Question

An all equity firm with a 10% cost of capital pays a 20% income tax and expects to generate annual perpetual EBIT of $80M with 75% probability or $20M. The firm would like to replace $200M of equity with debt. A bank offers the firm this loan amount at 15% annual interest rate. The firm estimates the PV cost of a potential bankruptcy to be $120M.

(A)      Should the firm accept/reject this loan offer? (Support your answer with actual numbers, that is by how much would firm value increase or decrease after a recapitalization financed with this loan?)

(B)       How big does the PV cost of a potential bankruptcy have to be to justify forgoing this loan offer?

Answer 1

Part A

First of all we need to calculate the current value of equity capital which is given by

Firm value = EBIT(1-t)/Kc

Where

EBIT = earnings before interest and tax =80M with 75% probability and 20M with 25% probability

Hence Expected value EBIT = 80×.75+20×.25= 65M $

t= tax rate = 20%

EBIT(1-t) = 65(1-.20) = $ 52M

Kc = cost of capital, since enitre capital amount is comprised of equity capital so Kc = Ke i.e. cost of equity capital let us check.

Kc = We×Ke + Wd×Kd

Where

We =portion of equity capital in capital structure= 100% for an all equity firm

Ke= cost of equity =10%

Wd = portion of debt capital in capital structure =0

For an all equity firm

Kd = post tax cost of debt = interest rate(1-t)= 15%×.80 = 12%

Kc= 100%×10% +0= 10%

Firm value = 52/10% = $520M

Here the firm value= value of equity capital as the firm is all equity financed

The new capital structure would be

Replacement of 200M equity with debt i.e. new equity will be =520- 200 = 320 M and debt = 200M new We= equity/total capital = 320/520= .6154 and Wd = 1-We = 1- .6154 = .3846

Cost of capital Kc = .6154×10% + .3846× 12%= 10.76%

Value of firm ( assuming firm will generate same cashflowsas ut is generatingnow)= EBIT after tax / Kc = 52/.1076 = $483.27M

Now the value of equity = value of firm - debt value- PV of distress cost

= 483.27 - 200 - 120 = 163.27M

Since equity value has been eroded by 520-163.27= 357M

This recapitalisation is not viable.

Part 2

As we can see there is huge erosion in the value ao there should not be any distress cost to make recapitalisation viable let us get the numbers

The net equity value should be unchanged at 520 M

483.27-200- d = 520

d = -236.73 M this is the negetive figure which there should not be any distress cost rather there should be high interest tax savings from the debt.