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FINM7402 Tutorial 2: Capital Structure

Nota bene:

I have set more questions than can be covered in a 2 hour session. The questions to be covered by your tutor are indicated by an asterisk (*); the rest should be viewed as extra practice problems.

 

Solutions are also provided. Resist the temptation to look at the solutions while attempting the questions. It is surprisingly easy to convince yourself that you understand the material if you peek at the solutions first.

Part I:  MM theory in perfect capital markets

Question 1 *

Consider two firms that are identical in every respect (i.e., industry, risk, cash flows generated, and so on) except for their capital structure.  Firm A is financed entirely by equity.  A's current share price is $0.70 and there are 10 million issued shares.  Firm B also has 10 million shares issued, but also has some debt financing.  The market value of B's debt is $2 million and B pays 15% p.a. interest on this debt.  Both A and B generate an annual cash income of $3,500,000.

Assume a world in which capital markets are perfect.  That is, there are no taxes at the corporate or personal level, no transaction costs, and no financial distress costs.

Required:

a) Modigliani and Miller’s “irrelevance proposition” is that, in a world of perfect capital markets, capital structure choices are irrelevant.  Two firms that are identical in all respects except for their capital structure must have the same total value.

If MM's irrelevance proposition holds, what is the market price of B's shares?

Now let's see what happens if the irrelevance proposition does not hold.  Ignore your answer to (a), and assume that B's share price is $0.40.  In which case the total value of B is:

Hence, B is cheaper than the otherwise identical Firm A.

b) Assume you purchase 20% of B's shares and 20% of B's debt, both at current market prices.  How much will this cost you in total?  What is the annual income from your investment in B?

c) Being unlevered, Firm A pays all cash income out as a dividend to shareholders.  What proportion of A must you purchase in order to get the same annual income as calculated in (b)?  How much will this shareholding cost you?

Commentary:

· You can see the arbitrage opportunity here because your total outlay is less for B than A; yet the annual income from each is identical.  Rational investors would invest in B forcing its value up until such time as the values of A and B were equal.

· A slightly different way of illustrating the arbitrage opportunity is to buy the cheaper firm (B) and short-selling the more expensive firm (A).  This produces an immediate profit, with no further cash flow implications in the future.

· You could re-do this question again assuming B's shares were valued at (say) $0.80.  In that case, A would be cheaper than B.  How could you demonstrate that an arbitrage opportunity exists in that case?

Question 2

Assume perfect capital markets and no taxes.  A company with D/V = 0.30 pays 6% p.a. interest on its outstanding debt.  The firm's weighted average cost of capital is 12% p.a.

a) What is the firm's required rate of return on equity ?

b) Imagine a firm identical to the one described above, except that this new firm is financed entirely by equity.  Without doing any calculations, what is the weighted average cost of capital of this firm, and what is the required return on this firm's equity?

Question 3

Assume a world with perfect capital markets and no taxes.  HotDog Software has a debt-equity ratio of 0.45.  HotDog is paying 7.5% p.a. interest on its outstanding debt.  The risk-free rate is 4%.  The expected return on the market portfolio is 14% p.a. and HotDog's beta is 1.6.

a) What is the return on equity demanded by HotDog's shareholders?

b) What is HotDog's weighted average cost of capital?

Question 4

Assume perfect capital markets and no taxes.  A company begins its existence financed entirely by equity.  The required rate of return on this company is 10% p.a.  Obviously, the WACC on this all-equity company is also 10% p.a.

a) Several years into its life, the company raises some funds by issuing bonds.  Interest payments on these bonds are 6% p.a.  After the bond issue, borrowings represent 25% of the total value of the firm.

Calculate the return required by equityholders after the bond issue.  Also calculate the firm's new WACC.

b) Assume a further bond issue is made.  The interest on debt remains at 6% p.a.  Borrowings now represent 40% of the total value of this firm.

Calculate the return required by equityholders after the second bond issue.  Also calculate the firm's new WACC.

Commentary:

· From MM, we know that leverage does not affect the total value of a firm or its WACC (assuming perfect capital markets and no taxes).  Hence, the WACC will not change in (a) and (b).  We have seen this on the graph in lectures where WACC is a flat line.

