An 8.5 percent coupon bond issued by the State of Ohio sells for $1,000. What coupon rate on a corporate bond selling at $1,000 par value would produce the same after-tax return to the investor as the municipal bond if the investor is in the 25 percent marginal tax bracket?

Question

Quizplus · Accepted Answer

The after-tax return of the municipal bond is given by: 
After-tax return = Coupon payment * (1 - Marginal tax rate) + Capital gain / Purchase price
Since the bond is selling at par value, the capital gain is zero. 
Therefore, the after-tax return = Coupon payment * (1 - Marginal tax rate) / Purchase price
For the municipal bond, the after-tax return is 8.5% * (1 - 0.25) = 6.38%
To find the coupon rate on the corporate bond that would produce the same after-tax return, we can set up the equation: 
Coupon payment * (1 - Marginal tax rate) / Purchase price = 6.38%
Coupon payment * (1 - 0.25) / $1,000 = 0.0638
Coupon payment = $15.95
Therefore, the coupon rate on the corporate bond is $15.95 / $1,000 = 1.595% or 15.95%. However, this is the pre-tax coupon rate. To find the after-tax coupon rate, we need to adjust for the investor's 25% marginal tax rate. 
After-tax coupon rate = Pre-tax coupon rate * (1 - Marginal tax rate) 
After-tax coupon rate = 15.95% * (1 - 0.25) = 11.96%
Therefore, the coupon rate on the corporate bond that would produce the same after-tax return as the municipal bond is 11.33%. (Option C)

An 85 Percent Coupon Bond Issued by the State of Ohio