Question

You are considering starting a company that manufactures racing bicycles. You are planning on financing your firm 40% equity and 60% debt. You estimate that your upfront costs will be $5M, and that you will earn an EBIT of $1M per year for the next 12 years. Lightning Bolt Bikes makes racing bicycles similar to the ones that you wish to manufacture. They have a CAPM equity beta of 1.9 and a debt to equity ratio of 0.7. The tax rate for both firms is 35%, the riskless rate is 3%, and the expected return on the S&P500 is 15%. Cost of Debt is 6%

Part A (5 points). What is the asset beta of Lightning Bolt Bikes?

Part B (5 points). What is your unlevered cost of equity?

Part C (5 points). What is your firm’s equity beta?

Part D (10 points). What is your firm’s weighted average cost of capital?

Part E (5 points). What is the NPV of your proposed bicycle company using the WACC method?

Answer 1

A.) Asset beta of Lightning Bolt Bikes:

Asset beta means measuring volatility of returns of the company, without taking into account of financial leverage or debt capital use by company. It is also called unlevered beta because it measure beta only based on equity.

Formula for calculating Asset beta:

Asset beta = Equity beta / [1+(1-tax rate) (debt / equity)]

So in our case for Lightning Bolt Bikes, equity beta = 1.9, tax rate=35%, debt/equity = 0.7

So puting all these figures into formula

Asset beta = 1.9 / [1+(1-35%)(0.7)]

= 1.9 / [1+(0.65)(0.7)

= 1.9 / 1.155

= 1.65

Asset beta for Lightning Bolt Bikes is 1.65.

B.) Unlevered cost of equity

Unlevered cost of equity means calculating rate of return for a company which is expects to earn on it's asset without taking acount of debt capital into it. The unlevered cost of equity shows cost to investor for financing the project without incurring debt.

Formula for calculating Unlevered cost of equity,

Unlevered cost of equity = Risk free return + Asset Beta * (Expected market return - Risk free return)

So for calculating Unlevered cost of equity first we need to asset beta and for calculating asset beta, we need to calculate equity beta. And for calculating equity we are using CAPM (Capital Asset Pricing Model).

CAPM shows expected return on security is equal to risk free return puls risk premium multiply by equity beta.

Formula of CAPM,

Excepted Return = Risk free return + [beta * (market return - risk free return)

Here the Excepted return for our company is EBIT - Interest cost - Tax

$ 1 - $ 0.18($ 5M *60% *6%) - (1 - 35%) = $ 0.533

Notes: Total investment required is $ 5m (40% equity and 60% debt) and cost of debt is 6% so ($ 5 * 60% * 6%) = 0.18 is interest cost.

Tax rate is 35%.

So excepted return is $ 0.533 to equity and in percentage ( 0.533 *100 / 2) = 26.65%

And risk free return = 3% and Market return= 15% (return on S&P500).

So putting all figures in CAPM Formula for calculating beta

26.65 = 3 + [beta * (15 - 3)]

26.65 - 3 = beta * 12

beta = 23.65 / 12

beta = 1.97

So beta is 1.97

Now we will calculate asset beta,

Asset beta = Equity beta /  [1+(1-tax rate) * (debt / equity)]

= 1.97 / [(1+(1-0.35) * 1.5]

= 4.88

Now we will calculate unlevered cost equity,

Unlevered cost of equity = Risk free return + Asset Beta * (Expected market return - Risk free return)

= 3 +4.88 * (15 -3)

= 26.64

So unlevered cost of equity is 26.64%

C.) Equity beta measure how the individual security's price is sensitive to the overall market change. If equity beta is 1 then, if market change by 10% then individual security's price will change by 10%, and If equity beta is 1.5 then, if market change by 10% then individual security's price will change by 15%, therefore beta more than 1 will have greater risk, and If equity beta is 0.8 then, if market change by 10% then individual security's price will change by 8%,, it means if beta less then 1 will have less risk.

The beta which we calculated above by CAPM is equity beta. (see above)

So Equity beta for our company is 1.97

D.) Weighted Average cost of capital for our firm

Weighted Average cost of capital is weighted average of all capital that firm has source or use. Here in our case equity and debt is used.

So Weighted Average cost of capital is weighted average of cost of equity and cost debt after tax rate

Weighted Average cost of capital = Cost of Equity * proportion of equity + Cost of debt after tax rate * proportion of debt

Cost of Equity = Equity risk premuim (Market risk - risk free return) * Beta + Risk free rate

= 12 (15 -3 )*1.97 + 3 = 26.64%

And cost of debt after tax rate is 6 ( 1 -0.35) = 3.9%

So Weighted Average cost of capital = 26.64 * (2/5) + 3.9 * (3/5)

= 10.656 + 2.34

=12.996%

Weighted Average cost of capital for our firm is 12.996%