Question

Two ambitious business graduates, Boris and Isabelle, are considering purchasing Premier Pizza, a frozen pizza manufacturer. Forecasted annual sales for the coming year are $9 million, with operating costs equal to 73% of sales, depreciation is 5% of sales and required annual investment in equipment is 5% of sales. Sales, costs, and investments are expected to grow 4% in perpetuity. On the basis of their analysis of the industry, Boris and Isabelle anticipate financing their company with 29% debt. The required rate of return on the debt will be 6% and the required rate of return on the equity will be 18%. Premier Pizza’s corporate tax rate is 35%. The risk-free interest rate is 3% and the market risk premium is 6%.

a.	What is the maximum price Boris and Isabelle should be willing to pay for Premier Pizza? (Round your answer to 2 decimal places.)
	Maximum price   $ _____million

b.	A national grocery chain, Fresh Foods, is also considering making an offer for Premier Pizza. The levered equity beta of the grocery chain is 0.7, its cost of debt is 5%, it is 44% debt-financed, and it has a 35% tax rate. What is the maximum price that Fresh Foods should be willing to pay for Premier Pizza? Assume that Fresh Foods’s forecast for Premier’s cash flows is the same as Boris and Isabelle’s. (Round your answer to 2 decimal places.)
	Maximum price    $ _____million

Answer 1

Given in the Question

Sales = 9 Million

Operating Costs = 73% of Sales

Depreciation = 5% of Sales

Capital Expenditure (Investment in Equipment) = 5% of sales

Expected future growth rate of Sales, Costs & Investment = 4% perpetually

Debt Capital (D) = 29%

Equity Capital (E) = 71%

Cost of Debt (Rd) = 6%

Cost of Equity Capital (Re) = 18%

Risk Free Rate (Rf) = 3%

Market Risk Premium (Rm) = 6%

Part (a)

We are being asked the Price which should be paid for purchasing the firm Premier Pizza. In other words, we are being asked to value the firm Premier Pizza.

We will apply the Discounted Cash Flow (DCF) method of valuation to find the above.

For this we will have to project the future cash flows of the firm and then find the Present Value of the stream of the future cash flows.

To find the Present Value, we will need to discount the future cash flows, for which we need an appropriate Discounting Factor, which will be the Weighted Average Cost of Capital (WACC) of this firm

Formula for WACC is given as:

WACC = [Proportion of Debt Capital * Cost of Debt * (1 - Tax Rate)] + [Proportion of Equity Capital * Cost of Equity Capital]

These values are given in the question, so we will plug the values from the question into the above formula

WACC = [29% * 6% * (1 - 35%)] + [71% * 18%]

= [0.29 * 0.06 * 0.65] + [0.71 * 0.18]

= 13.91%

Now we will project the future cash flows (Free Cash Flow to the Firm) of the firm as per the conditions given in the question

1 2 Sales 10.12 9.00 9.36 9.73 10.53 4% 4% 4% 4% Operating Costs 73% 7,39 6.57 6.83 7.11 7.69 4% 4% 4% 4% Depreciation 5% 0.45 0.47 0.49 0.51 0.53 4% 4% 4% 4% EBIT (Earnings Before Interest & Tax) 2.06 2.14 2.23 1.98 2.32

NOTE:

(a) Sales, Operating Costs & Depreciation have all increased by 4% per year as mentioned in the question

(b) Operating Cost is 73% of Sales, Depreciation is 5% of sales, & Corporate Tax Rate = 35%

Now we will have to calculate Capital Expenditure for each year

It is given that Capital Expenditure is 5% of sales and will increase at a rate of 4% annually in future

2 5 Sales 9.00 9.36 9.73 10.12 10.53 4% 4% 4% 4% Operating Costs 73% 6.57 6.83 7.11 7.39 7.69 4% 4% 4% 4% Depreciation 5% 0.45 0.47 0.49 0.51 0.53 4% 4% 4% 4% EBIT (Earnings Before Interest & Tax) 1.98 2.06 2.14 2.23 2.32 5% 0.49 Сарех 0.45 0.47 0.51 0.53 4% 4% 4% 4%

Formula for Free Cash Flow to the Firm is given as:

Free Cash Flow to the Firm = EBIT * (1 - Tax Rate) + Depreciation & Amortization - Changes in Working Capital - Capital Expenditure

Here, there is no working capital

So FCFF for the next few years will be given as:

Free Cash Flow to the Firm = 1.29 1.34 1.39 1.45 1.51

Here, we can see that the FCFF is increasing by a rate of 4% annually

Thus, we will use the formula for a growing perpetuity to find the Present Value of this stream of cash flow.

PV = Cash Flow/(Discount Rate - Growth Rate)

= 1.29 / (13.91% - 4%) ................... (Here, Discount Rate is the WACC, which has been calculated earlier in the question)

= 12.99 Million $

Thus, Boris & Isabelle should pay a maximum of 12.99 Million $ for buying this firm

Part (b)

Given is that:

Levered Equity Beta for Grocery Chain = 0.7

Cost of Debt = 5%

Proportion of Debt = 44%

Tax Rate = 35%

Proportion of Equity = 1 - Proportion of Debt = 56%

It is assumed that the Cash Flow projection in this part is the same as in the first part

So, we will have to calculate the WACC for this case

We have all the required values except for the Cost of Equity

As per the CAPM;

Expected Return or Cost of Equity = Risk Free Rate + (Beta * Market Risk Premium)

Risk Free Rate = 3% (Given in the Question)

Market Risk Premium = 6% (Given in the Question)

Levered Equity Beta = 0.7 (Given in the Question)

So, Required Rate of Return on Equity/Cost of Equity = 3% + (0.7 * 6%) = 7.2%

Therefore,

WACC = [D * (1 - t) * Rd] + [E * Re] = [0.44 * (1 - 0.35) * 0.05] + [0.56 * 0.072] = 0.055 = 5.5%

Now as we have WACC, we will use the Growing Perpetuity Formula to calculate the Present Value of the stream of the future cash flows of the firm

PV = CF / (WACC - Growth Rate) = 1.29/(5.5% - 4.0%) = 85.80 Million $

Thus, Fresh Foods should pay a maximum of 85.80 Million $ for the firm Premier Pizza