copyright © 2011 pearson prentice hall. all rights reserved. chapter 15 debt and taxes

Chapter 15

Debt and Taxes

Chapter Outline

15.1 The Interest Tax Deduction

15.2 Valuing the Interest Tax Shield

15.3 Recapitalizing to Capture the Tax Shield

15.4 Personal Taxes

15.5 Optimal Capital Structure with Taxes

Learning Objectives

1. Explain the effect of interest payments on cash flows to investors.

2. Calculate the interest tax shield, given the corporate tax rate and interest payments.

3. Calculate the value of a levered firm.

4. Calculate the weighted average cost of capital with corporate taxes.

5. Describe the effect of a leveraged recapitalization on the value of equity.

6. Describe the effect of personal taxes on the corporate tax benefits of leverage.

Learning Objectives (cont'd)

7. Given corporate and personal tax rates on equity and debt, calculate the tax benefit of debt with personal taxes.

8. Discuss why the optimal level of leverage from a tax-saving perspective is the level at which interest equals EBIT.

9. Describe the relationship between the optimal fraction of debt and the growth rate of the firm.

10.Assess the apparent under-leveraging of corporations, both domestically and internationally.

15.1 The Interest Tax Deduction

• Corporations pay taxes on their profits after interest payments are deducted. Thus, interest expense reduces the amount of corporate taxes. This creates an incentive to use debt.

15.1 The Interest Tax Deduction (cont'd)

• Consider Safeway, Inc. which had earnings before interest and taxes of approximately $1.85 billion in 2008, and interest expenses of about $350 million. Safeway’s marginal corporate tax rate was 35%.

• As shown on the next slide, Safeway’s net income in 2008 was lower with leverage than it would have been without leverage.

Table 15.1 Safeway’s Income with and without Leverage, 2008 ($ millions)

• Safeway’s debt obligations reduced the value of its equity. But the total amount available to all investors was higher with leverage.

• Without leverage, Safeway was able to pay out $1,202 million in total to its investors.

• With leverage, Safeway was able to pay out $1,325 million in total to its investors.

• Where does the additional $123 million come from?

• Interest Tax Shield

– The reduction in taxes paid due to the tax deductibility of interest

• In Safeway’s case, the gain is equal to the reduction in taxes with leverage: $648 million − $525 million = $123 million. The interest payments provided a tax savings of 35% × $350 million = $123 million.

Interest Tax Shield Corporate Tax Rate Interest Payments= ×

Textbook Example 15.1

Textbook Example 15.1 (cont'd)

15.2 Valuing the Interest Tax Shield

• When a firm uses debt, the interest tax shield provides a corporate tax benefit each year.

• This benefit is the computed as the present value of the stream of future interest tax shields the firm will receive.

The Interest Tax Shield and Firm Value

• The cash flows a levered firm pays to investors will be higher than they would be without leverage by the amount of the interest tax shield.Cash Flows to Investors Cash Flows to Investors

(Interest Tax Shield)with Leverage without Leverage

⎛ ⎞ ⎛ ⎞= +⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

Figure 15.1 The Cash Flows of the Unlevered and Levered Firm

The Interest Tax Shield and Firm Value (cont'd)

• MM Proposition I with Taxes

– The total value of the levered firm exceeds the value of the firm without leverage due to the present value of the tax savings from debt.

(Interest Tax Shield)L UV V PV= +

Alternative Example 15.2

• Problem– Suppose ALCO plans to pay $60 million in

interest each year for the next 8 years, and then repay the principal of $1 billion in year 8.

– These payments are risk free, and ALCO’s marginal tax rate will remain 39% throughout this period.

– If the risk-free interest rate is 6%, by how much does the interest tax shield increase the value of ALCO?

• Solution– The annual interest tax shield is:

• $1 billion × 6% × 39% = $23.4 million for 8 years.

1 1(Interest Tax Shield) $23.4 million (1 )

6% 1.06$145.31 million

PV = × −

The Interest Tax Shield with Permanent Debt

• Typically, the level of future interest payments is uncertain due to changes in the marginal tax rate, the amount of debt outstanding, the interest rate on that debt, and the risk of the firm.

– For simplicity, we will consider the special case in which the above variables are kept constant.

