## Summary

The chapter covered the following major points:

• In the imperfect real world, the U.S. tax code favors debt over equity. Managers should take this corporate income tax advantage into account.

• The calculation of the income tax advantage can be done either through the flow-to-equity method (a full pro forma employing a financing scenario that subtracts the interest and thereafter the tax burden), or through a tax-adjusted WACC method, or through the APV method.

• Both the WACC and the APV method begin with cash flows as if fully equity-financed and thus fully taxed, which is why they need to put back the tax advantage derived from the presence of debt.

- WACC does so by lowering the cost of debt capital:

APV does so by adding back the tax benefit:

interest payment

For the discount rate E (r) applicable to the right term (the expected tax shelter), the following guidelines may help: If the firm's debt ratio will decline over time, use the debt's cost of capital. If it will remain constant, use the firm's overall cost of capital. If it will increase, use the equity's cost of capital.

These methods usually arrive at very similar but not exactly identical valuations. We are rarely sure about the appropriate discount rate that should be applied to the future tax benefits in the APV formula; and the WACC formula cannot really deal with changing costs of capital or debt ratios over time. However, the errors that an incorrect discount rate on the tax shield would cause are usually dwarved by other simplifications and uncertainty in expected cash flows and discount rates.

The one error you should never commit is to use the wrong expected cash flows. That is, never add an APV tax-subsidy or lower the WACC cost of capital when the cash flows are not "as if fully equity financed."

The following heuristic is often convenient: A constant extra dollar of debt forever increases the value of the firm by the firm's marginal income tax rate. A $100 eternal debt increase will create $30 in value for a firm in the 30% marginal income tax bracket.

In the imperfect real world, financing and investment decisions can no longer be separated: projects that add more debt capacity may add value through the financing channel.

### 12 Key Terms

APV; Adjusted Present Value; Debt Capacity; Flow-to-equity; Hamada Equation; L.B.O.; Leasing; Leveraged Buyout; NOL; Net Operating Losses; WACC; Weighted Average Cost Of Capital.

### End of Chapter Problems

Q 18.14 Assume a 20% corporate income tax. Does a project that returns 16% pre-corporate income tax have a negative NPV if it cost $100 today and if the appropriate after-tax cost of capital is 11%.

Q 18.15 A $1 million construction project is expected to return $1.5 million in two years. Your firm is in a 40% combined federal and state marginal income tax bracket. Your annual income is $200,000 per year. If you finance the project with an $1,300,000 mortgage at an interest rate of 8%, how much will Uncle Sam receive? If you finance the project with cash, how much will Uncle Sam receive? If other equivalent firms are offering investors expected rates of return of 10%, what is the PV of the tax savings from financing the project with a mortgage?

Q 18.16 A firm would have to invest $1 million to earn a net return of $500 million next year. The firm estimates its debt cost of capital to be E(rDr) = 5% + 10% ■ wDx- (This may be the case for different reasons covered in the next chapter.) The firm is in the 25% marginal tax bracket.

(a) If the firm is fully equity financed, what is its value?

(b) Using APV, if the firm is financed with equal amounts of debt and equity today, what is its value?

(c) Using WACC, if the firm is financed with equal amounts of debt and equity today, what is its value?

(d) Does this firm have an optimal capital structure? If so, what is its APV and WACC.

Q 18.17 Construct a pro forma for the following firm: A 4-year project costs $150 (year 1), and produces $70 in year 1, $60 in year 2, $50 in year 3, and $40 in year 4. Depreciation, both real and financial, is 4 years. Projects of this riskiness (and with this term structure of project payoffs) have a 15% cost of capital. The marginal corporate income tax rate is 33%.

(a) Assume that the firm is 100% equity financed. Construct the pro forma, and compute expected project cash flows.

(b) Compute the Project IRR.

(c) Compute the project NPV.

