1. Out of the perfect capital market: Role of taxes
Capital structure II
Out of the perfect capital market:
Role of taxes

2. Back to the assumptions of MM
Taxes are ignored
Bankruptcy was cheap, quick and painless.
There are costs associated with financial distress.
Ignoring potential interest conflicts between firm’s security holders. (transaction cost due to agency problem)
=> Introducing taxes

3. The pie again All-Equity firm Levered firm Debt Taxes Taxes Equity
The sum of the debt plus the equity of the levered firm is greater than the equity of the unlevered firm
With tax, what is the optimal capital structure of firms?

4. Capital structure and corporate taxes
EBIT
EBIT -B× RB
B× RB
(EBIT - B× RB)
× (1-TC )
(EBIT - B× RB) ×TC
Operating cf: ebit
We depart from MM since future cash-flows available for investors depend on the amount of taxes, i.e. on the amount of leverage.

5. MM Proposition I (With Taxes)
The present value of this stream of cash flows is VL
The cash flow to all stakeholders is made up of cash flow to stockholders plus cash flow to bondholders.
The present value of the first term is VU
The present value of RBBTC is PV(interest tax shield)
=> VL =VU + PV (Interest tax shield)

6. Present value of the tax shield
Advantage to debt
Interest = B× RB
Per period tax shield from debt:
TC × B× RB
Ex: Suppose DFB plans to pay $100 million in interest each year for the next 10 years, and then to repay the principal of $2 billion in year 10. These payments are risk free, and DFB’s marginal tax rate will remain 35% throughout this period. If the risk-free interest rate is 5%, by how much does the interest tax shield increase the value of DFB?
- The interest payment is exempt from the tax. The amount of exemption is just tc X rb X D.
Tax shield can be valuable asset.
At what discount rate should the tax shield perpetuity be discounted?
Since the it is generated by the interest payment, a common assumption is that the risk of the tax shields is the same as that of the interest payments generating them.

7. Present value of the tax shield
Solution:
In this case, the interest tax shield is 35% * $100 million = $35 million each year for the next 10 years. Therefore, we can value it as a 10-year annuity. Because the tax savings are known and not risky, we can discount them at the 5% risk-free rate:
The final repayment of principal in year 10 is not deductible, so it does not contribute to the tax shield.
- The interest payment is exempt from the tax. The amount of exemption is just tc X rb X D.
Tax shield can be valuable asset.
At what discount rate should the tax shield perpetuity be discounted?
Since the it is generated by the interest payment, a common assumption is that the risk of the tax shields is the same as that of the interest payments generating them.

8. Interest tax shield with permanent debt
Per period tax shield from debt:
TC × B× RB
Assume that the debt payment is fixed and permanent. => the tax shield cash flow is perpetual.
Assume that the cash flow from tax shield has the same risk as the interest on debt:
The PV of tax shield: (TC × B× RB)/RB = TC × B
It is independent of the interest rate.
- The interest payment is exempt from the tax. The amount of exemption is just tc X rb X D.
Tax shield can be valuable asset.
At what discount rate should the tax shield perpetuity be discounted?
Since the it is generated by the interest payment, a common assumption is that the risk of the tax shields is the same as that of the interest payments generating them.

9. Value of the unlevered firm
VU = (EBIT×(1-TC ))/R0
VU = PV of an unlevered firm
EBIT×(1-TC ))= Firm cash flow after corporate taxes
TC = corporate tax rate
R0 = The cost of capital for an all-equity firm
= Required return on assets
= Discount rate for aftertax cash flow

10. Value of the levered firm
MM Proposition I (with Corporate Taxes)
Firm value increases with leverage
VL = (EBIT×(1-TC ))/R0 + (TC RB B )/ RB
= VU + TC B VL VU
Debt (B)

11. Example. Larger pie with leverage
Firm U Firm L(borrow $1,000 at 8%)
EBIT $1,000 $1,000
Interest
EBT
Taxes at 35%
Net income $ $598
Total cash flow = =678
to both B &S
Interest tax shield $ $28
Interest tax shield = total cf of levered- CF of unlevered = interest X tax rate.

12. Example (cont.): Value of firms
Assume that both firm U and L are in the same industry.
Firm U has a cost of equity capital of 20%.
What will be the value of both firms?

