Ch14Capital Leverage

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Chapter 14

LEVERAGE

Alex Tajirian


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1 OBJECTIVE

! Does amount of a company's debt matter? If it does, is there anoptimal proportion of debt to total assets? ( optimal ] (Debt/Asset)

level that maximizes value of firm)

! What happens to EPS, Cost of Capital, and Price of stock when debt

is substituted for equity?

! Are companies, in reality, at their optimal (Debt/Asset) or do theyhave a target capital structure?

! Practical considerations and Leverage.

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2 MOTIVATION

2.1 WHAT IS CAPITAL STRUCTURE ANALYSIS?Finding firm's lowest cost of capital, other things (dividends,

projects, total assets) constant. ] Choose (Debt/Asset) thatmaximizes value of firm

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3 THEORIES EXPLAINING CAPITAL STRUCTURE

#Simplification: Assume only two alternatives; debt and equity

# What are a firm's optimal proportions of Debt (D) and Equity (E)? ]What is a firm's optimal Debt/Asset ratio?

# Need a theory to tell us factors influencing optimal (Debt/Asset)

ratio.

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Value of Firm with no debt

=

value of the firm with debt, i.e. changing the mix of debt and equity

does not change the value of the firm.

3.1 M&M I (Modigliani & Miller I)

Assumptions:

No taxes, no floatation costs, no bankruptcy associated costs,unlimited lending and borrowing capacity

Analysis:

Given assumptions, both investor and firm have same

opportunities. If a firm _ Debt, it is equivalent to investorborrowing and investing proceeds in firm. Thus, firm provides

no added value.

Result:

Capital structure is irrelevant

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Valuewith debt

' Valueno debt

% tax shield

3.1.1 M&M With TaxesAssumptions:

As above, save firms (not individuals) can deduct interest fromtax bill.

Analysis:

Here, unlike in M&MI, firm has advantage over individual.

Thus, firm can provide benefit from leverage through interestdeductions.

Result:Value of firm increases as debt increases. Thus, 100% debt isoptimal.

As the proportion of debt increases, the tax shieldincreases, Thus, the value of the firm increases.

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3.2 BANKRUPTCY CONSIDERATIONSAssumptions:

As above, save now we include in analysis cost of financialdistress associated with higher debt. These include:

! ` in sales due to unknown life of product/firm

! Suppliers less willing to replenish inventory or provide

new products

! legal fees

! cost of correct-sizing

Analysis:

As (Debt/Asset)_, there are two factors working in oppositedirections; interest savings (+), and financial distress (-).

if (+) > (-) Y value _.

Result:

As debt is increased, price of company increases, then starts to

fall. Thus, optimal capital structure is between 0 and 100%

debt.

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Capital Structure theory tells us that there exists an optimal capitalstructure and that all future projects ought to be financed using this

optimal (Debt/Asset).

3.3 CAPITAL STRUCTURE CONCLUSION

There are two factors influencing the optimal amount of debt: taxesand cost of financial distress.

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As debt increases

Value of firm

with leverage=

value of firm

with no leverage+

Benefit

=

PV

(interest savings)

+

Cost

=

PV

(distress)_ 6 + > -

maximized 6 + = -

` 6 + < -

Thus, given our simplification, the optimal capital structure is a combination of Debt and Equity.

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4 Debt/Asset, EPS, WACC, & VALUE OF FIRM

Question: What happens to EPS, WACC, and price of stock, as debt isincreased, holding every thing else (total assets, dividends,

projects) constant?

4.1 EXPERIMENT:

Objective:Change (Debt/Asset), holding everything else constant, then observe

what happens to P, EPS, WACC. Choose (Debt/Asset) that

maximizes value of firm.

Procedure:

Manager, while riding BART to work, using his/her laptop financialmodels spreadsheet, tries different financing combinations of D and

E, then observes what happens to the price of stock, EPS, andWACC.

