Final answer:
The present value of the interest tax shield for Rappaport Industries' perpetual bonds can be calculated using the formula: PV = (1 - tax rate) * coupon rate * face value / yield to maturity. Substituting the given values, the present value is $92,925. Option 4 is correct.
Step-by-step explanation:
The present value of the interest tax shield can be calculated using the formula: PV = (1 - tax rate) * coupon rate * face value / yield to maturity.
In this case, the tax rate is 21 percent, the coupon rate is 5.9 percent, and the yield to maturity is 6.2 percent.
Substituting these values into the formula, we get:
PV = (1 - 0.21) * 0.059 * $1,000 / 0.062 = $92,925
Therefore, the present value of the interest tax shield is $92,925.
The question posed is regarding the calculation of the present value of the interest tax shield for Rappaport Industries' perpetual bonds. The present value of the interest tax shield can be computed using the formula: Tax Rate x (Coupon Payment x Number of Bonds). Given the information, the coupon payment per bond is 5.9% of $1,000, which equals $59. With 4,500 bonds in existence, the total annual coupon payment is 4,500 x $59 = $265,500.
The present value of the interest tax shield is the tax rate of 21% applied to the total annual interest, which results in $265,500 x 21% = $55,755. However, as this is a perpetual bond, the interest tax shield is a perpetuity, and to find its present value, we divide the tax shield per period by the yield to maturity. Hence, the present value of the interest tax shield equals $55,755 / 6.2% = $92,925.