For the remaining questions, assume that the firm instead has a capital structure financing $100 in debt raised in year 1 at a 10% (expected) interest rate. Interest is paid out in each year. Principal and interest are paid out in the final year. Money in excess of interest payments is paid out as dividends.

(e) Construct the pro forma now. What is the IRR of this project?

(f) From the pro forma, what is the NPV of the debt-financed project?

(g) Compute the NPV via the APV method.

(h) Via the APV method, how much would firm value be if the firm would have taken on not $50 but $40 in debt (assuming the same interest rate of 10%)?

(i) How much money must the equity provide in year 1? What is the debt ratio of the firm? Does it stay constant over time? Is this a good candidate firm for the WACC method?

Q 18.18 Compute the 2005 tax shield for PepsiCo, using information from Yahoo!Finance.

Q 18.19 Estimate how PepsiCo's value would have changed in 2003 if it had announced that it planned to take on an additional $10 billion in debt in order to repurchase equity?

Q 18.20 Estimate how PepsiCo's value would have changed in 2003 if it had announced that it planned to increase its debt-asset target by an additional 5% and that it would use the generated funds to repurchase equity?

Q 18.21 A firm has a current debt:equity ratio of 2:3. It is worth $10 billion, of which $4 billion is debt. The firms' overall cost of capital is 12%, and its debt currently pays an (expected) interest rate of 5%. The firm estimates that its debt rating would deteriorate if it were to refinance to a 1:1 debt-equity ratio through a debt-for-equity exchange, so it would have to pay an expected interest rate of 5.5%. The firm is solidly in a 35% corporate income tax bracket. The firm reported net income of $500 million. On a corporate income tax basis only, ignoring all other capital-structure related effects, what would you estimate the value consequences for this firm to be? When would equity holders reap this benefit? What would be the stock price's announcement price reaction?

Solve Now: 13 Solutions

1. This is the example in the text: PV = -$100 + ($117.13 - $17.13 ■ 30%)/(1 + 12%) < 0.

2. $500 if designated an interest payment. $750 if designated a dividend distribution, because only $500 is left after corporate income taxes have been paid.

3. With an internal rate of return of 20%, Uncle Sam would see $90,000 if you pay cash. If you finance with 80% debt, you will have $40,000 in interest to deduct from $200,000 in return, and thus pay taxes only on $160,000. This lowers your tax bill to $72,000. (Side Advice: If you borrow $800,000, you may have to invest your $800,000 elsewhere. If you do not choose tax-exempts, Uncle Sam may receive more taxes therefrom.)

4. The net subsidy is $90,000 - $72, 000 = $18, 000 next year. At an appropriate cost of capital of 8%, this is an PV of $16, 667.

5. The WACC valuation is PVo

$256

APV0

$57.45 of debt and $172.35 in equity value today. Its APV is T ■ E (fDT) ■ DT

$229.80

6. The APV valuation is

APVq

$230.90

Therefore, the $100 debt is 43.3% of the firm's value today, and $256

$230.90

7. WACC for ratio, APV for dollar amounts. Look at the previous two questions. You cannot figure out the APV in the first question before you determine the WACC, and the opposite in the second question.

8. • The firm's overall cost of capital today is 6% ■ 1/3 + 12% ■ 2/3 = 10%. (Because 4% + 3%-2 = 10%, the beta is 2.) • The easy way is to recognize that the firm is sheltering $500 ■ 6% = $30 through interest payments. If it refinanced with $1,000, it couldnow shelter $1, 000 ■ 8% = $80. Uncle Sam would get to see an additional $50 less in income, which means that the firm would pay $50-20% = $10 less in income tax nextyear. • Nowyou need to determine the appropriate discount rate for $10 in tax savings. For convenience, use the debt cost of capital: 8%. This means that our recapitalization increases firm value by $10/1.08 » $9.26. (If you prefer to use the overall firm cost of capital, you would obtain $9.09.) • The question intentionally gave additional irrelevant information.

