Question

It is December 2018. You are analyzing YKNOT Inc., a company headquartered in Waukesha, WI, which is manufacturing sailing ropes. You look at managerial projections of earnings, and in 2019, the company is expected to produce EBITDA of $18M. In the same projections for 2019, you discover that the depreciation and amortization expenses of $2M are expected. And in the same projections, the company expects to invest $2.3M in property, plant, and equipment in that year. Additionally, the company expects to invest an additional $300,000 into Net Working Capital in that year. They do not expect to sell any equipment currently in place.

The owners ask you to value the firm and the firm’s equity. You decide to use Discounted Cash Flow methodology to do that. To provide a better estimate, you decide to use both WACC and APV methods. Clearly, you need some additional information for that.

You ask managers about their debt policy. They tell you that the company currently has about $30M of bank loans, on which the company pays an average interest rate of 5% per year. But managers also tell you that they try to maintain the proportion of debt financing at 20% of total capital, which is an industry’s average. Managers say that 2019 is expected to be very representative of the future. In the future, they expect the firm’s free cash flow to grow at 3% per year forever.

You perform some research and discover that the asset beta of firms in the YKNOW’s industry is 1.5. As a finance professional, you know that the current rate on U.S. Treasury 10-year bonds is 2.9% per year, considered risk-free, the prevailing market risk premium is 5%, and the marginal Federal tax rate on U.S. corporations is 21%.

a.) Please calculate the weighted average cost of capital (WACC) of the firm.

b.) Using WACC, calculate firm value using discounted cash flow approach.

c.) Using firm value obtained in b, calculate the value of the firm’s equity.

d.) Calculate firm value using adjusted present value (APV) approach assuming 30M debt is held forever

e.) Using firm value obtained in d, calculate the value of the firm’s equity.

Answer 1

a) Since asset beta of firms in the industry of YKNOT is 1.5. therefore we can take

Asset beta of YKNOT = Unlevered beta = 1.5

Debt as percentage of capital = D/T = 20%, Equity as percentage of capital = E/T 1 - D = 1 - 20% = 80%

So we get, D/E = 20%/80% = 0.25

Levered Beta or Equity Beta = Unlevered Beta [ 1 + (1-tax rate) (D/E)] = 1.5 [ 1 + (1-21%) (0.25)] = 1.5(1 + 79% x 0.25) = 1.5 x 1.1975 = 1.79625

Cost of equity = r_e = Risk free rate + Levered Beta x market risk premium = 2.9% + 1.79625 x 5% = 2.9% + 8.98125% = 11.88125%

b) Cost of debt = interest rate on bank loan = r_d = 5%

WACC = r_d (D/T)(1-tax rate) + r_e (E/T)

WACC = 5%(20%)(1-21%) + 11.88125%(80%) = 5% x 20% x 79% + 11.88125% x 80% = 0.79% + 9.505% = 10.295%

EBITDA for 2019 = $18M , Depreciation and amortization for 2019 = $2M, Net Capital expenditure for 2019 = $2.3M, Net Investment in working capital for 2019 = $300000 = $(300000/1000000)M =0.3M

Free cash flow to firm for 2019 = FCFF₂₀₁₉ = EBITDA(1-tax rate) + Depreciation x tax rate - Net Capital expenditure - Net investment in working capital = 18(1-21%) + 2 x 21% - 2.3 - 0.3 = $12.04M = 12.04 x 1000000 = $12040000

Constant growth rate of free cash flow to firm = g = 3%

Let V₂₀₁₈ = Value of firm at end of 2018 or in December 2018, then applying constant growth rate model to find the value of the firm using discounted cash flow approach

V₂₀₁₈ = FCFF₂₀₁₉ / (WACC - g) = 12040000 / (10.295% - 3%) = 12040000 / 7.295% = $165044551.0624 =

$ (165044551.0624 / 1000000) M = 165.0445510624M

c) Current Value of debt at end of 2018 = $30M

Value of Equity of firm at end of 2018 = Value of firm at end of 2018 - Current Value of debt = 165.0445510624M - 30M = $135.0445510624M

d) Asset beta = 1.5

Unlevered cost of equity = Risk free rate + Asset beta x market risk premium = 2.9% + 1.5 x 5% = 2.9% + 7.5% = 10.40%

According to Adjusted present value method

Value of firm at end 2018 = Value of unlevered firm + Present value of interest tax shield

Now using constant growth rate model we get

Value of unlevered firm at end of 2018 = FCFF₂₀₁₉ / (Unlevered cost of equity - g) = 12040000 / (10.40% - 3%) = 12040000 / 7.40% = 162702702.7027

Interest tax shield for 2019 = Debt x cost of debt x tax rate = $30M x 5% x 21% = 0.315M

Since debt of the company will remain constant at 30M, therefore interest tax shield will form a perpetuity

Present value of perpetuity = Perpetuity / Discount rate

In this case discount rate = cost of debt = 5%, therefore

Present value of interest tax shield = Interest tax shield / cost of debt = 0.315 / 5% = $6.30M

Value of firm at end of 2018 using APV = Value of unlevered firm + present value of interest tax shield = 162.7027027027M + 6.30M = $169.0027027027M = $169002702.7027

e)

Value of equity of firm at end of 2018 = Value of firm using APV - Value of debt = 169.0027027027 - 30 = $139.0027027027M = $139002702.7027