Solutions for Chapter 9

Problem #1

  1. If the firm moves to 50% debt ratio, D/(E + D) = 0.5, and by doing so increases the value of the firm by $300 million then the target debt amount is ($2,000 + $300) x 0.5 = $1,150 million in debt.

If it chooses to move immediately this target debt/equity structure it can 1) sell debt for $1,150 million and retire $1,150 of stock (stock repurchase) or 2) it can sell debt of $1,150 and pay a special dividend of $1,150 effectively dropping the value of the stock in half. If it chooses to move slowly it can think of the debt sales as funding of new projects and keep the cash in the company so it can sell $2,300 million of debt (equal to current equity value) and then over time fund the new projects with cash on hand. But you would not want to have cash just lying around, so it would be invested and the gains go to the equity holders so this may be a long process to get the $300 million gain by moving to a 50/50 debt/equity ratio.

  1. The only difference may be the tax treatment for the recipient. For a stock repurchase, if it has a business purpose, the shareholders are taxed at the capital gains rate on their profit, (repurchase price – original purchase price) x (capital gains tax rate). Special dividends are taxed at an ordinary income tax rate so the entire distribution is taxable.
  1. The cash balance impacts the decision only if it is used as part of the repurchase or special dividend, then the debt required is reduced by the amount of cash used for the repurchase or dividend,

$1,150 – ($250 x (1 - 0.5)) = $1,025

Note – where does a dividend payment come from? Answer: Retained Earnings which are part of the equity value of the firm. So paying a cash dividend reduces the equity value of the firm.

Problem #2

  1. Start with a current D/E and then make a table to show the changes in equity.

Current D/E

Market Value of the Debt is $100 million

Market Value of Equity is $100 x 9 million shares = $900 million

D/E = 1/9 or Debt ratio is 1/ (9+1) = 10%

Current Net Income is $7.50 x 9 million shares = $67.5 million

Dividend payout (constant) is 0.20 so dividend is 0.20 x $67.50 = $13.5

Retained Earnings is 0.80 x $67.5 = $54.0

Beta provides expected return = 7% + 1.10 x (5.5%) = 13.05%

Dividends provide a yield of $13.5 / $900.0 = 0.015 or 1.5%

Anticipated growth in the stock is 13.05% - 1.50% = 11.55%

New equity value for end of year 1 is $900 x (1 + 0.1155) = $1,003.95

Net Income for coming year is $67.5 x 1.10 = $74.25

Unlevered Beta is, 1.10 /(1 + (1/9) (1 - 0.40)) = 1.03125

New D/E = $100 / $1,003.95 = 0.0996

New Beta for coming year is 1.03125 x (1 + (0.0996) (0.6)) = 1.093

Expected Return for coming year is 7% + 1.093 (5.5%) = 13.0115%

Repeat above for each year…given debt stays at $100 million

(note I have rounded in the Table)

Year / 1 / 2 / 3 / 4 / 5
Debt / $100 / $100 / $100 / $100 / $100
Equity / $1,003.95 / $1,119.72 / $1,248.68 / $1,392.35 / $1,552.92
D/E / 9.96% / 8.93% / 8.01% / 7.18% / 6.44%
Net Income / $74.25 / $81.68 / $89.84 / $98.83 / $108.71
Dividends / $14.85 / $16.34 / $17.97 / $19.77 / $21.74
Beta / 1.09 / 1.09 / 1.08 / 1.08 / 1.08
E(Return) / 13.01% / 12.98% / 12.94% / 12.92% / 12.89%
Dividend Yield / 1.48% / 1.46% / 1.44% / 1.42% / 1.40%
Expected Growth / 11.53% / 11.52% / 11.51% / 11.50% / 11.49%
Debt Ratio / 0.0906 / 0.0820 / 0.0741 / 0.0670 / 0.0605
  1. Do this again with the added feature that it doubles its dividends (now assume we use 40% of the net income for dividends and it buys back 5% of the stock each year beginning at the end of year 1.

