Question

Consider an all‐equity firm with EBIT of $10MM, expected to stay at that level over time. There is no
depreciation and no investment: all after‐tax earnings paid as dividends. The current market
capitalization is $100MM. There are 10MM shares, which are priced at $10 per share. The corporate
tax rate is 30%.

Now suppose the firm issues $80MM in perpetual debt (i.e., a perpetuity) at an interest rate of 5%
per year and uses debt proceeds to buys back shares.
e. What are the expected after‐tax earnings each year?
f. What is the sum of total annual payments to equityholders and debtholders?
g. What is the sum of the PVs of all future payments to equityholders and debtholders?
h. How many shares of stock will the firm buy back with the $80MM?
i. Does the debt issuance create value, destroy value, or neither?
j. If there is value creation/destruction, who gets it or who pays for it?

Answer 1

All financials below except share price are in $ MM unless otherwise stated. Share price is in $.

e. What are the expected after‐tax earnings each year?

EBIT = 10

Debt, D = 80

Interest rate, R = 5%

Interest expense, I = R x D = 5% x 80 = 4

EBT = EBIT - I = 10 - 4 = 6

Tax rate, t = 30%

Taxes, T= t x EBT = 30% x 6 = 1.8

Expected after tax earnings = EAT = EBT - T = 6 - 1.8 = 4.2

f. What is the sum of total annual payments to equityholders and debtholders?

Payment to debt holders = I = 4

Payment to equity holders = after tax earnings = EAT = 4.2

sum of total annual payments to equity holders and debt holders = 4 + 4.2 = 8.2

g. What is the sum of the PVs of all future payments to equityholders and debtholders?

PV of all the future payments to equity holders and debt holders = Value of the firm = Value of the unlevered firm + PV of interest tax shield.

Value of the unlevered firm = 100

PV of interest tax shield in case of perpetual debt = Tax rate x Debt = t x D = 30% x 80 = 24

PV of all the future payments to equity holders and debt holders = Value of the firm = Value of the unlevered firm + PV of interest tax shield = 100 + 24 = 124

h. How many shares of stock will the firm buy back with the $80MM?

Funds to buy back shares = 80

Share price = $ 10 / share

Nos of shares bought back = Funds to buy back share / share price = 80 / 10 = 8

i. Does the debt issuance create value, destroy value, or neither?

Value of the firm prior to buyback = 100

Value of the firm after buyback = 124

Clearly, the debt issuance has created value.

j. If there is value creation/destruction, who gets it or who pays for it?

The value created / destroyed belongs the equity holders or shareholders. This can be seen below:

Price per share prior to buyback = $ 10 per share

Value of the firm after buyback = 124

Debt =80

Value of equity = 124 - 80 = 44

Nos. of shares outstanding after buyback = 10 - 8 = 2

Price per share after buyback = 44 / 2 =$ 22 > 10 = Price per share before buyback

So, there is a value creation for the equity holders.