In: Finance
JJP Corporation is a publicly traded firm. The market value of
its equity is£35,000,000 and its debt £15,000,000. The yield to
maturity of the debt is 5%, the equity–holders require a 20%
return, and the company pays 30% corporate tax. They have recently
decided to repurchase £5,000,000 worth of equity, and finance the
repurchase through the issuance of new debt.
a) Will this change in capital structure affect the market value of
the firm?
b) How will the return on equity be affected by this change? What
is the new return on equity of the company?
a. Change in capital structure affect the market value of the firm:
Before repurchase,
Market value of equity = 35,000,000
Market value of debt = 15,000,000
Total market value of the firm = 35,000,000 + 15,000,000 = 50,000,000
Post repurchase of 5,000,000 worth of equity by issuance of debt
Market value of equity = 35,000,000 - 5,000,000 = 30,000,000
Market value of debt = 15,000,000 + 5,000,000 = 20,000,000
Total market value of the firm = 30,000,000 + 20,000,000 = 50,000,000
Thus, the total market value of the firm remains same as 50,000,000 both before repurchase and after repurchase. Hence the capital structure does not affect the market value of the firm.
b. Impact to return on equity
Before repurchase:
Market value of equity = 35,000,000
Market value of debt = 15,000,000
Total market value of the firm = 35,000,000 + 15,000,000 = 50,000,000
Propotion of equity = 35,000,000 / 50,000,000 = 70%
Propotion of debt= 15,000,000 / 50,000,000 = 30%
Cost of equity = 20% (required rate of return)
Cost of debt = Yield to maturity * (1-tax rate) = 5%*(1-30%) = 3.5%
Weighted average cost of capital = (Propotion of equity * Cost of equity )+(propotion of debt * cost of debt) =
(70%*20%)+(30%*3.5%) = 15.05%
Post repurchase,
Market value of equity = 35,000,000 - 5,000,000 = 30,000,000
Market value of debt = 15,000,000 + 5,000,000 = 20,000,000
Propotion of equity = 30,000,000 / 50,000,000 = 60%
Propotion of debt= 20,000,000 / 50,000,000 = 40%
Cost of debt = Yield to maturity * (1-tax rate) = 5%*(1-30%) = 3.5%
Let new cost of equity be X
Weighted average cost of capital = (Propotion of equity * Cost of equity )+(propotion of debt * cost of debt) =
15.05% = (60%*X%)+(40%*3.5%)
15.05% = (60%*X%)+1.40%
15.05%-1.40% = 60%*X%
13.65% = 60%*X%
X = 13.65%/60% = 22.75%
Thus, new cost of equity = 22.75%
Hence, the change in capital structure has increased the cost of equity from 20% to 22.75% (2.75% increase).