· The return required by equityholders increases as more debt is issued (equityholders are last in line for annual payments and in the event of liquidation).  We have seen this upward-sloping line for  on the graph in the lecture, and your calculations in (a) and (b) should confirm this.

Question 5 *

Assume perfect capital markets and no taxes. Currently ABC Limited is all equity financed. The shareholder’s demand a 12.6% return and the firm’s equity beta is 1.1. The Chief Financial Officer for ABC Limited states: “we should borrow funds and retire some existing equity with the proceeds since this will make shareholders better off”.

a) Show that the shareholder’s return will be enhanced by adopting some leverage. For this purpose assume that the firm is now financed with three parts debt to seven parts equity and that the cost of debt is 6%.

b) Calculate the new equity beta for ABC Limited under this scenario.

c) Does the greater return on equity earned under leverage, as calculated in part (a), mean that shareholders are better off? Use the CAPM to explain why or why not. Assume for this purpose that the market risk premium is 6% and that the debt is riskless.

Question  7

Explain what is wrong with the following argument: “If a firm issues debt that is risk free, because there is no possibility of default, the risk of the firm’s equity does not change. Therefore, risk-free debt allows the firm to get the benefit of a low cost of capital of debt without raising its cost of capital of equity.”

Question  8

In mid-2015, Qualcomm Inc. had $11 billion in debt, total equity capitalization of $89 billion, and an equity beta of 1.43 (as reported on Yahoo! Finance). Included in Qualcomm’s assets was $21 billion in cash and risk-free securities. Assume that the risk-free rate of interest is 3% and the market risk premium is 4%.

(a) What is Qualcomm’s enterprise value?

(b) What is the beta of Qualcomm’s business assets?

(c)      What is Qualcomm’s WACC?

Part II: MM theory with taxes

Question 1*

Assume that the Munch Company operates in a perfect capital market, with one exception being that companies pay tax at the rate of 30%.  Munch generates an annual cash flow of $1 million.  No funds are retained in the firm.  That is, each year Munch pays interest to debtholders, tax to the government, and the balance as dividends to equityholders.

In each of the following cases, calculate (i) the total interest paid on debt, (ii) the tax payment, and (iii) the dividend paid to equityholders. Also add (i) and (iii) to get the total payout to Munch's claimholders.

a) Assume Munch is unlevered.

b) Now assume Munch is slightly levered.  The cost of debt  is 10% p.a. and the annual interest payments on its debt amount to $100,000.

c) Now assume Munch has substantially more debt in its capital structure.  The cost of debt is still 10% p.a., but annual interest payments on the debt amount to $400,000.

Commentary:

· The series of calculations above show two things: (i) as the level of debt increases, Munch pays less tax, and (ii) as the level of debt increases, the total cash payouts to claimholders increases.

· The introduction of corporate tax effectively subsidizes the firm's interest payment to debtholders.  That is, interest payments on debt are tax deductible but dividends paid to equity holders are not.  This creates a bias towards debt financing and leads to the conclusion that firms will be financed entirely by debt.

Question 2*

Assume the same information as Question 1. When the Munch Company is unlevered, its weighted-average cost of capital  is 15% p.a. For cases (a), (b), and (c) above, calculate (i) the return required by equity holders, and (ii) the weighted average cost of capital.

Commentary:

· These calculations show that, in a world with corporate taxes, (i) the WACC decreases as the proportion of debt increases, and (ii) the return required by equity holders increases as the proportion of debt increases.

Question 3*

Assume the same information as Questions 1 & 2. If the Munch Company has an unlevered beta (asset beta) of 1, what will be the levered equity beta for cases (b) and (c)?  Now assume that for case (c) debt is no longer risk free and that the beta of the debt is 0.2, calculate the levered equity beta.

Commentary:

These calculations show that, in a world with corporate taxes, (i) the equity beta for a firm increases as leverage increases, and (ii) as debt becomes risky the debt holders demand a higher return since they are bearing risk.

The following are the questions from the text

Chapter 15: Questions 1, 2, 3, 6, 8, 10, 12, 16, 19*

15-1. Pelamed Pharmaceuticals has EBIT of $133 million in 2006. In addition, Pelamed has interest expenses of $49 million and a corporate tax rate of 35%.

a. What is Pelamed’s 2006 net income?

b. What is the total of Pelamed’s 2006 net income and interest payments?

c. If Pelamed had no interest expenses, what would its 2006 net income be? How does it compare to your answer in part b?

d. What is the amount of Pelamed’s interest tax shield in 2006?

