# Question on WACC

how to do this ? can someone solve this with proper explanation plz .

Degen Company is considering a project in the commercial printing business. Its debt currently has a yield of 12%. Degen has a leverage ratio of 2.3 and a marginal tax rate of 30%. Hodgkins Inc., a publicly traded firm that operates only in the commercial printing business, has a marginal tax rate of 25%, a debt-to-equity ratio of 2.0, and an equity beta of 1.3. The risk-free rate is 3% and the expected return on the market portfolio is 9%. The appropriate WACC to use in evaluating DegenĂ˘â‚¬â„˘s project is closest to:

A) 8.9%. B) 8.6%. C) 9.2%.

Regards,

HedgeFudge

Unlever Hodgkinsâ€™ (equity) beta to get its asset beta, then and relever the asset beta to get Degenâ€™s (equity) beta:

Î˛asset = Î˛equity{1 / [1 + (1 â€“ t)D/E]}

= 1.3{1 / [1 + 0.75(2.0)]}

= 0.52

Î˛equity = Î˛asset[1 + (1 â€“ t)D/E]

= 0.52[1 + 0.7(1.3)]

= 0.9932

Now that you have Degenâ€™s Î˛, Iâ€™m sure that you can take it form here.

You are trying to estimate a projectâ€™s beta or its measure of systematic or market risk. However, this is very hard to observe in real life as most projects and businesses are combined. Think of GE and its various businesses. Its appliance business is very different in how it reacts to business conditions and its value - risk/reward to the market as its jet engines businesses. We canâ€™t say its Jet Engines business has a project beta of 1.2 vs its appliance business of 1.0 as its not directly observable.

Thus we use comps of pure play businesses that are publicy traded. Think of a maytag that may be a pure-play of GEâ€™s appliance business. This is used to measure the sensitivity to the market - Project Beta.

1. Target the pure-play company or Hodgkins. Unlever the asset beta using formula Beta Equity (1+(1/(1+D/E(1-t))).

1.3 (1/(1+2.0(1-0.25))) = 0.52

1. Relever using your companyâ€™s capital and tax structure.

.52(1+(1-0.3)2.3) = 1.36 = Beta Project

1. Now that we have Beta of the project of 1.36 that is used in our CAPM calcuation of Risk Free Asset + Beta Project (Equity Risk - Risk Free)

3% + 1.36 (9%-3%) = 11.11%

1. Now we use WACC or weighted average cost of capital for each of the components of our target capital structure.

70% (1-.3) (0.12) + 0.3 (11.11%) = .0918 or 9.18% or C 9.2% rounded up.

FYI - how I get 70/30% is from the leverage ratio of 2.3. If Leverage or Debt is 2.3, this is saying for every \$2.30 dollars of debt, there is \$1.00 dollar of equity. So if you want to conver that to a percentage then think of it is:

D / D+E

D of 2.3 numerator divided by 2.3 debt + 1.0 of equity on denominator = 2.3/3.3 or 70%

1 Like

S2000 the firm leverage ratio is 2.3 (not 1.3)

Yes. So A/E = 2.3. So D/E = 1.3.

S2000 - thx you are right. my mistake reading it. Its leverage ratio not D/E or debt / assets so 2.3 so debt / equity is 1.3.

Feeling brain dead today, how did you D/E = 1.3. Is it because Assets/equity = 2.3, Hence 2.30 to everyone 1 dollar equity. Assets = Liab + Equity. 2.3 = Liab + Equity, Liab = 1.3, so 1.3 in debt to every 1 equity?

A / E = 2.3

(L + E) / E = 2.3

L / E + E / E = 2.3

L / E + 1 = 2.3

L / E = 1.3

Although technically liabilities and debt arenâ€™t exactly the same thing, for the purposes of this question, we assume that they are.

Thank you so much!

My pleasure.

Thank you so much for your explanation !