Question

Your firm has debt worth $200,000, with a yield of 9 percent, and equity worth $300,000. It is growing at a 5 percent rate, and faces a 40 percent tax rate. A similar firm with no debt has a cost of equity of 12 percent. Under the MM extension with growth, what is your firm's cost of equity, rEL?

Answer 1

Debt D = $200,000 and yield of debt rd = 9%

Equity E = $300,000

Cost of equity for an unleveraged firm re (u) = 12% or 0.12

Growth rate g = 5% or 0.05

Tax rate t = 40% or 0.4

Total value of the firm = D + E = $200,000 + $300,000 = $500,000

Now,

Total value of unlevered firm + firm's tax shield = Total value of the firm = $500,000

Or the total value of unlevered firm = $500,000 - firm's tax shield

Where firm's tax shield = (rd * t * D) /(re (u) – g)

= ( 0.09 * 0.40 * $200,000 ) / (0.12 – 0.05) = $102,857

Therefore,

Total value of unlevered firm = $500,000 – $102,857 = $397,143

Debt decreases the firm’s taxable income and builds a tax shield for the firm. This tax shield increases the value of the firm. Here the value of your firm's tax shield is $102,857