Current Net Income is $7.50 x 9 million shares = $67.5 million

Dividend payout (double) is 0.40 so dividend is 0.4 x $67.50 = $27.0

Retained Earnings is 0.60 x $67.5 = $40.5

Beta provides expected return = 7% + 1.10 x (5.5%) = 13.05%

Dividends provide a yield of $27.0 / $900.0 = 0.03 or 3.0%

Anticipated growth in the stock is 13.05% - 3.0% = 10.05%

New equity value for end of year 1 is $900 x (1 + 0.1005) = $990.45

Buy back 5% of stock $990.45 x 0.05 = $49.52

End of Year Equity is $990.45 - $49.52 = $940.93

Net Income for coming year is $67.5 x 1.10 = $74.25

Unlevered Beta is, 1.10 /(1 + (1/9) (1 - 0.40)) = 1.03125

New D/E ratio is, $100 / $940.93 = 0.1063

New Beta for coming year is 1.03125 x (1 + (0.1063) (0.6)) = 1.097

Expected Return for coming year is 7% + 1.097 (5.5%) = 13.03%

Repeat above for each year…given debt stays at $100 million

(note I have rounded in the Table)

Year / 1 / 2 / 3 / 4 / 5
Debt / $100 / $100 / $100 / $100 / $100
Equity / $940.93 / $982.20 / $1,023.51 / $1,064.61 / $1,105.25
D/E / 10.63% / 10.18% / 9.77% / 9.39% / 9.05%
Net Income / $74.25 / $81.68 / $89.84 / $98.83 / $108.71
Dividends / $27.90 / $32.67 / $35.94 / $39.53 / $43.48
Repurchase / $49.52 / $51.69 / $53.86 / $56.03 / $58.17
Beta / 1.10 / 1.09 / 1.09 / 1.09 / 1.09
E(Return) / 13.03% / 13.02% / 13.00% / 12.99% / 12.98%
Dividend Yield / 3.16% / 3.33% / 3.51% / 3.71% / 3.93%
Expected Growth / 9.88% / 9.69% / 9.49% / 9.28% / 9.05%
Debt Ratio / 0.0961 / 0.0924 / 0.0890 / 0.0859 / 0.0830

Problem #7

  1. We need to estimate the duration based on the change in firm value and the change in the bond rates…using Excel regression from data analysis…

% Δ Firm Value = 0.08 -6.46 Δ Long Bond Rates

The duration of 6.46 years is used to select the duration of the bond. If you choose a zero coupon bond you would select seven years for the maturity date of the bond.

  1. We regress % Δ Firm Value on GNP Growth and get

% Δ Firm Value = 0.20 - 1.65 GNP Growth

With a negative coefficient the firm is counter cyclical. (Note the author runs the regression with a year lag on growth or maybe just a mistake in the regressions.) You would probably issue bonds in a down market as your firm value would be increasing when bond rates are probably falling.

  1. We regress % Δ Firm Value on change in Exchange Rate (FX) and get

% Δ Firm Value = 0.10 - 0.072 Δ FX Rate

The firm is not very sensitive to exchange rates so you would probably use domestic bonds.

  1. We regress % Δ Firm Value on change in Inflation and get

% Δ Firm Value = 0.098–6.87Inflation

Firm value falls during high inflation times (negative coefficient) so you would not issue bonds during rising inflation.

  1. Industry averages may be better due to low t-stats on all these regressions.

Problem #8

  1. We need to estimate the duration based on the change in operating income and the change in the bond rates…using Excel regression from data analysis…

% Δ Operating Income = 0.12+9.22 Δ Long Bond Rates

The regression suggests that as bond rates rise, the operating income increases. Bonds should be issued when rates are rising (this almost seems counter-intuitive and so we want to interpret with caution).

  1. We regress % Δ Operating Income on GNP Growth and get

% Δ Operating Income = 0.09+7.30 GNP Growth

The regression suggests that bonds should be issued when the economy is growing as the operating income will increase to allow the firm to carry more debt.