The Interest Tax Shield with Permanent Debt (cont'd)

• Suppose a firm borrows debt D and keeps the debt permanently. If the firm’s marginal tax rate is c , and if the debt is riskless with a risk-free interest rate rf , then the interest tax shield each year is c × rf × D, and the tax shield can be valued as a perpetuity. ( ) Interest

(Interest Tax Shield)

× ××= =

• If the debt is fairly priced, no arbitrage implies that its market value must equal the present value of the future interest payments.Market Value of Debt (Future Interest Payments)D PV= =

• If the firm’s marginal tax rate is constant, then:(Interest Tax Shield) ( Future Interest Payments)

(Future Interest Payments)

= ×= ×= ×

The Weighted Average Cost of Capital with Taxes

• With tax-deductible interest, the effective after-tax borrowing rate is r(1 − c) and the weighted average cost of capital becomes

(1 ) wacc E D c

E Dr r r

E D E D= + −

Pretax WACC Reduction Dueto Interest Tax Shield

wacc E D D c

E D Dr r r r

E D E D E D= + −

+ + +1 4 4 4 42 4 4 4 43 1 4 2 4 43

Figure 15.2 The WACC with and without Corporate Taxes

The Interest Tax Shield with a Target Debt-Equity Ratio

• When a firm adjusts its leverage to maintain a target debt-equity ratio, we can compute its value with leverage, VL, by discounting its free cash flow using the weighted average cost of capital.

The Interest Tax Shield with a Target Debt-Equity Ratio (cont'd)

• The value of the interest tax shield can be found by comparing the value of the levered firm, VL, to the unlevered value, VU, of the free cash flow discounted at the firm’s unlevered cost of capital, the pretax WACC.

15.3 Recapitalizing to Capture the Tax Shield

• Assume that Midco Industries wants to boost its stock price. The company currently has 20 million shares outstanding with a market price of $15 per share and no debt. Midco has had consistently stable earnings, and pays a 35% tax rate. Management plans to borrow $100 million on a permanent basis and they will use the borrowed funds to repurchase outstanding shares.

The Tax Benefit

• Without leverage– VU = (20 million shares) × ($15/share) = $300 million

• If Midco borrows $100 million using permanent debt, the present value of the firm’s future tax savings is– PV(interest tax shield) = cD = 35% × $100 million = $35 million

The Tax Benefit (cont'd)

• Thus the total value of the levered firm will be– VL = VU + cD = $300 million + $35 million = $335 million

• Because the value of the debt is $100 million, the value of the equity is– E = VL − D = $335 million − $100 million = $235 million

The Tax Benefit (cont'd)

• Although the value of the shares outstanding drops to $235 million, shareholders will also receive the $100 million that Midco will pay out through the share repurchase.

• In total, they will receive the full $335 million, a gain of $35 million over the value of their shares without leverage.

The Share Repurchase

• Assume Midco repurchases its shares at the current price of $15/share. The firm will repurchase 6.67 million shares.– $100 million ÷ $15/share = 6.67 million shares

• It will then have 13.33 million shares outstanding. – 20 million − 6.67 million = 13.33 million

The Share Repurchase (cont'd)

• The total value of equity is $235 million; therefore the new share price is $17.625/share.– $235 million ÷ 13.33 million shares = $17.625

• Shareholders that keep their shares earn a capital gain of $2.625 per share.– $17.625 − $15 = $2.625

The Share Repurchase (cont'd)

• The total gain to shareholders is $35 million.– $2.625/share × 13.33 million shares = $35 million

• If the shares are worth $17.625/share after the repurchase, why would shareholders tender their shares to Midco at $15/share?

No Arbitrage Pricing

• If investors could buy shares for $15 immediately before the repurchase, and they could sell these shares immediately afterward at a higher price, this would represent an arbitrage opportunity.

No Arbitrage Pricing (cont'd)

• Realistically, the value of the Midco’s equity will rise immediately from $300 million to $335 million after the repurchase announcement. With 20 million shares outstanding, the share price will rise to $16.75 per share.– $335 million ÷ 20 million shares = $16.75 per share

• With a repurchase price of $16.75, the shareholders who tender their shares and the shareholders who hold their shares both gain $1.75 per share as a result of the transaction.– $16.75 − $15 = $1.75

• The benefit of the interest tax shield goes to all 20 million of the original shares outstanding for a total benefit of $35 million.– $1.75/share × 20 million shares = $35 million

• When securities are fairly priced, the original shareholders of a firm capture the full benefit of the interest tax shield from an increase in leverage.

