Question

Your firm is considering purchasing firm Z and they have asked for your help in valuing it. You are struggling a bit because of the uncertain prospects for this industry. Firm Z most recently generated FCF of $30M last year, but you are uncertain of what might happen over the next few years. Specifically, your company’s sales team thinks that it is 40% likely that firms in the industry will grow by 6% this year and for 4 years after that, and 60% likely that they will only grow at 4%. After that, you estimate that firms in the industry, and consequently firm Z, will continue to grow at 2.5% in perpetuity. Firm Z’s cost of capital is 10%. For simplicity, assume that all past cash flows have been paid out as dividends.

1. What is the value of firm Z as of today?

2. Looking at firm Z’s balance sheet, you recognize that they have $150M in debt, and 20M shares outstanding. What is the value of each share, according to your analysis?

3. Suppose you revise your long term growth rate downward, and now believe that firm Z’s growth rate beyond year 5 will only be 1.5%. What is the percent reduction in enterprise value as a result of the lower growth rate? What about the percent change in your estimate share price?

Answer 1

a.

Recent FCF = $30 million 

Growth rate = g = 2.5%

Cost of capital = r = 10%

Value of the firm = FCF (1+g)/(r-g)

                               = 30 (1.025)/(0.10-0.025)

                               = $410 million

 

Value of Z firm Today = $410 million

 

b.

Debt=$150 M

Value of firm = Debt + Equity

410 = 150 + Value of equity

Value of equity = $260 million

 

Number of shares outstanding = 20M

Price of share = Value of equity/Number of share outstanding

Price of share = 260/20 = $13

Price of share = $13

 

c.

Growth 5 year onward is 1.5%

Value of firm = 30(1.015)/(0.1-0.015) = $358.24 million

Value of the firm = $358.24 million

Percentage reduction in value = Value before- Value now/Value before

                                                       = 410-358.24/410 x 100 

                                                        = 12.62%

Percentage reduction in value =12.62%

 

Value of equity = 358.24-150 = $208.24 million

Value of equity = $208.24 million

Price of share = 208.24/20 = $10.14

Price of single share = $10.14

Percentage reduction in price = Price before- Price now/Price before x 100

                                                      = 13-10.14/13 x 100

                                                      = 22%

Percentage reduction in price of share = 22%

a. Value of Z firm Today = $410 million

b. Price of share = $13

c. Percentage reduction in price of share = 22%