9. Because you know that the cost of capital if all financed by debt has to be the cost of capital for the firm, you know that the firm's overall cost of capital is E(fDT) = 15% + 100% ■ 5% = 20%. Now, this project will offer $200 pretax profit in year 1. Discounted back at the firm's cost of capital, the NPV without taxes is -$300 + $500/(1 + 20%) = $116.67. But, if equity financed, the IRS will declare taxes due on $200 of profit, or $80. Therefore, the NPV with taxes and all equity financed is -$300 + $420/(1 + 20%) = $50.

Now, right after the investment, the firm has a value of $420/1.2 = $350. With debt of $50 ($100), the firm carries a debt load of around 15% (30%). The cost of debt capital formula given in the question suggests that E(rbT) = 15% + 15% ■ 5% = 15.75% (16.5%). (Note: the question is a bit ambiguous in that it does not tell you what to use as firm value. The 15% and 30% debt ratios are reasonable values, though.)

Interest payments on $50 ($100) at a cost of capital of 15.75% (16.5%) are $7.88 ($16.50) nextyear. Facing a tax rate of about 40%, Uncle Sam would thereby subsidize the project to the tune of 40% ■ $7.88 = $3.15 ($6.60), which in today's value would be worth around $3.15/(1 + 20%) » $2.63 ($6.6/1.2 » $5.50). Therefore, under APV, if financed with $50 in debt ($100 in debt), the project is worth $50 + $2.63 = $52.63 ($50 + $5.50).

The cost of capital, if 15% of the firm is financed by debt at an interest rate of 15.75% is the solution to 15% ■ 15.75 + 85% ■ E(fEQ) = 20% - E(fEQ) = 20.75%. Therefore, the WACC is given by the formula, wEQ ■ E(fEQ) + wDT ■ E(fDT) ■ (1 - t) = 85% ■ 20.75% + 15% ■ 15.75% ■ (1 - 40%) ^ 19.06%. Similarly, if $100

is borrowed, E(tQ = 21.5%, and WACC = wEQ ■ E(rEQ) + wDT ■ E(■fDT) ■ (1 - t) = 70% ■ 21.5% + 30% ■ 16.5% ■ (1 - 40%) - 18.02%. The WACC based value is thus -$300 + $420/(1 + 19.06%) - $52.76. Note that you have made enough little assumptions and approximations that it would make little sense to now worry about being off by a little in the APV and WACC computations ($52.76 and $52.63).

(a) The pro forma for a 100% equity financed firm is

Year 1 |
Year 2 |
Year 3 | |

EBITDA (=Net Sales) |
$70 |
$60 |
$55 |

- Depreciation |
$50 |
$50 |
$50 |

= EBIT (=Operating Income) |
$20 |
$10 |
$5 |

- Interest Expense |
$0 |
$0 |
$0 |

- Corporate Income Tax |
$8 |
$4 |
$2 |

= Net income |
$12 |
$6 |
$3 |

Cash Flow Statement | |||

Net income |
$12 |
$6 |
$3 |

+ Depreciation |
$50 |
$50 |
$50 |

= Operating Cash Flow |
$62 |
$56 |
$53 |

capital expenditures |
-$150 |
$0 |
$0 |

= Investing Cash Flow |
-$150 |
0 |
0 |

Economic Project Cash Flows (Operating CF+ Investing CF+ Interest)

Economic Project Cash Flows (Operating CF+ Investing CF+ Interest)

Project Cash Flows

Thus, the IRR of a purely equity financed project is 15.7%. (c) The NPV of the purely equity financed project is

This is in line with the fact that the project IRR of 15.7% is less than the 18% cost of capital.

(d) The cash flows would increase to -$88, +$58, and +$55. The IRR would increase to 18.6%.

