Question

Your firm is trying to decide on its target capital structure. You expect free cash flows in year 1 to be $100, with constant growth at a rate of 5% forever after. Your firm has an unlevered cost of capital of 10%, and you expect your debt cost of capital will be 5% no matter how much debt you take on. After you borrow, you plan to keep the debt-to-value ratio constant forever. Given the present value of financial distress costs for each level of debt below, how much should your firm borrow today? Assume your firm has a 20% tax rate.

Debt	Present Value of Distress Costs
$0	$0.00
$500	$32.34
$1,000	$106.88
$1,500	$223.59
$2,000	$382.50

$0

$500

$1,000

$1,500

$2,000

Answer 1

First we need to find out the cost of capital Kc at different debt level.

Kc = Wa×Ke + Wb× Kd

Where

Ke = cost of equity = 10% why? Because unlevered cost of capital is nothing but the cost of equity as the capital of an unlevered firm comprised of equity only.

Kd =post tax cost of debt = cost of debt×(1-tax rate) = 5%×(1-.20) = 4%

We = weight of equity in capital structure = (1-Wd)

Wd = weight of debt in capital structure i.e. debt to value ratio  

= Wd = debt/(equity +debt)

For calculating these we need value of equity capital which is equal to the present value of future cashflows @ Ke

Market worth of Equity capital = freecashflows/( ke -g)

g = constant growth = 5%

= 100/(.10-.05) = $ 2000

Wd in different debt level is as follows

Debt Wd        We Kc

0 0/2000 =0   1-0=    1 1×10% +0 =10%

500 500/2000=.25 1- .25=.75   .75×10%+.25×4%= 8.4%

1000 1000/2000= .5 1-.5 = .50 .5×10% +.5×4% = 7%

1500 1500/2000=.75 1-.75=.25 .25×10%+.75×4%= 5.5%

2000 2000/2000=1 1-1 =0 0+ 1×4% =4%

Lets calculate company's value at different debt levels assuming it will generate same cashflows as it is generating now i.e.$100 company's value = present value of future inflows/(Kc-g) =100/(Kc-.05)

Debt level company value   PV of distress cost   Net value   

(A) (B) (A)-(B)

0 100/(.10-.05)

2000 0 2000

500 100/(.084-.05)

2941 32.34 2908.66

1000 100/(.07-.05)

   5000 106.88 4893

1500 100/(.055-.05)

20000 382.5 19617.5

2000 can't be calculated as it will give negative value because Ke=4%< g=5% logic behind this is that a company cannot survive for longer period if it is completely financed by debt because it has repay the debt within a finite period. And interest payment will be made regularly irrespective that whether company earns profits or not.

Now let us calculate the value for equity holders

Value for equity holder= net value- value for debt

Equity holder value at different debt levels are as follows

2000-0=$2000

2908-500=$2408

4893 -1000= $3893

19617- 1500= $18117

As we can see at debt level of 1500 equityholders will get higher worth for their contribution hence this captial capital structure is optimal i.e. firm should borrow at most 1500$