• Problem– Suppose Midco still chooses to borrow $100 million, but only wishes to repurchase $75 million worth of its shares. What is the lowest price it could offer and expect shareholders to tender their shares?

Alternative Example 15.4 (cont’d)

• Solution Repurchase Price

Shares Repurchased

(millions)

Shares Remaining (millions)

New Share Price

PR R = 125/PR N = 20 - R Pn = 235/N$13.50 5.56 14.44 $16.27$13.75 5.45 14.55 $16.16$14.00 5.36 14.64 $16.05$14.25 5.26 14.74 $15.95$14.50 5.17 14.83 $15.85$14.75 5.08 14.92 $15.76$15.00 5.00 15.00 $15.67$15.25 4.92 15.08 $15.58$15.50 $4.84 $15.16 $15.50$15.75 4.76 15.24 $15.42$16.00 4.69 15.31 $15.35$16.25 4.62 15.38 $15.28$16.50 4.55 15.45 $15.21$16.75 4.48 15.52 $15.14

Analyzing the Recap: The Market Value Balance Sheet

• In the presence of corporate taxes, we must include the interest tax shield as one of the firm’s assets.

Table 15.2 Market Value Balance Sheet for the Steps in Midco’s Leveraged Recapitalization

15.4 Personal Taxes

• The cash flows to investors are typically taxed twice. Once at the corporate level and then investors are taxed again when they receive their interest or divided payment.

15.4 Personal Taxes (cont'd)

• For individuals:

– Interest payments received from debt are taxed as income.

– Equity investors also must pay taxes on dividends and capital gains.

Including Personal Taxes in the Interest Tax Shield

• The amount of money an investor will pay for a security depends on the the cash flows the investor will receive after all taxes have been paid.

• Personal taxes reduce the cash flows to investors and can offset some of the corporate tax benefits of leverage.

Including Personal Taxes in the Interest Tax Shield (cont'd)• The actual interest tax shield depends on both corporate and personal taxes that are paid.

• To determine the true tax benefit of leverage, the combined effect of both corporate and personal taxes needs to be evaluated.

Figure 15.3 After-Tax Investor Cash Flows Resulting from $1 in EBIT

Table 15.3 Top Federal Tax Rates in the United States, 1971–2009

Including Personal Taxes in the Interest Tax Shield (cont'd)• In general, every $1 received after taxes by debt holders from interest payments costs equity holders $(1 − *) on an after-tax basis, where:– Effective Tax Advantage of Debt

(1 ) (1 ) (1 ) (1 ) (1 ) 1

(1 ) (1 )i c e c e

∗ − − − − − −= = −

− −

Including Personal Taxes in the Interest Tax Shield (cont'd)

– When there are no personal taxes on debt income (i = 0) or when the personal tax rates on debt and equity income are the same (i = e ), the formula reduces to * = c.

– When equity income is taxed less heavily (e is less than i), then * is less than c.

(1 ) (1 ) (1 ) (1 ) (1 ) 1

(1 ) (1 )i c e c e

∗ − − − − − −= = −

− −

• Problem– Given the following tax rates:

– What is the effective tax advantage of debt for each of the years listed?

YearCorporate Tax

RateAverage Personal Tax Rate on Equity Income

Average Personal Tax Rate on Interest

Income

1985 46% 35% 50%

1995 35% 34% 28%

2009 35% 15% 35%

• Solution

) (1 ) (1 1

−−−

−=∗

%8.29) .50 (1

.35) (1 ) 46. (1 1 1985 =

−−−

−=∗

%4.40) .28 (1

) .34 (1 35). (1 1 1995 =

−−−

−=∗

(1 .35 ) (1 .15 ) 1 15.0%

(1 .35 ) ∗ − −

= − =−

Figure 15.4 The Effective Tax Advantage of Debt with and without Personal Taxes, 1971–2009

Valuing the Interest Tax Shield with Personal Taxes

• With personal taxes and permanent debt, the value of the firm with leverage becomes

– If * is less than c, the benefit of leverage is reduced in the presence of personal taxes.

