1. M&M Proposition I with Taxes No Bankruptcy Costs
Lecture 18
M&M Proposition I with Taxes
No Bankruptcy Costs

2. Topics covered Assumptions Valuation formulae Graphical interpretation
Implications
Numerical example
Practice problem

3. M&M I with taxes: Assumptions
Relaxed assumption: Corporate taxation
Remaining assumptions:
Perfect market
No bankruptcy costs
Perpetual going concern

4. M&M I with taxes: Valuation Formulae
Unlevered (0 Debt) firm
VU = EBIT (1 – TC) / RU
Levered (In Debt) firm
VL = VU + TCD
EL = VL - D
Variables:
VU = value of unlevered (0 Debt) firm
EBIT = Earnings before interest and taxes
TC = corporate tax rate
RU = cost of capital for unlevered firm
VL = value of levered (In Debt) firm
D = dollar amount of debt in the levered firm
EL = dollar amount of equity in the levered firm

5. M&M I with taxes: Graph
Firm Value (V) VL = VU + TC D TC x D VU VU VU Debt (D)

6. M&M Proposition I with taxes: Implications
Debt financing is good
Debt   WACC 

7. Numerical example
ABC Inc. and XYZ Co. are identical except for their financing policy. ABC is financed with all equity, whereas XYZ has $1,000,000 in debt financing. Both firms have earnings before interest and taxes of $500,000, and both are subject to 35% corporate tax rate. ABC’s cost of capital is estimated to be 18%. a. What is XYZ’s firm value and equity value? b. What happens to the firm value and equity value if XYZ increases its debt financing to $2,000,000?

8. Numerical example (cont.)

9. Numerical example (cont.)

10. Practice problem
We have two firms, Firm U and Firm L, that are identical in every respect except for their financing policy. Firm U has zero debt, and its assets have an estimated value of $10 million. Firm L is partly financed with debt, and its assets have an estimated value of $12.5 million. Given that both firms are subject to a corporate tax rate of 40%, and both have an EBIT of $2 million, calculate the cost of capital for Firm U and the debt-equity ratio for Firm L.

11. Check Answer: Cost of equity of Firm U
Information given: VU = $10,000,000 VL = $12,500,000 TC = 0.4 EBIT = $2,000,000 To find RU: VU = EBIT(1 – TC) / RU Multiplying both sides by RU, we get RU x VU = EBIT(1 – TC) Dividing both sides by VU, we get RU = EBIT(1 – TC) / VU Plugging in EBIT = $2 million, TC = 0.4, and VU = $12.5 million, we get RU = $2,000,000 (1 – 0.4) / $12,500,000 = 0.12 = 12%

12. Check Answer: D/E ratio of Firm L
Information given: VU = $10,000,000 VL = $12,500,000 TC = 0.4 EBIT = $2,000,000 First, we calculate the debt-level in Firm L by using the levered firm valuation formula: VL = VU + TC D Subtracting VU from both sides, we get VL – VU = TC D Dividing both sides by TC, we get (VL – VU) / TC = D Plugging in VL = $12.5 million, VU = $10 million, and TC = 0.4, we get D = ($12,500,000 - $10,000,000) / 0.4= $2,500,000 / 0.4 = $6,250,000 We can now calculate the equity of the levered firm: EL = VL – D = $12,500,000 - $6,250,000 = $6,250,000 The debt-equity ratio of Firm L is therefore: D/EL = $6,250,000 / $6,250,000 = 1