Your firm has debt worth $200,000, with a yield of 9%, and equity worth $300,000. It is growing at a 5% rate, and its tax rate is 40%. A similar firm with no debt has a cost of equity of 12%. Under the MM extension with growth, what is the value of your firm's tax shield, i.e., how much value does the use of debt add?
A) $92,571
B) $102,857
C) $113,143
D) $124,457
E) $136,903

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the cost of equity for our firm using the MM formula with growth:
Re = R0 + (1-T) * (D/E) * (R0 - Rb) + g
Where,
Re = Cost of equity for our firm
R0 = Cost of equity for the unlevered firm (given as 12%)
T = Tax rate (given as 40%)
D/E = Debt-to-equity ratio (200,000/300,000 = 0.67)
Rb = Cost of borrowing (given as 9%)
g = Growth rate (given as 5%)

Plugging in the values, we get:
Re = 12% + (1-0.4) * (0.67) * (12% - 9%) + 5%
Re = 15.14%

Next, we need to calculate the value of the unlevered firm. Using the formula:
Vu = E / Re
Where,
Vu = Value of the unlevered firm
E = Equity value (given as $300,000)
Re = Cost of equity for the unlevered firm (calculated as 15.14%)

Plugging in the values, we get:
Vu = 300,000 / 15.14%
Vu = $1,980,861

Now, we can calculate the value of the levered firm using the formula:
Vl = Vu + Tc * D
Where,
Vl = Value of the levered firm
Tc = Tax shield (to be calculated)
D = Debt value (given as $200,000)

Plugging in the values, we get:
Vl = 1,980,861 + 0.4 * 200,000
Vl = $2,058,861

Finally, we can calculate the value of the tax shield as the difference between the value of the levered firm and the value of the unlevered firm:
Tc = Vl - Vu
Tc = 2,058,861 - 1,980,861
Tc = $78,000

Therefore, the value of the tax shield is $78,000, which corresponds to answer choice B.

Your Firm Has Debt Worth $200,000, with a Yield of 9