5F.8
8. Your company is worth $200 million and is financed 100% with equity. You think that it may be value-increasing to replace $80 million of the equity with $80 million in debt.
a. How could such a capital structure change affect the value of the company? [3]
If a change in capital structure affects the value of a company, it must do so through one of three channels (M&M Proposition):
Taxes, Transaction Costs, or Changes in Investment Policy
b. Assume that the tax rate on your company’s profits is 34%. The debt would be permanent and have a 9% coupon. Your investment bankers will charge you $1 million to issue $80 million in debt and repurchase $80 million in equity. The capital structure shift won’t change your investment plans. What will be the new value of your company after the change in capital structure? [6]
The description tells you that this will affect taxes, it will have transaction costs, but it will not affect investment policy, so once you figure out the tax effect net of transaction costs, you will have the total effect. First figure out the PV of the interest tax shields created by this debt:
so this debt creates future tax shields with a total present value of 27.2M, which is added to the value of the firm. The transaction costs of $1M reduce the value of the firm, leaving you with a net increase of $26.2M, so that the new value of the firm is $226.2M.
c. What is the new total value of your equity? What is the total value of your debt? [6]
The changes in value of the firm go straight to the equity. Thus, the new value of the equity will be the old value $200M minus the $80M that you repurchased, plus the $26.2M in new value, or $146.2M. The value of the debt is exactly what the debtholders paid, or $80M. It's always nice to check that the value of the debt and the value of the equity add-up to the total value of the firm: $146.2 + $80 = $226.2.