Question

an express dog food delivery service based in Frankfurt is considering changing its capital structure. its capital structure is as follows: it has 2000 5% annual coupon 10 year bonds outstanding which currently trade at 85. the book value for these bonds is 2.0 million. its common stock sells at $20 per share with 200,000 shares issued and outstanding . its par value is 5.00 per share and 400,000 shares are authorized. its common stock has a book value o $23 per share.

it has a current beta of 0.8. the risk free rate is 4.5%, the market rate of return is 11.0%. there is no preferred stock outstanding and there are no plans to issue preferred stock. it is subject to a 40% marginal income tax rate.

its investment bank say its optimal capital structure should be at 50% debt,50% equity. at this level of debt, the cost of debt would be 6%. this level of debt will of course change its stock beta and result in a different cost of equity.

e. what is its cost of equity if it were to reflect only business risk.(i.e if there were no debt employed?)

f. what will its new after tax cost of debt be?

g. what will its new cost of equity be?

h. what will its new WACC be?

Answer 1

e) Cost of equity if it were to reflect only business risk.(i.e if there were no debt employed)

Given in the question,

Current beta = 0.8, the risk free rate (Rf)= 4.5%, the market rate of return (Rm) 11.0%.

As per CAPM, Cost of Equity(Re)= Rf+B(Rm-Rf) = 4.5%+0.8(11-4.5%) = ( 4.5% +5.2%) = 9.7%

f). New after tax cost of debt be.

Given that the cost of debt would be 6% ,tax rate =40%

New aftertax cost would be = Interest Rate *(1-tax rate) = 6%*(1-40%) = (6%*60%) = 3.6%

g) New cost of equity will be:

To calculate new coost of Equity first we have to convert Unlevered beta into levered beta as the comoany has decided to introduce debt of 50%

Conversion of Unlevered beta into Levered beta(Bi)=Bu(1+(1-t)D/E))

where, Bi=levered beta, Bu= Unlevered beta,t= Tax rate, D= Debt, E=Equity

Bi= 0.8(1 +(1-.40)0.5/0.5)

=0.8(1+0.60)1

= 2.4

So new cost of Equity= Rf+Bi(Rm-Rf) = 4.5%+ 2.4(11-4.5%) = (4.5% + 15.6%) = 20.1%

h). New WACC will be:

Given in the question that optimal capital structure should be at 50% debt,50% equity. at this level of debt, the cost of debt would be 6%.

So, ratio of DEBT: EQUITY = 1:1

NEW WACC= [Weight of Debt *Cost of debt(1-tax rate)] +[Weight of Equity * Cost of Equity]

= (1/2 *3.6%) + (1/2 *20.1%)

= (1.8% + 10.05%) = 11.85%

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