Question

Compute the present value of interest tax shields generated by these three debt issues. Consider corporate taxes only. Assume that the marginal tax rate is T_c = 0.30.


a. A $2,900, one-year loan at 7%. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. A three-year loan of $2,900 at 7%. Assume no principal is repaid until maturity. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. A $2,900 perpetuity at 6%. Figure the present value.

Answer 1

(1) Interest tax shield is the tax saved by an interest expense.We will first find an interest expense

=$2,900*7%

=$203

Tax saved on interest = $203*0.30

=$60.9

we will apply 7% cost of debt as cost of capital to find present value of an interest tax shield

=FV /(1+r)^n

• n= year 1
• r =0.07
• FV=$60.9

=($60.9)/(1+0.07)^1

=$56.92

(2) 3 year loan $2,900 at 7%

There will be an interest tax shield of $60.9[as calculated in 1 above] for three years

=($60.9)/(1+0.07)^1+($60.9)/(1+0.07)^2+($60.9)/(1+0.07)^3

=$159.82

(3)The perpetuity loan of $2,900 at 6% offers an annual interest tax shield of $2,900*6%*30%=$52.2

• Value of tax shield in perpetuity = Annual Interest Tax shield/cost of capital            

                                                              =$52.2/0.06

                                                              =$870