Question

Which are true for after-tax cost of debt: 1. Increases as firm's bond increases II. Increases when market interest rate increases III. Increases as tax-rates decrease IV. Increases as bond prices increase Select one a. ll and Ill only b. I and Ill only C. II, III, and IV only d. 1, II, III, and IV O

Answer 1

Answer:

When bonds issued increases, absolute amount of debt increases. As a result, given other things including tax rate constant, amount of interest on debt in absolute terms increases but not the cost of debt in percentage terms.

Once a bond is issued, subsequent changes in market interest rate has no effect on the cost of debt of the issuer, though the same will cause change in the price of the bond. Hence statements II and IV are not correct.

Interest on debt is exempted for tax. After tax cost of debt is the cost of debt minus tax exemption on the interest. When the tax rate decreases, the tax exemption thus reduced while computing after-tax cost gets reduced. As a result, the net product of after tax cost of debt will be higher when tax rate is reduced.

Example:

Bond Face Value: $1,000 Coupon rate: 10% Amount of interest: $100

If the tax rate is 25%, tax exemption on interest on bond= $100*25% = $25. Net cost ==$100-$25 = $75.

After tax cost of debt= ($75/$1000)*100 = 7.5%

If tax rate decreases to 20%, tax exemption= $100*20%= $20. Net cost= $100-$20 = $80

After tax cost of debt= ($80/$1000)*100 = 8%

Hence the statement III is true.

Selecting from the options given, answer is b. Statements I and III only