15-2. Grommit Engineering expects to have net income next year of $24.21 million and free cash flow of $12.11 million. Grommit’s marginal corporate tax rate is 30%.

a. If Grommit increases leverage so that its interest expense rises by $9.2 million, how will its net income change?

b. For the same increase in interest expense, how will free cash flow change?

15-3. Suppose the corporate tax rate is 30%. Consider a firm that earns $1000 before interest and taxes each year with no risk. The firm’s capital expenditures equal its depreciation expenses each year, and it will have no changes to its net working capital. The risk-free interest rate is 8%.

a. Suppose the firm has no debt and pays out its net income as a dividend each year. What is the value of the firm’s equity?

b. Suppose instead the firm makes interest payments of $700 per year. What is the value of equity? What is the value of debt?

c. What is the difference between the total value of the firm with leverage and without leverage?

d. The difference in part (c) is equal to what percentage of the value of the debt?

15-6. Arnell Industries has just issued $15 million in debt (at par). The firm will pay interest only on this debt. Arnell’s marginal tax rate is expected to be 35% for the foreseeable future.

a. Suppose Arnell pays interest of 7% per year on its debt. What is its annual interest tax shield?

b. What is the present value of the interest tax shield, assuming its risk is the same as the loan?

c. Suppose instead that the interest rate on the debt is 6%. What is the present value of the interest tax shield in this case?

15-8. Bay Transport Systems (BTS) currently has $60 million in debt outstanding. In addition to 10% interest, it plans to repay 4% of the remaining balance each year. If BTS has a marginal corporate tax rate of 35%, and if the interest tax shields have the same risk as the loan, what is the present value of the interest tax shield from the debt?

15-10. Rogot Instruments makes fine violins and cellos. It has $1.3 million in debt outstanding, equity valued at $2.7 million, and pays corporate income tax at rate of 33%. Its cost of equity is 12% and its cost of debt is 6%.

a. What is Rogot’s pretax WACC?

b. What is Rogot’s (effective after-tax) WACC?

15-12. Summit Builders has a market debt-equity ratio of 1.30, a corporate tax rate of 38%, and pays 9% interest on its debt. The interest tax shield from its debt lowers Summit’s WACC by what amount?

15-16. Milton Industries expects free cash flow of $18 million each year. Milton’s corporate tax rate is 38%, and its unlevered cost of capital is 16%. Milton also has outstanding debt of $75.25 million, and it expects to maintain this level of debt permanently.

a. What is the value of Milton Industries without leverage?

b. What is the value of Milton Industries with leverage?

15-19. Rally, Inc., is an all-equity firm with assets worth $25 billion and 10 billion shares outstanding. Rally plans to borrow $10 billion and use these funds to repurchase shares. The firm’s corporate tax rate is 35%, and Rally plans to keep its outstanding debt equal to $10 billion permanently.

a. Without the increase in leverage, what would Rally’s share price be?

b. Suppose Rally offers $2.75 per share to repurchase its shares. Would shareholders sell for this price?

c. Suppose Rally offers $3.00 per share, and shareholders tender their shares at this price. What will Rally’s share price be after the repurchase?

d. What is the lowest price Rally can offer and have shareholders tender their shares? What will its stock price be after the share repurchase in that case?

 

 SOLUTIONS

PART I:  MM theory in perfect capital markets

Question 1

a) In a perfect capital market, Modigliani and Miller (MM) show that capital structure is irrelevant so the value of a levered firm is equal to the value of an otherwise identical unlevered firm.  In this case we have:

V^U =  V^L

V^U =  10m  x  $0.70    =    $7 million  =  V^L_.

The market value of a levered firm is equal to the market value of its debt plus the market value of its equity:

V^L =  D^L + E^L

7m =  2m + E^L

in which case, the market value of equity is $5 million and the stock price is:

 per share.

b) Buying 20% of B’s equity will cost:  20% ´ $4m = $800,000.  Buying 20% of B’s debt will cost:  20% ´ $2m = $400,000.  Thus, the total cost of your investment is $1.2 million.

Your annual income from this investment is given in the following table.

