Use the information for the question(s)below.
Suppose that Rose Industries is considering the acquisition of another firm in its industry for $100 million.The acquisition is expected to increase Rose's free cash flow by $5 million the first year,and this contribution is expected to grow at a rate of 3% every year thereafter.Rose currently maintains a debt to equity ratio of 1,its corporate tax rate is 21%,its cost of debt rD is 6%,and its cost of equity rE is 10%.Rose Industries will maintain a constant debt-equity ratio for the acquisition.
-Given that Rose issues new debt of $50 million initially to fund the acquisition,the present value of the interest tax shield for this acquisition is closest to:
A)$24 million.
B)$50 million.
C)$20 million.
D)$15 million.

Question

Quizplus · Accepted Answer

The present value of the interest tax shield can be calculated as follows:
PV(Tax Shield) = TC x D x PV(rD)
where TC = corporate tax rate, D = new debt issued to fund the acquisition, and PV(rD) = present value factor for rD.

First, we need to calculate the present value factor for rD:
PV(rD) = [1 - 1 / (1 + rD)^n] / rD
where n = number of years the tax shield will exist.
Here, n = infinity, since the tax shield will exist as long as the debt is outstanding.
PV(rD) = [1 - 0] / rD = 1 / rD

Next, we can calculate the interest tax shield:
PV(Tax Shield) = TC x D x PV(rD)
PV(Tax Shield) = 0.21 x $50 million x (1 / 0.06)
PV(Tax Shield) = $17.5 million

However, the question asks for the present value of the tax shield for the entire acquisition, not just the initial debt issuance. To calculate this, we need to take into account the fact that Rose's free cash flow will increase as a result of the acquisition. The present value of the tax shield over the entire acquisition can be calculated as follows:
PV(Tax Shield) = TC x (D + PV(Free Cash Flow)) x PV(rD)
where PV(Free Cash Flow) = present value of the expected increase in free cash flow due to the acquisition.

The expected increase in free cash flow due to the acquisition is $5 million in the first year, growing at a rate of 3% per year thereafter. To calculate the present value of this cash flow stream, we can use the perpetuity formula:
PV(Perpetuity) = C / r
where C = cash flow in the first period, and r = discount rate.

Here, C = $5 million, and r = Rose's cost of equity, rE = 10%. The perpetuity formula can be simplified as follows:
PV(Perpetuity) = C / r = $5 million / 0.10 = $50 million

Therefore, the present value of the tax shield over the entire acquisition is:
PV(Tax Shield) = TC x (D + PV(Free Cash Flow)) x PV(rD)
PV(Tax Shield) = 0.21 x ($50 million + $50 million) x (1 / 0.06)
PV(Tax Shield) = $20.83 million

Rounding to the nearest million, the closest answer choice is (A)$24 million.

Use the Information for the Question(s)below