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Step 1: Value of Assets = value of debt + value of equity

value of debt = PV of all outstanding debt

value of equity = (pstock) x (# of shares outstanding)

Step 2: Assume company has Debt = 0 ] value of assets = value

of equity

Step 3: Increase proportion of debt by, say 10%

Total Assets _ (from Step 1)

Step 4: Change the mix of debt and equity ]] Substitute debt for

company equity ] To hold total assets constant, firm has

to reduce total value of equity Y firm has to re-purchase

enough of its own shares to maintain value of total assets

constant.

Step 5: Repeat step 3.

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4.2 Experiment Starting Information

EBIT $6 million

shares outstanding 1 million

Debt 0

price of stock $20

tax rate 40%

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Notes for tables below:

! kd obtained from rate of similar bonds

! interest = interest paid to bond (debt) holders = kd x (amount ofdebt)

! earnings before taxes = (EBIT - interest )

! Tax = (Earnings before taxes) x ( tax rate)

! NI = net income = earnings before taxes - Tax

!# of Shares repurchased = (amount of debt)/ (price of stock)

! Amount of shares after re-purchase = [(original # of shares) - (#

of shares repurchased)] = [10,000 - (# of shares re-purchased)]

! Debt = (Debt/Asset)(Assets)

! ks =kRF + (km - kRF)$s; as debt increased, beta was adjusted based on

estimates from similar companies rather than the Hamada

equation

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p0 'Dividend

ks

'

EPS

ks

; assume all earnings paid as dividends

EPS 'Net Income

# of shares outstanding

WACC ' wd(1&T)k

d% w

sk

s

wd'

Debt

Asset

$leverage

' $no debt

(1 %Debt

Equity)(1 & T)

P/E 'price

earnings per share'

price

NI per share'

price

NI

# of shares

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S ' (EBIT & Amount of Debt)(1 & tax rate)k

s

; assumes a perpetuuity for simplicity

4.3 EXPERIMENT RESULTS

Amountof Debt

($ million)

kd ks S A Price D/A WACC EPS SharesOutstanding

(millions)

0 7.5% 12.0% 30.0 30.0 20.00 0.00 12.00% 2.4 1.00

2 7.9% 12.4% 28.3 30.3 30.27 0.07 11.89% 3.8 0.93

4 8.2% 12.9% 26.4 30.4 30.38 0.13 11.85% 3.9 0.87

6 9.0% 13.2% 24.8 30.8 30.82 0.19 11.68% 4.1 0.81

8 10.0% 14.0% 22.3 30.3 30.29 0.26 11.89% 4.2 0.74

10 12.0% 15.2% 18.9 28.9 28.95 0.35 12.44% 4.4 0.65

12 15.0% 16.8% 15.1 27.1 27.13 0.44 13.27% 4.6 0.56

14 19.0% 20.0% 10.2 24.2 24.23 0.58 14.86% 4.8 0.42

D = Amount of DebtA = Total Assets = D + S

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D/A & Cost of Capital

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

0.00 0.10 0.20 0.30 0.40 0.50 0.60

D/A

costo

fcapital

kd

ks

WA

kd : cost of debt _ as default risk_ks:: cost of equity _ as company's exposure (sensitivity) to

interest rates _ Y$_

L At (Debt/Asset) = 0%, WACC = ks , since wd = 0

At (Debt/Asset) = 100%, WACC = kd (1 - T), since ws = 0

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D/A & Price Of Stock

$20.00$24.23

$30.38$28.95

$30.29$30.82$30.27

$27.13

0.00

5.00

10.00

15.00

20.00

25.00

30.00

35.00

0.00 0.10 0.20 0.30 0.40 0.50 0.60

D/A

Pirce

optimal capital structure = (Debt/Asset)* = 19%

# level of (Debt/Asset) at minimum cost of capital = that of

maximum price

theoretically, you should finance all future projects using

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(Debt/Asset) = 19%.

# The level of (Debt/Asset) that maximizes EPS is not same level as

maximum priceY

maximizing EPS does not maximize value offirm.

# To the right of the optimal level we have too much debt Y ifcompany reduces the level of debt, then the price of the stock

should go up. The opposite would be happen if debt is increased.

