Question

an express dog food delivery service based in Frankfurt is considering changing its capital structure.

its current capital structure is as follows:

it has 2,000 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 per share and 400,000 shares are armortized. its common stock has a book value of $ 23 per share.

it has a current beta of 0.8. The risk rate is 4.5% , the market rate of return is 11%.

there is no preferred stock.

it is subject to a 40% marginal income tax rate.

its invest bank, Gebrueder Lehmann of Zuerich ,say that its optimal capital structure should be at 50%, 50% equity. At this level of debt, the cost of debt would be 6%. this level of debt will, of course, chnage its stock beta and result in 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 =8.66%

Market value of the equity = Share price*Number of shares outstanding = 20*200,000 = $4,000,000

Market value of the bond = Price per bond*number of bonds = 850*2000 = $1,700,000

The total market value of the bond = Price per bond*number of bonds = 850*2000 = $1,700,000

Total capital = Total market value of the bond + Total market value of the equity

= $1,700,000 + $4,000,000

= $5,700,000

Weight of the equity (We) = Total market value of the equity/Total capital

= 4,000,000/5,700,000 = 70.1754% = 70%

Weight of the debt (Wd) = Total market value of the debt/Total capital

= 1,700,000/5,700,000 = 29.8246% = 30%

If there are no debt employed then beta of equity will be same as before debt issued

now,we have to calulate the revised equity beta. as follows:

debt/Equity =30/70 =0.43.

Thus asset beta is:

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

Asset Beta =0.8/[1+(1-0.40)*0.43]

Asset Beta =0.64

Now,cost of equity is calculated as follow;

cost of equity =Risk free rate+Beta(market rate of return-Risk free rate)

cost of equity =4.5%+0.64(11%-4.5%)

cost of equity =8.66%

f)

new after tax cost of debt = 3.60%

Calculation of new after tax cost of debt

After tax cost of debt=New Cost of debt(1-tax rate)

=6%(1-0.40)

new after tax cost of debt=3.60%

g)

New cost of equity=12.326% or 12.33%

Calculation of new cost of equity:

First,we should calculate the beta of new equity;

Asset beta=Beta/[1+(1-tax rate)*Debt/Equity]

0.64=Equity beta/1+(1-0.40)*1

Equity beta=0.64*1.6=1.204

Cost of equity=4.5%+1.204(11%-4.5%)

=12.326% or 12.33%

h)

New WACC =12.326% or 12.33%

Calculation of New WACC

WACC=Cost of equity*weight+After tax cost of debt*weight

=12.326%*0.5+3.60%*0.50

=6.163%+1.80%

=7.963% or 7.96%