Question

You have a new start-up firm. You think that the value of your start-up is around $60 million, but you will need to do a serious NPV analysis before you know the precise value. You are planning to have a 50% debt-to-value ratio, and that you will continuously rebalance to maintain this leverage. You have information on two other companies. The names of these companies are “Comp A” and “Comp B”. Comp A has the same business risk as your start-up but different financial leverage. Comp A is continuously rebalancing its leverage to maintain a 30% debt-to-value ratio. Comp A’s equity beta is 1.5 and the debt beta is 0.5. CompA’s most recent annual sales figure was $3 million. Comp A’s total market value (debt + equity) is $10 million. Comp B has the same leverage as your start-up (50% debt-to-value ratio) and operates in a different line of business than your start-up. Comp B is also continuously rebalancing its leverage. Comp B’s equity beta is 2 and the debt beta is 0.7. CompB’s most recent annual sales figure was $8 million. Comp B’s total market value (debt + equity) is $60 million. The market risk premium is 10% and the risk free rate is 3%. The tax rate is 30%. Your cost of debt (expected return on debt) will be 4%. What is your best estimate for the equity beta of your start-up? What is the WACC for your start-up?

Answer 1

The market risk premium = 10%

The risk free rate = 3%

The tax rate = 30%.

Cost of debt = 4%.

Comp A

Debt-to-value ratio = 30%.

Equity beta = 1.5

Debt beta = 0.5

Annual sales figure = $3 million.

Total market value (debt + equity) = $10 million.

Calculation of WACC via CAPM

Cost of Debt = interest rate x (1-tax rate)

Cost of Debt = 0.04 x (1-0.3)

Cost of Debt = 0.028 or 2.8 %

Levered Beta = Unlevered equity beta x ( 1+ (1-t) x (Debt/equity)

Levered Beta = 1.5 x (1+ (0.7 x 3/7)

Levered Beta = 1.5 x (1+ 0.3)

Levered Beta = 1.95

Cost of Equity (CAPM) = risk free rate + beta x (market risk premium)

Cost of Equity (CAPM) = 0.03 + 1.95 x (0.1)

Cost of Equity (CAPM) = 0.225 or 22.5 %

WACC = { cost of equity x (% of equity) } + { cost of debt x (% of debt)}

WACC = { 0.225 x 0.70 } + { 0.028 x 0.30 }

WACC = 0.1659 or 16.59 %

Comp B

Debt-to-value ratio = 50%

Equity beta = 2

Debt beta = 0.7

Annual sales figure = $8 million.

Total market value (debt + equity) = $60 million.

Calculation of WACC via CAPM

Cost of Debt = interest rate x (1-tax rate)

Cost of Debt = 0.04 x (1-0.3)

Cost of Debt = 0.028 or 2.8 %

Levered Beta = Unlevered equity beta x ( 1+ (1-t) x (Debt/equity)

Levered Beta = 2 x (1+ (0.7 x 1/2)

Levered Beta = 2 x (1+ 0.35)

Levered Beta = 2.7

Cost of Equity (CAPM) = risk free rate + beta x (market risk premium)

Cost of Equity (CAPM) = 0.03 + 2.7 x (0.1)

Cost of Equity (CAPM) = 0.3 or 30 %

WACC = { cost of equity x (% of equity) } + { cost of debt x (% of debt)}

WACC = { 0.3 x 0.50 } + { 0.028 x 0.50 }

WACC = 0.164 or 16.4 %

Since the market value, debt-to-value ratio of Comp B is approximately equal to your startup, the equity beta of Comp B and WACC of Comp B can be estimated and considered the same as yours.

Your Startup:

Equity Beta = 2

WACC = 16.4%