  1. We regress % Δ Operating Income on change in Exchange Rate (FX) and get

% Δ Operating Income = 0.085 - 0.094 Δ FX Rate

The firm is negatively impacted by the exchange rate but the t-stat is very low and so this is marginal. There does not appear to be a need to consider issuing foreign bonds as part of the debt structure of the firm.

  1. We regress % Δ Operating Income on change in Inflation and get

% Δ Operating Income = 0.09+4.06 Inflation

The operating income is very sensitive to inflation and rides up as inflation increases so it can issue debt in times of high inflation as the operating income would support more debt. But t-stat is low (0.5) so this relationship is not significant.

  1. Industry averages may be better due to low t-stats on some of the regressions.

Problem #10

  1. Arguments for a gradual movement – 1) D/E change is fairly significant moving from 10.30% debt ratio to 30% but only a small movement in WACC from 14.51% to 13.45% so the gain may not be significant from the equity perspective 2) Pfizer should look at the trend in D/E not just a single point in time and see if the trend is moving to a lower D/E for the industry and therefore it could move gradually to the moving target and 3) moving immediately to the new D/E would reduce flexibility in the future for this drug giant that relies on R and D for future success.

Arguments for a quick movement – 1) With a low probability of being a take-over target a quick move would allow equity holders to capture some of the value immediately 2) it may have many potential projects that need funding and moving immediately could provide additional investment dollars that could increase the speed at which new products reach the market (drugs take a long time to move through the approval process and first movers usually get strong rewards ahead of generic substitutes hitting the market).

  1. A gradual movement to more debt could be accomplished by increasing dividends or stock repurchases if funds are available or issuing more debt to fund NPV projects or a combination of both.

A quick movement could be accomplished by a debt for equity swap in which Pfizer issued debt and used the proceeds to retire stock (stock repurchase).

  1. If Pfizer is going to use its excess debt capacity as its source of funding for an acquisition then it should consider the acquisition just like any other NPV project. If the NPV is positive and better than its internal projects it should acquire another company (or two). The key is does the cash flow used to assess the NPV of the acquisition include the impact of the new WACC with the combined firms?

Problem #13

  1. The regression is being used to estimate duration (not sure this is an accurate measure of duration…but nevertheless let’s assume for argument’s sake that it is) of the assets at 6 years (from the slope coefficient of the regression). If current debt has a duration of 1 year there is a mismatch between assets and liabilities that could help or hurt the company. The question that should arise before deeming the debt structure appropriate is:What is the likelihood of interest rates moving up or down. In the current situation (asset duration greater than liability duration) the rising interest rates would hurt firm value (assets prices would fall faster than liabilities) and vice versa falling interest rates would help the firm, which is more likely? For example, right now in the USA the chance of falling interest rates seems much more likely as the Fed is trying to stave off a recession.
  1. Using short-term debt to finance long-term projects would appear to be a recipe for bankruptcy as the cash flow for paying back the loan would not be realized until after the repayment is due. The only way this makes sense is if 1) current cash flow is very high and can pay off the loan or 2) the firm plans on rolling over the short-term debt until the project cash flows can retire the debt. In the later case it suggests that Bethlehem Steel believes that it can exploit the term structure of interest rates by borrowing at the lower short-term rates over and over staying below the long-term rates. It also assumes that the current future short-term rates will not rise above current long-term rates.

Problem #14

Railroad companies have long-term, fixed rate, dollar denominated debt because:

1)Railroad companies operate within the U.S. and therefore are not exposed to exchange rate issues, thus dollar denominated debt is appropriate.

2)Railroads are mature industries with steady cash flow and therefore can set their debt at a level where they can meet the debt payments (most of the time, exception Penn Central) so fixed rates are best.

3)Railroad companies have long-lived assets so that they produce cash flow over long periods and so long-term debt is appropriate. (There is a major misconception here though…Railroad companies lease their engines and railcars, they do not buy them. Lease companies buy the railcars and then lease them to the Railroad companies. But this long-term lease could be considered debt and so it has a long-term debt commitment).