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4.4 EXPERIMENT CONCLUSION

! (Debt/Asset) at Minimum WACC = level of maximum price

! (Debt/Asset) for maximum price not equal to maximum EPS

! WACC is U-shaped

! If no financial distress cost, then 100% debt is optimal

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5 CHECKLIST FOR CAPITAL STRUCTURE DECISIONS

! Sales Stability/predictability

! Asset Structure:

The more a firm's ability to use its assets as collateral, the

higher the debt. (real-estate v. R&D companies)

! Operating Leverage

!Earnings/expansion Growth Rate:High growth rate companies need heavy external financing.

Also, flotations costs of debt < that of equity. Thus, they tend

to issue more debt.

! Profitability Rate:

Highly profitable companies issue less debt, since they tendto rely more on retained earnings. (Apple, Microsoft, Coca

Cola)

! Tax: higher tax rates, more debt

! Rating Agencies: Some firms like to maintain a certain level

of rating.

Alex Tajirian


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6 TARGET CAPITAL STRUCTURE

# Firms never issue both Debt & Equity simultaneously

! Current stock price vs. Expected (by firm) price

! Current kd vs. expected (by firm)

# There is evidence that firms have a target capital structure inmind!

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7 SUMMARY

T The optimal capital structure is a trade-offbetween a tax shield, due to interest expense

being tax deductible, & bankruptcy, due to excess burden of having to meet interestpayments.

T Capital structure analyzes the effect of debt (leverage) on the price of the firm, holdingevery thing else (total assets, dividends, projects) constant.

T If you include taxes and bankruptcy costs in analysis, then the value of the firm initiallyincreases then decreases as debt is increased.

T Debt level that maximizes EPS is not same as that of maximum price.

T A number of factors determine optimal debt in practice.

T Firms generally do not issue both debt and equity at the same time

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8. QUESTIONS

I. Agree/Disagree-Explain

1 Project cash flows should be discounted at the rate of the source of financing. Thus, if it is100% equity financed, then the discount rate is the company's required rate of return.

2 Since debt is tax-deductible, then it makes no sense for a firm to issue equity.

3 As you increase debt in the capital structure from a level of zero, WACC first decreases thenincreases.

4 The optimal capital structure is given by the level of debt that maximizes EPS.

5 If there are no bankruptcy costs, then the optimal capital structure is 100% debt.

6 The level of debt that maximizes the value of the firm is the same as the one that minimizesthe WACC.

7 A firm will maximize value if it operates at a level of minimum cost.

8 Capital structure involves the analysis of a firm's optimal amount of debt.

9 Every time you want to finance a new project, you need to re-estimate the optimal capital

structure.

10 Increasing the amount of debt has no impact on cost of debt.

11 Increasing the amount of debt, the firm's cost of equity does not change.

12 The higher the firm's profitability, the lower the debt, other things equal.

13 Preferred stocks have a higher required return than common equity, other things constant.

14 Increasing the (Debt/Asset) ratio has no impact on a company's required return.

15 Financial distress refers to a firm's inability to meet its debt obligation.

16 The higher the sales stability, other things equal, the higher is a firm's (Debt/Asset).

17 The higher the operating leverage, other things equal, the higher a firm's (Debt/Asset).

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18 Company XYZ Inc. needs financing and management believes that its stock price isovervalued. Other things equal, the firm would be better off issuing debt now.

19 Company XYZ Inc. needs financing and management believes that interest rates are headingdown. Thus, XYZ Inc. is more likely to issue debt than equity now.

20 A firm, with zero debt, is planning to issue new equity to finance an expansion project. IfNPV of project > 0 using ks, then the manager might be accepting a bad project.

II. Numerical.

1 Uno Inc. has one product that is selling at $10 per unit. Suppose that it sold 20,000 units thelast year. The firm's operating costs were $100,000 and its NWC was $45,000. The

company has 10,000 shares outstanding, $30,000 debt with 8% coupon, its required return= 15%, and subject to a 40% tax rate.

(a) What is its EPS?(b) Assume that Uno Inc. is retaining only 10% of its earnings. What would be a fair

price for its stock?

(c) What is its P/E?

2 XYZ Inc. is considering issuing new equity. The firm's stock is currently trading at $12, with$.25 dividends per share which are expected to grow annually at 5%. The company isconsidering issuing 100,000 new shares at the current market price. Their investment banker

would charge them $2 per share to issue and sell the new shares.(a) What is the cost of new equity to the firm?(b) How much new capital would XYZ Inc. raise if it were to go ahead with the deal?

