Question

In the year in which it intends to go public, a firm has revenues of $20 million and net income after taxes of $2 million. The firm has no debt, and revenue is expected to grow at 20% annually for the next five years and 5% annually thereafter. Net profit margins are expected remain constant throughout. Capital expenditures are expected to grow in line with depreciation and working capital requirements are minimal. The average beta of a publicly traded company in this industry is 1.50 and the average debt/equity ratio is 20%. The firm is managed very conservatively and does not intend to borrow through the foreseeable future. The Treasury bond rate is 6% and the tax rate is 40%. The normal spread between the return on stocks and the risk free rate of return is believed to be 5.5%. Reflecting the slower growth rate in the sixth year and beyond, the firm’s discount rate is expected to decline to the industry average cost of capital of 10.4%. Estimate the value of the firm’s equity.

Answer 1

In the year in which it intends to go public, a firm has revenues of $20 million and net income after taxes of $2 million. The firm has no debt, and revenue is expected to grow at 20% annually for the next five years and 5% annually thereafter. Net profit margins are expected remain constant throughout. Capital expenditures are expected to grow in line with depreciation and working capital requirements are minimal.

Based on this information, Free cash flow to the equity holder, C = Net Income + Depreciation - Increase in working capital - Capital expenditure - Net debt repayment

Capital expenditure = Depreciation

Increase in working capital = 0

There is no borrowing or repayment, hence net repayment = 0

Hence, C = Net income.

Since margins are constant, growth rate in revenue translates into growth rate in net income or earnings and hence cash flows.

Hence, year wise cash flows will be as shown in the table below:

All the financials below and elsewhere in the solution are in $ mn

Year	0	1	2	3	4	5	6
Cash flows, Ci	2.00	2.40	2.88	3.46	4.15	4.98	5.23
Growth rate, g		20%	20%	20%	20%	20%	5%

where cash flow in year i = C_i = C_i-1 x (1 + g); g = 20% for year 1 to 5 and from year 6 onward, g = terminal growth rate, g_t = 5%

The average beta of a publicly traded company in this industry is 1.50 and the average debt/equity ratio is 20%. The firm is managed very conservatively and does not intend to borrow through the foreseeable future. The Treasury bond rate is 6% and the tax rate is 40%. The normal spread between the return on stocks and the risk free rate of return is believed to be 5.5%.

Levered beta, B_L = 1.50; Tax rate, T = 40%, D/E = 20%

Hence, unlevered beta, B_U = B_L / [1 + (1 - T) x D / E] = 1.50 / [1 + (1 - 40%) x 20%] = 1.339285714

Risk free rate = 6%, Market risk premium = 5.5%

Hence, cost of equity for this firm = cost of equity of unlevered firm as this firm doesn't intend to borrow = risk free rate + B_U x market risk premium = 6% + 1.339285714 x 5.5% = 13.37%

Hence, appropriate discount rate for year 1 to 5, R₁ = 13.37%

Reflecting the slower growth rate in the sixth year and beyond, the firm’s discount rate is expected to decline to the industry average cost of capital of 10.4%. This means discount rate from year 6 onward, R = 10.4%

Horizon value of cash flows at the end of year 5 = HV_{C, 5} = C₆ / (R - g_t) = 5.23 / (10.4% - 5%) = 96.768

Value of the equity of the firm = Present value of all the future cash flows

=63.58

Hence, the value of the firm’s equity = $ 63.58 mn