Question

if excel is used, show all formulas please :)

Two ambitious business graduates, Boris and Isabelle, are considering purchasing Premier Pizza, a frozen pizza manufacturer. Forecasted annual sales for the coming year are $10.3 million, with operating costs equal to 85% of sales, depreciation is 6% of sales and required annual investment in equipment is 4% 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 26% debt. The required rate of return on the debt will be 6% and the required rate of return on the equity will be 17%. Premier Pizza's corporate tax rate is 35%. The risk-free interest rate is 3% and the market risk premium is 7%. 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 $0 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 0.5, its cost of debt is 5%, it is 39% 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

a. Part a requires valuation of the business using Discounted Cash Flow (DCF) approach. In DCF approach, enterprise value i.e. value of equity + debt is computed as present value of future free cash flows to firm (FCFF) discounted by weighted average cost of capital (WACC). WACC is computed as below:

WACC = (Equity contribution)*cost of equity + (Debt contribution)*cost of debt*(1-Tax Rate)

Here, Cost of equity = required return on equity = 17%; Cost of debt = 6%, tax rate = 35% and proposed debt is 26% of total funding

WACC = 74%*17% + 26%*6%*(1-35%) = 13.594%

Now, we calculate FCFF for year 1 (FCF1) as below:

US$	Year1	Year1
Sales	10300000	10300000
Operating cost	85%	85%
EBITDA	=(1-B3)*B2	1545000
Depreciation (Dep)	=6%*B2	618000
EBIT	=B4-B5	927000
Tax Rate (T)	35%	35%
Investment (Inv)	=4%*B2	412000
NOPAT	=EBIT(1-T)	602550
FCF1	=NOPAT+Dep-Inv	808550

Enterprise value is the sum of discounted free cash flows to perpetuity. Now, in this example, sales, costs and investments are all projected to grow by 4% annually. Thus, FCF will also grow by 4% in perpetuity since it is a linear relationship. Now, when we discounted back Free cash flows growing at 4% (g) in perpetuity by discount rate (WACC), the formula will reduce to the sum of an infinte Geometric Progression (GP) as below:

Enterprise Value, EV = FCF1 / (WACC - g)

WACC	13.594%	13.594%
Growth Rate (g)		4%
EV	=FCF1/(WACC-g)	8427663
Debt	=26%*B20	2191192
Equity	=74%*B20	6405024

Thus the maximum price that should be paid for Premier Pizza is $6.41million

b) In part b, the free cash flow assumptions are same as part a but the WACC will change since Fresh Foods (the acquiring company) has different cost of debt and equity as well as debt to equity ratio

Cost of debt = 5%

Using Capital asset pricing model, Cost of equity = Risk-free rate + unlevered beta * market risk premium

Unlevered beta = levered beta / [1+D/E(1-Tax rate)] = 0.5 / [1 + (0.39/0.61) * (1-35%)] = 0.35

cost of equity = 3% + 0.35 * 7% = 5.47%

WACC = 61% * 5.47% + 39% * 5% * (1-35%) = 4.61%

Enterprise Value = FCF1 / (WACC - g) = 808550 / (4.61% - 4%) = $133485251

Equity = 61% * EV = 81426003 = $81.42million

Fresh Foods can pay upto $81.42million for Premier Pizza. The significant difference in valuations is a result of hugely different cost of capital for two companies in part a and part b.