As a consultant or business analyst, you have been asked by one of your clients to value a clothing store that earned

pretax operating income of $$300,000$ last year. 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 $5\mathrm{.}5\%,$ and the firms tax rate is $40\%.$ The beta

and debt$-$to$-$equity ratio for publicly traded firms in the restaurant industry are $2$ and $1\mathrm{.}5,$ 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 marketability 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?

g$.$ What is the business worth?

h$.$ How much should the purchase price the investor has to pay