D. l. tuckers has $48,000 of debt outstanding that is selling at par and has a coupon rate of 6.75 percent. the tax rate is 35 percent. the firm intends to keep this level of debt financing for the foreseeable future. what is the present value of the tax shield?

$16,800 ($1,134 tax shield discounted at 6.75% to infinity)

Explanation:

Since debt interest payment is tax deductible, D.L. Tuckers, will enjoy an annual tax shield from the interest payment. This is computed as follows.

Debt Outstanding: $48,000

Interest payment: 6.75% * $48,000 = $3,240

Let's assume the in a given year, the profit of the Company was $x.

The tax payable on the profit (without the shield from debt interest) would be

= $x * 35% = 0.35x

However, due to the tax shield, the taxable profit of the Company will be reduced by the interest payment.

Taxable Profit = $x - $3,240

Tax payable = 35% * (x - 3,240) = 0.35x - 1,134

Thus, as a result of the tax shield from interest payment, the tax payable by the company is reduced by $1,134. This will recur annually since the company intends to keep this level of debt financing for the foreseeable future.

The effective interest payable (after tax) can also be computed using the formula below.

Effective after tax interest =

= $3,240 * (1 - 35%)

= $3,240 * 65% = $2,106.

With an effective after tax interest of $2,106, the tax shield is the difference between the actual interest and the effective after tax interest

Tax shield = $3,240 - $2,106 = $1,134

Therefore, the present value of the tax shield is derived by discounting the tax shield with the appropriate discount rate, assumed to be the coupon rate in this case.

PV of Tax shield =

=

PV of Tax Shield = $16,800.

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