Question

You are building a free cash flow to the firm model. You expect sales to grow from $1 billion for the year that just ended to $2 billion five years from now. Assume that the company will not become any more or less efficient in the future. Use the following information to calculate the value of the equity on a per-share basis.

1. Assume that the company currently has $270 million of net PP&E.
2. The company currently has $90 million of net working capital.
3. The company has operating margins of 10 percent and has an effective tax rate of 31 percent.
4. The company has a weighted average cost of capital of 8 percent. This is based on a capital structure of two-thirds equity and one-third debt.
5. The firm has 2 million shares outstanding.

Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Value of Equity per share = $95.3 per share

Explanation:

Computation of Growth rate

Expected sales for the 1st year end is 1Billion and expected sales in the 5th year is 2 billion (which means total sales at the end of 1st year is i billion is expected to have sales in 5th year to 2billion, so in between to grow there is 4 years).

Growth rate of sales is found through annuity factor formula FV = PV * (1+r)^n

2B=1B *(1+r)^4

(1+r)^4= 2B / 1B

(1+r) =4 square root of 2   

(1+r) =1.1892

r =18.92% per year

Value of firm is computed as

Year	sales (in million)	operating profit (10% of sales)	Tax (31% on operating profit)	Profit after tax	changes in working capital)	FCFF (profit after tax - change in WC)	Discounting at WACC 8%
1	1000	100	31	69	17.03	51.97	47.65
2	1190	118.9	36.859	82.041	20.25	61.79	52.02
3	1410	141.4	43.741	97.566	24.08	73.48	56.72
4	1680	168.2	52.142	116.058	28.63	87.43	61.90
5	2000	200	62	138	34.05	103.95	67.56
Total value of the firm							285.9 million

Working capital changes ( based on growth rate 18.92%)

Year	Working capital (in millions)	changes
0	90
1	107.028	-17.03
2	127.27	-20.25
3	151.35	-24.08
4	180	-28.63
5	214.05	-34.05

NOTE:- the question does not provide any details regarding yearly capital investment in asset or depreciation rate hence it is ignored.

Capital structure = (2/3)rd equity and (1/3)rd debt

Value of equity using (FCFF model) = Total value of firm * 2/ 3  

=> $285.9 million * (2/3)

=>190.6 million

Value of Equity per share = 190.6 million / 2 million shares

Value of Equity per share =$95.3 per share