L UV V D ∗= +

Valuing the Interest Tax Shield with Personal Taxes (cont'd)

• Personal taxes have a similar effect on the firm’s weighted average cost of capital.

• While we still compute the WACC as (1 )

wacc E D c

E Dr r r

E D E D= + −

Valuing the Interest Tax Shield with Personal Taxes (cont'd)

• With personal taxes the firm’s equity and debt costs of capital will adjust to compensate investors for their respective tax burdens.

• The net result is that a personal tax disadvantage for debt causes the WACC to decline more slowly with leverage than it otherwise would.

• Problem– Estimate the value of Midco if it goes through with the $100 million recapitalization, accounting for personal taxes at their 1980 levels.

Alternative Example 15.6 (cont’d)

• Solution– From example 15.5, we know in 1980 was 8.2%. Given Midco’s current value of VU

=$300 millon, VL is estimated as VU + D = $300 million + 8.2%($100 million) = $308.20. With 20 million original shares outstanding, the stock price would increase by $8.2 million ÷20 million shares = $0.41 per share.

– In contrast, as shown in Example 15.6 in the text, at 2009 personal and corporate tax levels, the stock price would increase by $0.75 per share.

Determining the Actual Tax Advantage of Debt

• Several assumptions were made in estimating the effective tax advantage of debt after taking personal taxes into account that may need adjustment when determining the actual tax benefit for a particular firm or investor.

Determining the Actual Tax Advantage of Debt (cont'd)

• It was assumed that investors paid capital gains taxes every year.

• However, capital gains taxes are paid only when the investor sells the stock and realizes the gain. Deferring the payment of capital gains taxes lowers the present value of the taxes, which can be interpreted as a lower effective capital gains tax rate.

• Investors with accrued losses that they can use to offset gains face a zero effective capital gains tax rate.

• Thus, investors with longer holding periods or with accrued losses face a lower tax rate on equity income, decreasing the effective tax advantage of debt.

• It was also assumed that that shareholder gains from additional earnings were evenly split between dividends and capital gains.

• For firms with much higher or much lower payout ratios, however, this average would not be accurate.

• In addition, it was assumed that investors pay the top marginal federal income tax rates.

• In reality, rates vary for individual investors, and many investors face lower rates. – At lower rates, the effects of personal taxes are less substantial.

• Many investors face no personal taxes.– For example, investments held in retirement savings accounts or pension funds that are not subject to taxes.

– For these investors, the effective tax advantage of debt is the full corporate tax rate.

• The bottom line:

– Calculating the effective tax advantage of debt accurately is extremely difficult.• A firm must consider the tax bracket of its typical debt holders, and the tax bracket and holding period of its typical equity holders.

– The tax advantage of debt will vary across firms and from investor to investor.

15.5 Optimal Capital Structure with Taxes

• Do Firms Prefer Debt?

– When firms raise new capital from investors, they do so primarily by issuing debt.

– In most years aggregate equity issues are negative, meaning that on average, firms are reducing the amount of equity outstanding by buying shares.

Figure 15.5 Net External Financing and Capital Expenditures by U.S. Corporations, 1975–2008

Source: Federal Reserve, Flow of Funds Accounts of the United States, 2009.

15.5 Optimal Capital Structure with Taxes (cont'd)

– While firms seem to prefer debt when raising external funds, not all investment is externally funded.

– Most investment and growth is supported by internally generated funds. • Even though firms have not issued new equity, the market value of equity has risen over time as firms have grown. For the average firm, the result is that debt as a fraction of firm value has varied in a range from 30–45%.

Figure 15.6 Debt-to-Value Ratio [D / (E + D)] of U.S. Firms, 1975–2008

Source: Compustat and Federal Reserve, Flow of Funds Accounts of the United States, 2009.

15.5 Optimal Capital Structure with Taxes (cont'd)

– The use of debt varies greatly by industry.

– Firms in growth industries like biotechnology or high technology carry very little debt, while airlines, automakers, utilities, and financial firms have high leverage ratios.

Figure 15.7 Debt-to-Value Ratio [D / (E + D)] for Select Industries

Source: Capital IQ, 2009.

Limits to the Tax Benefit of Debt

• To receive the full tax benefits of leverage, a firm need not use 100% debt financing, but the firm does need to have taxable earnings.

– This constraint may limit the amount of debt needed as a tax shield.