(e) The debt-financed pro forma would now be

Year 1 |
Year 2 |
Year 3 | |

EBITDA (=Net Sales) |
$70 |
$60 |
$55 |

- Depreciation |
$50 |
$50 |
$50 |

= EBIT(=operating income) |
$20 |
$10 |
$5 |

- Interest Expense |
$0 |
$5 |
$5 |

- Corporate Income Tax |
$8 |
$2 |
$0 |

= Net income |
$12 |
$3 |
$0 |

Cash Flow Statement | |||

Net income |
$12 |
$3 |
$0 |

+ Depreciation |
$50 |
$50 |
$50 |

= Operating Cash Flow |
$62 |
$53 |
$50 |

Capital Expenditures |
-$150 |
$0 |
$0 |

= Investing Cash Flow |
-$150 |
0 |
0 |

Economic Project Cash Flows | |||

(Operating CF + Investing CF + Interest) | |||

Project Cash Flows |
-$150+$62 +$53+$5 |
+$50+$5 | |

= |
-$88 |
+$58 |
+$55 |

The Economics of Financing | |||

Debt |
+$50 |
+$5 |
+$55 |

Equity |
+$38 |
+$53 |
+$0 |

Not surprisingly, these are the same as the aforementioned cash flows, with a $2 income-tax subsidy in years 2 and 3. The IRR is again 18.6%. (f) The NPV of the debt-financed firm is

With the tax subsidy, this project becomes worthwhile. (g) The APV of this project would be the value as-if-100%-equity-financed, which is -$2.10 (computed above

"" $88 ' +$56 . +$53 ), plus the discounted tax subsidies in years 2 and 3. These

Therefore, the APV would be -$2.10 + $2.66 = $0.56. (h) By APV, the expected tax subsidy would shrink from t ■E(IP) = 40%-$5 = $2 per year to t ■E(IP) = 40% ■ $4 = $1.60 per year. The expected value of the tax subsidy would therefore be

Tax Subsidy

The net project value would be about $0.02. (i) In year 0, the weight of the debt is wdt,0 = $50/$88 » 57%. But after year 2 and before year 3, the debt is expected to be 100% of the capital structure, so its weight in the capital structure is drastically changing each year. This firm is not at all a good candidate for using WACC.

Do not try to compute a weighted average cost of capital from the debt and equity internal rates of return (10% and 40%, respectively). If the debt would remain at 57% of the firm's capital structure, then the appropriate rate of return of equity would have to be around 30% so that the weighted cost of capital would come out to E(tfm) = wdt-E(tot) + weq-E(-teq) = 18.6%. This is much lower than the equity IRR of 40% (which is the same as its expected rate of return from year 1 to year 2), because from year 2 to 3, the equity becomes a much smaller part of the firm. What bites you in this case is the fact that you have a strong term structure of investment weights.

### DIG DEEPER

11. With $1,691 in taxes on $5,670 on income before tax, Coca Cola was in a 30% income tax bracket. The $289 in interest payments therefore cost Uncle Sam about $86.7 million.

12. The weighted average cost of capital (WACC) is

The numerator has to be post corporate income tax; therefore, it is (1 - t) ■CF = $15. This is an annuity, therefore the NPV is PV = $15/6.875% = $218.18.

13. The cost of capital for a fully equity financed firm without a tax subsidy would be 7.5%, because it had 50% debt at 5% and 50% debt at 10%. Therefore, the "as if fully equity financed" value is PV = $15/7.5% = $200.00. Now, you need to add back the tax subsidy. With $50 in debt, risk-free and therefore with an interest rate of 5%, the interest payments would be E(rDT) ■ DT = $2.50 per year. The taxes saved would be t ■ $2.50 = $0.625, which is an eternal cash flow. At the interest rate of 5%, the value of the tax subsidy today is $12.50. Therefore, the value of this firm is $200+$12.50= $212.50.

All answers should be treated as suspect. They have only been sketched and have not been checked.

Nerd Appendix

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