13. Value of firms VU = Net Income / R0 =EBIT (1-tC)/ R0 VL = VU+ tC B
= 650/ 0.2
= 3250
VL = VU+ tC B
= *1,000
= 3600

14. Value of firms Market value balance sheet Market value balance sheet
Unlevered firm
Levered firm
VU =EBIT (1-tC)/ R
= 650/ 0.2
= 3250
Market value balance sheet
Assets | Equity 3250 |
Total | B+S 3250
VL = VU+ tC B
= *1,000
= 3600
Market value balance sheet
Assets | Equity 2600
PV of tax shield | Debt
350 | 1000
Total | B+S 3600
The value of the levered equity is reduced but all tax shield goes to shareholders
The value of equity= Physical assets – debt+ tax shield

15. Expected Return under taxes
MM Proposition II (with Corporate Taxes)
Some of the increase in equity risk and return is offset by the interest tax shield
RS = R0 + (B/S)×(1-TC)×(R0 - RB)
RB is the interest rate (cost of debt)
RS is the return on equity (cost of equity)
R0 is the return on unlevered equity (cost of capital)
B is the value of debt
S is the value of levered equity

16. MM Proposition II (With Taxes)
Start with M&M Proposition I with taxes:
Since
The cash flows from each side of the balance sheet must equal:
Divide both sides by S
Which quickly reduces to

17. The Effect of Financial Leverage
Cost of capital: R (%)
No tax
With tax
RWACC without tax R0
Beta: BetaAsset= B/V X beta debt X (1-Tc) + S/V X beta equity. RB
Debt-to-equity ratio (B/S)

18. Impact of personal taxes
Investors pay taxes too. Equity income is taxed at both the corporate and the personal levels.
The value of a firm= value of cash flows investors receive after all taxes have been paid.
When deciding the optimal capital structure of a firm, one should take into account the after tax cash-flows accruing to investors.
If personal tax rates differ according to the type of claim held, the optimal capital structure may change.

19. After tax cash-flows to investors
TB, Tax rate on interest income
TS: Tax rate on equity income
Suppose now that creditors have a personal tax rate TB, and that equity holders have a personal tax rate TS.

20. Personal & Corp taxes Operating Income ($1.00)
Or paid out as equity income
Paid out as interest
Corporate Tax
None Tc
Income after Corp Taxes 1
1 – Tc
Personal Taxes . TB
TS (1 -Tc)
Income after All Taxes
1 – TB
1-TC - TS (1- TC)
=(1- TC) (1-TS )
To bondholders To stockholders

21. Relative tax advantage of debt
Prefers debt to equity if
1- TB > (1-TC)(1-TS)
The relative tax advantage= (1- TB )/ (1-TC)(1-TS)
If debt and equity income were at the same rate (TB = TS): Relative advtg= 1/(1-TC ) >1
Tax advtg depends only on TC
What capital structure should the firm choose?
Eg: In the US: The top tax bracket TC = TB=35%. TS=15%.
What will be the optimal capital structure in the presence of dividend and interest taxes?
The firm should choose the capital structure that gets the most cash into the hands of its investors.
If 1- TB > (1-TC)(1-TS), then the firm should choose to use fully debt instead of equity.
If TB = TS , 1/(1-TC ) >1 then should use debt. Intuitively, the net income given to stockholders is taxed twice. Note that the case without personal tax is a special case of TB = TS =0. Hence it turns out that we should always use debt.
Some remark of the tax rate: Normally, the effective tax rate on the net income is lower. i.e. TS<15%.
This is because the capital gain is taxed only on the gain from sales. If the firm repurchase stock instead of paying dividends, the income of stockholders will not be taxed.
In china, the corporate tax rate is in general 33% (top tax bracket), individual will be taxed both for its interest income or for the capital payment. The tax rate is about 20%. However, the interest payment from the bond issued by the state is for free.

22. Implications to the capital structure
The tax-based explanation for firms’ capital structure choice implies the following.
When tax rates are « extremely » favorable to equity holders, we should observe more equity financing (e.g. venture capital)
Otherwise firms should use more debt when their pretax cash-flows are high: leverage should increase with EBIT.

23. Low leverage puzzle

24. Why are companies not all debt?
Back to the assumptions of MM
Taxes are ignored
Bankruptcy was cheap, quick and painless.
Ignoring potential interest between firm’s security holders. (transaction cost due to agency problem)
=> Introducing bankruptcy cost

25. Homework
In book of Ross, Westerfield and Jaffe, “Corporate Finance”, 9th edition.
Chapter 16—Questions and problems: 6, 9, 20, 25, 26.
Chapter 16—Minicase: Stephenson Real Estate Recapitalization.
To be submitted no later than 11:30 Thursday 13 October.
No electronic version is accepted.