12.15      VALUING THE EQUITY OF A PRIVATELY HELD FIRM. Refer to the projected financial statements for Massachusetts Stove Company (MSC) prepared for Case 10.2. The management of MSC wants to know the equity valuation implications of not adding gas stoves versus adding gas stoves under the best, most likely, and worst scenarios. Under the three scenarios from Case 10.2 and a fourth scenario involving not adding gas stoves, the projected free cash flows to common equity shareholders for Year 8 to Year 12, and assumed growth rates thereafter, are as follows:

 

Year                           Best            Most Likely            Worst                No Gas

 

8	$ 73,967	$ 47,034	$    3,027	$162,455
9	$ 52,143	$ (3,120)	$(84,800)	$132,708
10	$213,895	$135,939	$ 48,353	$106,021
11	$315,633	$178,510	$ 36,605	$ 81,840
12	$432,232	$220,010	$ 10,232	$ 60,007
13–17	20% Growth	10% Growth	Zero Growth	Zero Growth
After Year 17	10% Growth	5% Growth	Zero Growth	Zero Growth

 

MSC is not publicly traded and therefore does not have a market equity beta. Using the market equity beta of the only publicly traded woodstove and gas stove manufacturing firm

 

 

and adjusting it for differences in the debt-to-equity ratio, income tax rate, and privately owned status of MSC yields a cost of equity capital for MSC of 13.55 percent.

Required

a.    Calculate the value of the equity of MSC as of the end of Year 7 under each of the four scenarios. Ignore the midyear adjustment related to the assumption that cash flows occur, on average, over the year. Apply the growth rates in free cash flows to common equity shareholders after Year 12 directly to the free cash flow of the pre- ceding year. (That is, Year 13 free cash flow equals the free cash flow for Year 12 times the given growth rate; Year 18 free cash flow equals the free cash flow for Year 17 times the given growth rate.)

b.   How do these valuations affect your advice to the management of MSC regarding the addition of gas stoves to its woodstove line?