Question

Consider a firm that exists in a world with two periods (time 0 and time 1) and two equally likely states of the world at time 1. At time 0 the firm’s securities are traded. At time 1 the state is revealed. In the up-state the firm’s assets are worth $120 and in the down-state they are worth $40. The firm has debt outstanding with a face value of $60. Assume that the required rate of return is zero and investors are risk neutral. a) Compute the market value of debt, equity and the total market value of the company at time 0. b) Suppose that the company issues some additional debt with a face value of $40. This debt is pari passu (equal priority) with respect to the existing debt and the proceeds are invested in a zero NPV riskless project (i.e., the money is put in a safe box). How much money is the company able to raise with this debt issue?

Answer 1

Part a)

The expected value of the firm's assets at time 1 will be the average of up-state & down-state

= 0.5 * (120 + 40)

= 80

As the required rate of return is zero, the value at time 0 will also be the same as that of time 1 as:

value at time 0 = Value at time 1 discounted at 0% rate = 80 / (1 + 0%)

=80

Thus the total market value of the company at time 0 = $80

As this is greater than the face value of debt, so the debt can be repaid completely & thus it is worth its face value,

So the value of debt= $60

Value of equity = Total value of the firm - the value of debt

= 80 - 60

= $20

Part b)

After issuing additional debt of $40, the total outstanding debt = 60 + 40 = $100

As the total value of the firm is only $80, so the actual market value of the debt will be this much only.

At the time of repaying, this $80 will contribute on a pro-rata basis towards the old debt of 60 & new debt of 40 as:

Contribution to old debt = 60% * 80 = $48

Contribution to new debt = 40% * 80 = $32

Thus the market value of new debt is $32, so this is the amount that the company will be able to raise with this debt issue