3 0D Inc. currently has no debt and is considering increasing its (Debt/Equity) to 40%. Its

current Beta = 2 and is subject to 40% tax rate. If kRF= 4%, kM= 10% , what would its newcost of retained earnings be? (Assume for simplicity T=0)

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9.0 ANSWERS TO QUESTIONS

I. Agree/Disagree-Explain

1 Disagree. Discounted by the project's WACC/hurdle-rate, which reflects both the project'srisk and firm's capital structure.

2 Disagree. Excessive debt increases the cost of financial distress, thus, lowers the value of the

firm.

3 Agree. You are substituting low cost (debt) for expensive (equity) in the calculation of the

average cost (WACC).

4 Disagree. EPS is maximized at a level different than the level of optimal debt.

5 Agree, since debt interest is tax deductible and there are no offsetting disadvantages.

6 Agree. See Graph " Debt/Asset, WACC & PRICE" p. 18.

7 Disagree. At minimum WACC not at minimum cost, since at minimum cost (cost = 0) the

firm would not exist.

8 Disagree. Optimal proportion of debt to total assets.

9 Disagree. Theoretically, the optimal capital structure gives you the best combinations.

10 Disagree. Increasing a firm's debt, increases default risk, which increases DRP. Thus, kdincreases.

11 Disagree. Increasing debt, increases the firms exposure (sensitivity) to market interest rates.Since interest rates are part of the systematic risk (see chapter 4), the firm's beta increases.

Thus, ks increases.

12 Agree. With high profitability, the firm is able to finance projects using retained earnings.Thus, the firm does not need to raise new debt or equity.

13 Disagree. Preferred stock have a "desirable" feature in them from the point of view of aninvestor. The "good" feature is that holders get paid dividends before the common

stockholders. Hence, investors would require a lower compensation. Thus, required returnwould be less.

14 Disagree. As (Debt/Asset) _ , the firm's exposure to interest rates _. Since interest rate is a

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systematic factor, it would increase the firm's beta.

15 Disagree. A company might still be making its debt obligation. For a discussion on financial

distress, see p. 7.

16 Agree. With sales being stable, the firm is more likely, other things equal, to take theadditional CF burden of debt.

17 Disagree. High operating leverage means that the firm has a high commitment, in the short-run, to paying for fixed costs. This CF commitment makes the firm less likely to take

additional debt CF commitments.

18 Disagree. Since the stock is overvalued, then the firm would rather issue equity now at thehigher prices to reduce effect of dilution.

19 Disagree. The firm would be better off issuing debt in the future as the cost of debt wouldbe less then, assuming they are correct in their guess regarding the direction of interest ratechange.

20 Agree. The cost of the new project should be ke not ks. Since the former is >, then the projectmight end up with NPV < 0 using the correct cost of capital.

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EPS ' NI# of shares outstanding

NI ' EBIT & interest & Tax Bill

' (R&C) & interest & [(R&C) & interest]T

' [(R&C) & (amount of debt kd)](1 & T)

' [(1020,000) & 100,000) & (30,000.08)](1 & .4)

' (97,600)(.6) ' $58,560

EPS '$58,560

10,000' $5.856

p0' Dividend

k' Dividend

ks

' EPS(1 & retention ratio)k

s

'($5.856)(1 & .1)

.15'

5.27

.15' $35.136

II. Numerical.1. (a)

b)

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P/E 'price

earnings per share

'35.136

5.856' 6

Since F is measured in terms of $ per share and not % of price,

ks'

D0(1%g)

P0& F

% g

'.25(1% .05)

12 & 2% .05 ' .026 % .05 ' 7.6%

$leverage

' $no leverage

1 %Debt

Equity(1 & T)

' 2(1 % .4) ' 2.8

from CAPM

knew

' 4 % (10 & 4)(2.8) ' 20.8%

c)

2. (a)

(b) New equity = 100,000($12 -F) = 100,000 ($10) = $1 million

3.

Alex Tajirian

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