10.13 Based on its growth prospects, a private investor values a local bakery at $750,000. She believes that cost
savings having a present value of $50,000 can be achieved by changing staffing levels and store hours.
Based on recent empirical studies, she believes the appropriate liquidity discount is 20 percent. A recent
transaction in the same city required the buyer to pay a 5 percent premium to the asking price to gain a
controlling interest in a similar business. What is the most she should be willing to pay for a 50.1
percent stake in the bakery?
10.14 You have been asked by an investor to value a restaurant. Last year, the restaurant earned pretax operating
income of $300,000. Income has grown 4% annually during the last five years, and it is expected to
continue growing at that rate into the foreseeable future. The annual change in working capital is $20,000,
and capital spending for maintenance exceeded depreciation in the prior year by $15,000. Both working
capital and the excess of capital spending over depreciation are projected to grow at the same rate as
operating income. By introducing modern management methods, you believe the pretax operating income
growth rate can be increased to 6% beyond the second year and sustained at that rate into the foreseeable
future.
The ten-year Treasury bond rate is 5%, the equity risk premium is 5.5%, and the marginal federal, state,
and
local tax rate is 40%. The beta and debt-to–equity ratio for publicly traded firms in the restaurant industry
are 2 and 1.5, respectively. The business’s target debt–to-equity ratio is 1, and its pretax cost of borrowing,
based on its recent borrowing activities, is 7%. The business-specific risk premium for firms of this size is
estimated to be 6%. The liquidity risk premium is believed to be 15%, relatively low for firms of this type
due to the excellent reputation of the restaurant. Since the current chef and the staff are expected to remain
after the business is sold, the quality of the restaurant is expected to be maintained. The investor is willing
to pay a 10% premium to reflect the value of control.
a. What is free cash flow to the firm in year 1?
b. What is free cash flow to the firm in year 2?
c. What is the firm’s cost of equity?
d. What is the firm’s after-tax cost of debt?
e. What is the firm’s target debt–to-total capital ratio?
f. What is the weighted average cost of capital?