares in Blake plc and Hare plc are currently trading at 560p and 200p each,respectively, whilst the debentures are trading at par. Maclean plc owns 1%of the equity in Hare plc.

Required:

(i) Demonstrate the arbitrage opportunity open to Maclean plc if the Boardof that company wish to maximise their companys income (withoutchanging the exposure to risk),

(30%)(ii) Calculate the maximum capital gain that could be anticipated by an

arbitrageur holding 1% of the equity in Hare plc who wished to maintainboth their income and exposure to risk,

(30%)

(iii) Discuss critically the assumptions upon which the arbitrageur in (ii)relies.(40%)

[Total 100%]

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Question 6.14 [Question 2 June 2004]

Ghiberti plc and Brunelleschi plc are two companies operating in theconstruction industry. The companies enjoy the same business risk and areidentical in all material respects except for their capital structures. Both


Ghiberti plc000


75,00010% Debentures 25,000

100,000

Brunelleschi plc000


100,000

Shares in Brunelleschi plc and Ghiberti plc are currently trading at 140p and400p each, respectively, whilst the debentures are trading at par.

Required:

(i) Identify, explain, and justify the actions that an adherent to the views ofModigliani and Miller would take to improve their financial position if theyheld 1% of the equity in Ghiberti plc,

(20%)(ii) Calculate the maximum capital gain that could be anticipated by the

arbitrageur in (i) without reducing their income,(20%)

(iii) Discuss critically the assumptions upon which the arbitrageur in (i) relies.(60%)

[Total 100%]

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Question 6.15 [Question 3 June 2006]

Tey plc and Crispin plc are two companies operating in the electronicengineering industry. The companies enjoy the same business risk and areidentical in all material respects except for their capital structures. Both

companies anticipate annual earnings before interest and tax of 30m, andboth companies have a policy of paying out residual income by way ofdividend. The companies capital structures are as follows:

Tey plc000


75,00010% Debentures 25,000

100,000

Crispin plc000


100,000

Shares in Crispin plc and Tey plc are currently trading at 560p and 200p each,respectively, whilst the debentures are trading at par. Marsh plc owns 1% ofthe equity in Tey plc.

Required:

(i) Demonstrate the arbitrage opportunity open to Marsh plc if the Board ofthat company wish to maximise their companys income (without changingthe exposure to risk) from Tey plc,

(20%)(ii) Calculate the maximum capital gain that could be anticipated by an

arbitrageur holding 1% of the equity in Tey plc who wished to maintainboth their income and exposure to risk,

(20%)

(iii) Discuss critically the assumptions upon which the arbitrageur in (ii) relies.(60%)[Total 100%]

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Question 6.16 [Question 2 March 2007]

Cocteau plc and Renoir plc are two companies operating in the electronicengineering industry. The companies enjoy the same business risk and areidentical in all material respects except for their capital structures. Both


Cocteau plc000


75,00010% Debentures 25,000

100,000

Renoir plc000


100,000

Shares in Renoir plc and Cocteau plc are currently trading at 140p and 400peach, respectively, whilst the debentures are trading at par.

Required:

(i) Calculate the maximum capital gain that could be anticipated (without anyreduction in income) by an adherent to the views of Modigliani and Millerwho holds 1% of the equity in Cocteau plc,

(20%)(ii) Identify, explain, and justify the actions taken by the arbitrageur in (i),

(20%)(iii) Discuss critically the assumptions upon which the arbitrageur in (i) relies.

(60%)[Total 100%]

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Question 6.17 [Question 2 March 2008]

Bill plc and Suzanne plc operate in the electronic engineering industry. Thecompanies enjoy the same business risk and are identical in all materialrespects except for their capital structures. Both companies anticipate annual

earnings before interest and tax of 40m, and both companies have a policyof paying out residual income by way of dividend. The companies capitalstructures are as follows:

Bill plc000


75,00010% Debentures 25,000

100,000

Suzanne plc000


100,000

Shares in Suzanne plc and Bill plc are currently trading at 560p and 200peach, respectively, whilst the debentures are trading at par. Maclean plcowns 1% of the equity in Bill plc.

Required:

(i) Calculate the maximum capital gain that could be gained by Archie plc,an arbitrageur holding 1% of the equity in Bill plc, whilst maintainingthat arbitrageurs income and exposure to risk,

(30%)(ii) Explain how your scheme in (i) ensured that Archie plcs exposure to

risk remained unchanged,(30%)

(iii) Discuss critically the assumptions upon which Archie plc would have to

rely for your scheme to be effective. (40%)[Total 100%]

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Question 6.18 [Question 2 September 2008]

Haddad plc and Habash plc operate in the same engineering industry. Thecompanies enjoy the same business risk and are identical in all materialrespects except for their capital structures. Both companies anticipate annual

earnings before interest and tax of 23m, and both companies have a policyof paying out all residual income by way of dividend. The companies capitalstructures are as follows:

Haddad plc000


150,0006% Debentures 50,000

200,000

Habash plc000


200,000

Shares in Habash plc and Haddad plc are currently trading at 700p and 250peach, respectively, whilst the debentures are trading at par. Nayef owns 1%of the equity in Haddad plc.

Required:

(i) Demonstrate the arbitrage opportunity open to Nayef if he wishes tomaximise his income (whilst maintaining approximately the same level ofrisk),

(30%)(ii) Calculate the maximum capital gain that could be anticipated by Nayef if

he wished to maintain both his income and his level of exposure to risk,(40%)

(iii)Calculate the weighted average cost of capital for each of the companies

at equilibrium if their market value at that point is 325m. (30%)[Total 100%]

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Question 6.19 [Question 2, March 2009]

Rossini plc is identical in all operating and risk characteristics to Wagner plc,except in terms of capital structure: Rossini plc is financed by equity, whereasWagner plc is financed by a mixture of debt and equity. The market values of

Wagner plcs debt and equity are 2.1m and 0.9m, respectively. To serviceits debt, Wagner pays 72,000 p.a., and the company pays an annualdividend of 378,000. Rossini plc pays a dividend of 450,000 p.a.

Required:

(a) Calculate the market value of Rossini plc,(5%)

(b) Calculate the cost of capital for Rossini plc,(5%)

(c) Calculate the cost of equity for Wagner plc,

(10%)(d) Calculate the cost of debt for Wagner plc,

(10%)(e) Calculate the weighted average cost of capital for Wagner plc

(10%)(f) In a world where debt tax relief is available at 30%, calculate the

weighted average cost of capital for Wagner plc.(60%)

[Total 100%]

EM4001Ch6 Gearing and Cost of Capital

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