## CHAPTER 18

How Much Should a Firm Borrow?

1.                  For \$1 of debt income:

 Corporate tax = \$0 Personal tax = 0.44´\$1 = \$0.440 Total = \$0.440

For \$1 of equity income, with all capital gains realized immediately:

 Corporate tax = 0.35´\$1 = \$0.350 Personal tax = 0.44´0.5´[\$1 – (0.35´\$1)] + 0.20´0.5´[\$1 – (0.35´\$1)] = \$0.208 Total = \$0.558

For \$1 of equity income, with all capital gains deferred forever:

 Corporate tax = 0.35´\$1 = \$0.350 Personal tax = 0.44´0.5´[\$1 – (0.35´\$1)] = \$0.143 Total = \$0.493

2.                  Consider a firm that is levered, has perpetual expected cash flow X, and has an interest rate for debt of rD.  The personal and corporate tax rates are Tp and Tc, respectively.  The cash flow to stockholders each year is:

(X - rDD)(1 - Tc)(1 - Tp)

Therefore, the value of the stockholders’ position is:

where r is the opportunity cost of capital for an all-equity-financed firm.  If the stockholders borrow D at the same rate rD, and invest in the unlevered firm, their cash flow each year is:

The value of the stockholders’ position is then:

The difference in stockholder wealth, for investment in the same assets, is:

VL – VU = DTc

This is the change in stockholder wealth predicted by MM.  If individuals could not deduct interest for personal tax purposes, then:

Then:

So the value of the shareholders’ position in the levered firm is relatively greater when no personal interest deduction is allowed.

3.                  The book value of Pfizer’s assets is \$21,529 million.  With a 40 percent book debt ratio:

Long-term debt + Other long-term liabilities = 0.40 ´ \$21,529 = \$8,612

This is [\$8,612 – (\$2,123 + \$4,330)] = \$2,159 more than shown in Table 18.3(a).  The corporate tax rate is 35 percent, so firm value increases by:

0.35 ´ \$2,159 = \$756 million

The market value of the firm is now: (\$296,247 + \$756) = \$297,003 million.

The market value balance sheet is:

 Net working capital \$5,206 \$4,282 Long-term debt Market value of long-term assets 291,797 4,330 Other long-term liabilities 288,391 Equity Total Assets \$297,003 \$297,003 Firm market value

4.                  Answers here will vary depending on the company chosen.

5.                  The value of interest tax shields is determined by:

§         The on-going degree of profitability.

§         The ability to carry-forward and carry-back excess credits

§         The ability to maintain debt levels on an on-going basis.

§         The rates of personal and corporate taxes.

§         The amount of non-interest tax shields

6.                  When a firm defaults, the cause (absent fraud) is usually an operating problem.  Although both shareholders and debtholders are worse off, their respective expected rates of return are determined in a manner that compensates for this risk.  The combined positions of stockholders and bondholders in limited liability and unlimited liability firms are the same.  The ability to assign the assets to the creditors, and not have to repay, has value to the shareholders since it is a more efficient transfer of wealth.

7.                  Assume the following facts for Circular File:

 Book Values Net working capital \$20 \$50 Bonds outstanding Fixed assets 80 50 Common stock Total assets \$100 \$100 Total liabilities

 Market Values Net working capital \$20 \$25 Bonds outstanding Fixed assets 10 5 Common stock Total assets \$30 \$30 Total liabilities

a.         Playing for Time

Suppose Circular File foregoes replacement of \$10 of capital equipment, so that the new balance sheet may appear as follows:

 Market Values Net working capital \$30 \$29 Bonds outstanding Fixed assets 8 9 Common stock Total assets \$38 \$38 Total liabilities

Here the shareholder is better off but has obviously diminished the firm’s competitive ability.

b.                  Cash In and Run

Suppose the firm pays a \$5 dividend:

 Market Values Net working capital \$15 \$23 Bonds outstanding Fixed assets 10 2 Common stock Total assets \$25 \$25 Total liabilities

Here the value of common stock should have fallen to zero, but the bondholders bear part of the burden.

c.                  Bait and Switch

 Market Values Net working capital \$30 \$20 New Bonds outstanding 20 Old Bonds outstanding Fixed assets 20 10 Common stock Total assets \$50 \$50 Total liabilities

8.                  Static trade-off theory reduces the debt-equity decision to a trade-off between interest tax shields and the costs of financial distress.  In the real world, matters are not so simple because there are costs to adjusting the firm’s capital structure, and individual managers have different attitudes toward debt.  High-tech growth firms with risky assets tend to be equity financed while low risk mature businesses tend to have more debt.  Similarly, firms often issue equity to pay off excess debt.  However, many profitable firms have very little debt and changes in tax rates have little effect on debt-equity ratios.

9.                  Answers here will vary according to the companies chosen; however, the important considerations are given in the text, Section 18.3.

