Question

Assume you have just been hired as a business manager of Pizza Palace, a regional pizza restaurant chain. The company’s EBIT was $50million last year and is not expected to grow. The firm is currently financed with all equity,and it has 10million shares outstanding.When you took your corporate finance course,your instructor stated that most firms ’owners would be financially better off if the firms used some debt. When you suggested this to your new boss, he encouraged you to pursue the idea. As a first step, assume that you obtained from the firm’s investment banker the following estimated costs of debt for the firm at different capital structures: PERCENT FINANCED WITH DEBT, Wd rd 0% - 20 8.0% 30 8.5 40 10.0 50 12.0 If the company were to recapitalize, then debt would be issued and the funds received would be used to repurchase stock. PizzaPalace is in the 40% state-plus-federal corprate tax bracket, its beta is 1.0, the risk free rate is 6%, and the market risk premium is 6%. .Using the free cash flow valuation model, show the only avenues by which capital structure can affect value.

Answer 1

Calculation in tabular form has been presented below, after the text part. Please read the sequence of calculation below, along with the table subsequently to understand the problem conceptually and mathematically. The conclusions have been presented after the table.

1. As we introduce leverage in the capital structure, proportion of debt (w_d) represented by column no. 1 in the table below increases from 0% to 50%. Corresponding to each level of leverage, pre tax cost of debt (r_d) is given in column no. 2. These two columns are the same columns that are given in the question.
2. In column no. 3, we have worked out proportion of equity in capital structure = w_e = 1 - w_d
3. We have then calculated the Debt to Equity ratio, D / E in column no. 4. The D / E ratio will be same as the ratio of proportion of debt & equity in the capital structure. Hence, D / E = w_d / w_e
4. Tax rate, T = 40% is constant across all situations as shown in column no. 5. When the firm is unlevered, the Beta of equity is unlevered beta, B_u. Currently when the firm is fully equity financed, the beta is B_u = 1. As leverage in the firm increases, the beta of the equity also increases and now the beta is levered beta, B_l = B_u x (1 + D / E x (1 - T)). Column no. 6 has been populated using this formula.
5. Column no. 7 shows cost of equity, r_e = r_f + B_l x r_p where r_f = risk free rate = 6% and r_p = market risk premium = 6%. WACC has been calculated in column no. 8 using the standard formula, WACC = w_d x rd x (1 - T) + w_e x r_e.
6. We have a fully unlevered firm to begin with. It has an EBIT of $ 50 mn. EBIT is an unlevered cash flow. So, even if introduce leverage in the capital structure, the firm's EBIT will remain the same. That's why you will see column no. 9 representing EBIT at fixed level of $ 50 mn. Free cash flow to the firm, FCFF = EBIT x (1 - T). There is no growth in subsequent years. Hence FCFF remains constant in column no. 10.
7. Value of the firm using discounted free cash flow method = FCFF / WACC has been calculated at different levels of WACC in column no.11.

Please see the table below:

1	2	3	4	5	6	7	8	9	10	11
wd	rd	we	D / E	Tax Rate	Bl	re	WACC	EBIT ($ mn)	FCFF ($ mn)	Valuation ($ mn)
		1-wd	wd / we	T	Bu x (1 + D / E x (1-T))	rf + Bl x rp	wd x rd x (1 - T) + we x re		EBIT x (1 - T)	FCFF / WACC
0.0%	0.0%	100.0%	0.0%	40%	1.0000	12.00%	12.00%	50	30	250.00
20.0%	8.0%	80.0%	25.0%	40%	1.1500	12.90%	11.28%	50	30	265.96
30.0%	8.5%	70.0%	42.9%	40%	1.2571	13.54%	11.01%	50	30	272.48
40.0%	10.0%	60.0%	66.7%	40%	1.4000	14.40%	11.04%	50	30	271.74
50.0%	12.0%	50.0%	100.0%	40%	1.6000	15.60%	11.40%	50	30	263.16

Conclusions:

1. WACC decreases with leverage, reaches a minimum value when proportion of debt, w_d = 30%. Then WACC starts increasing. Thus this is the point of optimal leverage or optimal capital structure.
2. Valuation the firm is inversely proportional to WACC. Hence, valuation of the firm increases, reaches a peak corresponding to minimum WACC which in turn corresponds to proportion of debt, w_d = 30%. The value of the firm then starts declining.
3. Thus capital structure do impact the firm valuation. In fact leverage helps create additional value for the firm.
4. Leverage beyond the optimal capital structure, increases the cost of capital of the firm and hence leads to decline in the value of the firm.