Equity : 20%  ´  ($3,500,000 - $300,000) =     $640,000

Debt : 20%  ´  ($2m  ´ 15% p.a.) = $  60,000

Total =    $700,000

Note that the equityholders receive the firm’s entire cash flow ($3.5m) less the interest paid to debtholders ($300,000) and your share is 20% of this.

c) Firm A pays out the entire annual cash income of $3.5 million as dividends.  To get an annual income of $700,000, you must buy  = 20% of the shares of Firm A.  This will cost you 20% ´ $7million = $1,400,000.

Therefore, Firm B is underpriced.  By buying 20% of the equity and debt of Firm B, we can get $700,000 a year with an investment of only $1.2million.

Question 2

a)  For this firm, , so that .

Therefore .

The required return on equity for a levered firm is:

.

In this case we have:

=   0.12   +   (0.12 - 0.06)   ´  0.42857

=   14.57% p.a.

Note that because this firm operates in a perfect capital market, the WACC is independent of the firm’s capital structure so  Note also that this required return on equity gives us the correct WACC:

In an unlevered firm, the equity holders are the only claimholders so  That is, the equityholders would demand a return of 12% p.a. to compensate them for the inherent business risk of the firm.

In this case, however, the firm is levered and we have calculated that the equityholders will demand a return of 14.57% p.a. Of this, 12% p.a. is to compensate them for bearing the inherent business risk of the firm and 2.57% p.a. is to compensate them for the additional financial risk that is caused by introducing debtholders with a prior claim.

b) Modigliani and Miller have shown that in a perfect capital market, the WACC is independent of the firm’s capital structure. In this case, for an unlevered firm, we would have:

  and  

Question 3

In this case we have   and

a) We can compute the required return on equity using the CAPM:

 

b)  In this case, , so  which means that  and consequently

In a perfect capital market, the WACC is given by:

Question 4

In this case, the firm is entirely financed with equity so:

Also because the firm operates in a perfect capital market, the WACC is independent of capital structure so

a) The return demanded by the equity holders will be:

The WACC should be unchanged, at 10% p.a., because this firm operates in a perfect capital market – but let’s check to make sure:

b) The return demanded by the equity holders will be:

Again, the WACC should be unchanged at, 10% p.a., because this firm operates in a perfect capital market – but let’s check to make sure:

Question 5

Whenever we introduce any amount of debt we expose equity holders to financial risk. Willingness to bear this additional risk requires the equity holders to earn a return premium, in addition, to that demanded for exposure to the firm’s ordinary business risk.

a) According to M&M Proposition 2,

.

So,

b) Equity risk of a shareholder is a function of that firm’s business and financial risk:

 

The firm’s asset beta, , is a measure of business risk. Additionally shareholders in a levered firm bear financial risk that is proportional to the amount of leverage, . Without leverage the unlevered firm bears no financial risk, so that  = .  

So in this example:

.

c) The CAPM draws a direct link between systematic risk and a ‘fair’ return. It uses the equity beta of the entity as a measure of that entity’s systematic risk.  If we calculate the equity holder’s expected return from ABC Limited, with leverage, we can determine if they are receiving more than this ‘fair’ return.

The CAPM:

 

With leverage:

 

(here we use the levered beta calculated in part (b) and since debt is riskless this is also the risk free rate)

From part (a) we see that the shareholders under the levered scenario demand a premium for exposure to financial risk. Part (b) demonstrates that this additional risk translates to a higher equity beta under the levered scenario, as compared to the unlevered scenario. Furthermore, the CAPM demonstrates that this higher beta results in a required return that is exactly equal to that calculated in part (a), 15.43%. This shows that the additional return that the shareholders earn under the leveraged scenario (15.43% versus 12.6%), is mere compensation for greater risk (via its equity beat). They do not earn more (or less) than they should given the level of risk that they bear. Hence, the shareholders are neither better nor worse off with the introduction of leverage.  

QUESTION 6

Any leverage raises the equity cost of capital. In fact, risk-free leverage raises it the most (because it does not share any of the risk).

QUESTION 7

(a) 89 + 11 – 21 = 79 billion

(b) Because the debt is risk free,

(c)

Alternatively,

R_wacc = E/V *R_e + D/V *R_d  = 89/79*8.72% + (-10)/79*3% = 9.44%