Question

Assume you have just been hired as a business manager of PizzaPalace, a regional pizza restaurant chain. The company’s EBIT was $50 million last year and is not expected to grow. The firm is currently financed with all equity, and it has 10 million 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, 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 corporate tax bracket, its beta is 1.0, the risk-free rate is 6%, and the market risk premium is 6%.

a. Using the free cash flow valuation model, show the only avenues by which capital structure can affect value.

b. What is business risk? What factors influence a firm’s business risk? What is operating leverage, and how does it affect a firm’s business risk? Show the operating break-even point if a company has fixed costs of $200, a sales price of $15, and variable costs of $10.

Please provide a minimum 250 word explanation.

Answer 1

Part (a)

In this part we have to examine the impact of leverage on firm valuation and ultimately show if leverage increases the value of the firm.

Please see the solution in the table below. In order to create the table, we will follow the following steps:

• Column 1 is the proportion of debt, p_d in the capital structure. In column 2, I have mapped the pre tax cost of debt K_d as given in the question.
• Column 3 has proportion of equity in the capital structure, p_e = 1 - p_d. In the fourth column we have calculated the capital structure given by D / E = p_d / p_e.
• Then we have levered the beta using the standard formula of B_L = B_U x [1 + (1 - T) x D / E] where T = tax rate = 40% constant across across the scenarios. The beta corresponding to p_d = 0% is the unlevered beta. Hence, B_U = current beta = 1.00. This working has been done in column 5.
• In column 6, we have calculated the cost of equity, K_e using the CAPM equation: K_e = Risk free rate + B_L x Market risk premium = 6% + B_L x 6%.
• In the next column, we have calculated the WACC by the formula = p_d x K_d x (1 - T) + p_e x K_e
• In column 8, we have calculated the firm's valuation = FCFF / WACC where FCFF = free cash flow to the firm = EBIT x (1 - T) = 50 x (1 - 40%) = $ 30 mn, constant across all the scenarios.

Please see the table below now:

Please see the table below:

1	2	3	4	5	6	7	81
pd	Kd	pe	D / E	BL	Ke	WACC	Valuation ($ mn)
		1 - pd	pd / pe	BU x (1 + D / E x (1-T))	6% + BLx 6%	pd x Kd x (1 - T) + pe x Ke	FCFF / WACC
0.0%	0.0%	100.0%	0.0%	1.0000	12.00%	12.00%	250.00
20.0%	8.0%	80.0%	25.0%	1.1500	12.90%	11.28%	265.96
30.0%	8.5%	70.0%	42.9%	1.2571	13.54%	11.01%	272.48
40.0%	10.0%	60.0%	66.7%	1.4000	14.40%	11.04%	271.74
50.0%	12.0%	50.0%	100.0%	1.6000	15.60%	11.40%	263.16

We can now make the following inferences from the table:

• Refer column 7, WACC decreases with leverage first and then starts increasing. WACC is minimum at p_d = 30% and hence the leverage in optimal capital structure = 30%.
• Since FCFF remains constant but WACC changes due to leverage, the valuation behaves inversely with WACC. Firm's value increases as leverage increases and then after the optimal capital structure of 30% debt, the valuation starts decreasing with leverage.
• This clearly shows that capital structure does impact the firm's valuation. In fact leverage within controllable level helps create additional value for the firm.
• Leverage beyond optimal capital structure puts pressure on the firm's cost of debt as well as equity and hence on WACC as well. This in turn leads to decline in value of the firm.

Part (b)

Business risk is the risk associated with the firm to do the business, earn revenue and then translate the same into operating income, EBIT. Thus business risk is all the risk factors that impact operating income (EBIT) of the firm. Some common business risk factors are:

• Slowdown in sales volume
• Not able to increase the sale price
• Not able to pass on the cost to customers
• Higher proportion of fixed operating costs in total operating costs
• Lack of control on input prices or raw material prices
• Competition

Operating leverage

Operating leverage measures the sensitivity of operating income with respect to revenues. It measures the %change in EBIT corresponding to 1% change in revenues. Proportion of fixed costs in total operating costs of the firm has a bearing on the operating leverage. Higher the proportion of fixed costs, higher is the operating leverage and hence higher is the business risk. In case operating leverage is high, a small decline in revenues can put a heavy pressure on operating income.

At break even:

Revenue, R = Total operating costs = Fixed Costs, FC + Variable costs

Sale Price per unit, S x Break even Quantity, Q = FC + Variable cost per unit, VC x Q

Hence, S x Q = FC + VC x Q

Hence, break even quantity, Q = FC / (S - VC) = $ 200 / ($ 15 - $ 10) = 40