Table 15.4 Tax Savings with Different Amounts of Leverage

Limits to the Tax Benefit of Debt (cont'd)

• From the previous slide:

– With no leverage, the firm receives no tax benefit.

– With high leverage, the firm saves $350 in taxes.

– With excess leverage, the firm has a net operating loss and there is no increase in the tax savings.• Because the firm is already not paying taxes, there is no immediate tax shield from the excess leverage

• No corporate tax benefit arises from incurring interest payments that exceed EBIT.

• Because interest payments constitute a tax disadvantage at the investor level, investors will pay higher personal taxes with excess leverage, making them worse off.

• If the firm is not paying taxes, where c = 0, then the tax disadvantage of excess leverage is:

– Note: *ex is negative because (*e < i).

∗ =1−(1−e)(1− i )

=e− i (1− i )

• The optimal level of leverage from a tax saving perspective is the level such that interest equals EBIT.

– At the optimal level of leverage, the firm shields all of its taxable income and it does not have any tax-disadvantaged excess interest.

• However, it is unlikely that a firm can predict its future EBIT (and the optimal

level of debt) precisely.

– If there is uncertainty regarding EBIT, then

there is a risk that interest will exceed EBIT. As a result, the tax savings for high levels of interest falls, possibly reducing the optimal level of the interest payment.

Figure 15.8 Tax Savings for Different Levels of Interest

• In general, as a firm’s interest expense approaches its expected taxable earnings, the marginal tax advantage of debt declines, limiting the amount of debt the firm should use.

Growth and Debt

• Growth will affect the optimal leverage ratio.

– To avoid excess interest, a firm with positive earnings should have a level of debt such that interest payments are below its expected taxable earnings.

Interest Debt EBIT or Debt EBIT / D Dr r= × ≤ ≤

Growth and Debt (cont'd)

• From a tax perspective, the firm’s optimal level of debt is proportional to its current earnings. However, the value of the firm’s equity will depend on the growth rate of earnings:

– The higher the growth rate, the higher the value of equity. As a result, the optimal proportion of debt in the firm’s capital structure [D / (E + D)] will be lower, the higher the firm’s growth rate.

Other Tax Shields

• There are numerous provisions in the tax laws for deductions and tax credits, such as depreciation, investment tax credits, carryforwards of past operating losses, etc.

• To the extent that a firm has other tax shields, its taxable earnings will be reduced and it will rely less heavily on the interest tax shield.

The Low Leverage Puzzle

• The figure on the following slide reveals two important patterns.

– Firms have used debt to shield a greater percentage of their earnings from taxes in more recent years (mirroring the increase in the effective tax advantage of debt).

– Firms have far less leverage than our analysis of the interest tax shield would predict.

Figure 15.9 Interest Payments as a Percentage of EBIT for S&P 500 Firms, 1975–2008

Source: Compustat.

The Low Leverage Puzzle (cont'd)

• Firms worldwide have similar low proportions of debt financing.

– Although the corporate tax codes are similar across all countries in terms of the tax advantage of debt, personal tax rates vary more significantly, leading to greater variation in *.

Table 15.5 International Leverage and Tax Rates (1990)

• It would appear that firms, on average, are under-leveraged. However, it is hard to accept that most firms are acting suboptimally.

– In reality, there is more to the capital structure story than discussed so far.

• A key item missing from the analysis thus far is that increasing the level of debt increases the probability of bankruptcy.

• If bankruptcy is costly, these costs might offset the tax advantages of debt financing.

Discussion of Data Case Key Topic

• By how much did Home Depot’s debt/equity ratio actually change over the last year?

• With the benefit of hindsight, based on what really happened to the D/E ratio over the last year, should you have recommended that Home Depot issue additional debt and repurchase stock?

• Ir.HomeDepot.com

Chapter Quiz

1. How do corporate taxes impact a firm’s value as leverage changes?

2. How does leverage affect a firm’s weighted average cost of capital?

3. How can shareholders benefit form a leveraged recapitalization when it reduces the total value of equity?

4. Under current tax law, why is there a personal tax disadvantage of debt?

5. How does the growth rate of a firm affect the optimal fraction of debt in the capital structure?

copyright © 2011 pearson prentice hall. all rights reserved. chapter 15 debt and taxes

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