10.       a.         SOS stockholders could lose if they invest in the positive NPV project and then SOS becomes bankrupt.  Under these conditions, the benefits of the project accrue to the bondholders.

b.         If the new project is sufficiently risky, then, even though it has a negative NPV, it might increase stockholder wealth by more than the money invested.  This is a result of the fact that, for a very risky investment, undertaken by a firm with a significant risk of default, stockholders benefit if a more favorable outcome is actually realized, while the cost of unfavorable outcomes is borne by bondholders.

c.         Again, think of the extreme case: Suppose SOS pays out all of its assets as one lump-sum dividend.  Stockholders get all of the assets, and the bondholders are left with nothing.

These conflicts of interest are severe only when the company is in financial distress.  Adherence to a moderate target debt ratio limits the conflicts.

11.       a.         The bondholders benefit.  The fine print limits actions that transfer wealth from the bondholders to the stockholders.

b.                  The stockholders benefit.  In the absence of fine print, bondholders charge a higher rate of interest to ensure that they receive a fair deal.  The firm would probably issue the bond with standard restrictions.  It is likely that the restrictions would be less costly than the higher interest rate.

12.             Certainly part of this drop must be attributed to bankruptcy costs, which come out of the shareholders’ pockets.  It is likely, however, that the actual bankruptcy filing conveyed some negative information to the market about Caldor’s future prospects and that part of the drop must, therefore, be attributed to this negative information.

13.             Other things equal, the announcement of a new stock issue to fund an investment project with an NPV of \$40 million should increase equity value by \$40 million (less issue costs).  But, based on past evidence, management expects equity value to fall by \$30 million.  There may be several reasons for the discrepancy:

(i)                 Investors may have already discounted the proposed investment.  (However, this alone would not explain a fall in equity value.)

(ii)               Investors may not be aware of the project at all, but they may believe instead that cash is required because of, say, low levels of operating cash flow.

(iii)             Investors may believe that the firm’s decision to issue equity rather than debt signals management’s belief that the stock is overvalued.

If the stock is indeed overvalued, the stock issue merely brings forward a stock price decline that will occur eventually anyway.  Therefore, the fall in value is not an issue cost in the same sense as the underwriter’s spread.  If the stock is not overvalued, management needs to consider whether it could release some information to convince investors that its stock is correctly valued, or whether it could finance the project by an issue of debt.

14.       a.         Masulis’ results are consistent with the view that debt is always preferable because of its tax advantage, but are not consistent with the ‘tradeoff’ theory, which holds that management strikes a balance between the tax advantage of debt and the costs of possible financial distress.  In the tradeoff theory, exchange offers would be undertaken to move the firm’s debt level toward the optimum.  That ought to be good news, if anything, regardless of whether leverage is increased or decreased.

b.                  The results are consistent with the evidence regarding the announcement effects on security issues and repurchases.

c.                  One explanation is that the exchange offers signal management’s assessment of the firm’s prospects.  Management would only be willing to take on more debt if they were quite confident about future cash flow, for example, and would want to decrease debt if they were concerned about the firm’s ability to meet debt payments in the future.

15.       Let us assume that, as companies are started, grow, and mature, they stick to the same line of business and are consistently profitable.  Then, if the tradeoff theory is correct, because the types of assets the company has do not change over time, the firm’s debt ratio will likewise not be expected to change over time.  If the pecking-order theory is correct, the company’s debt ratio will tend to decrease over time because the company will fund projects from retained earnings, i.e., internally generated cash.

16.             In general, the pecking order theory explains intra-industry debt levels since less profitable firms end up borrowing more because they have lower internal cash flow.  However, the argument seems to fail on an inter-industry basis.  High-tech, high growth firms have low debt levels even though they need cash, and stable, mature industries (e.g., utilities) often do not pay down debt but pay the cash out as dividends.

17.             Bondholders require a higher interest rate than they would otherwise in order to compensate for the fact that interest attracts more tax than equity returns.

18.             a.

 Expected Payoff to Bank Expected Payoff to Ms. Ketchup Project 1 +10.0 +5 Project 2 (0.4´10) + (0.6´0) = +4.0 (0.4´14)+(0.6´0)=+5.6

Ms. Ketchup would undertake Project 2.

b.                  Break even will occur when Ms. Ketchup’s expected payoff from Project 2 is equal to her expected payoff from Project 1.  If X is Ms. Ketchup’s payment on the loan, then her payoff from Project 2 is:

0.4 (24 – X)

Setting this expression equal to 5 (Ms. Ketchup’s payoff from Project 1), and solving, we find that: X = 11.5

Therefore, Ms. Ketchup will borrow less than the present value of this payment.

19.             Internet exercise; answers will vary.

Challenge Questions

1.         a.         Internet exercise; answers will vary.