Peter Clemenza and Luca Brasi are arguing about the following bonds. Both bonds

Question

Peter Clemenza and Luca Brasi are arguing about the following bonds. Both bonds are for 5 years, each with the par value of $100,000. The coupon rates are compounded semi-annually. The coupon rate for bond #1 (favored by Mr. Clemenza) equals 1.8% and is tax free. The coupon rate for bond #2 (favored by Mr. Brasi) equals 2.6%, but it is subject to both federal and state taxes. The combination of federal and state taxes on this type of bonds usually average to about 30%. Peter Clemenza argues that since one does not have to pay taxes on bond #1, then it is a better investment. Luca Brasi says the bond #2 is a good investment, because it will earn higher return than the bond #1. Can you settle their argument? Which bond would you recommend?

Explanation / Answer

Par value = $100000

The coupon rates are compounded semi-annually. It means you receive two payments each year.

Mr. Clemenza – coupon rate for Bond 1 is 1.8% and it is tax free

Mr. Clemenza would receive 100000*(1.8/2) which is equal to 900 twice a year for the next n years

Note: The coupon rates are compounded semi-annually so we divide the coupon rate by 2

n= years of maturity (missing in the question)

So, Mr. Clemenza would receive (900*2) = 1800 each year. (Remember semi-annually)

Now Mr. Brasi - coupon rate for Bond 2 is 2.6% and it is subject to both federal and state taxes

The combination of federal and state taxes on this type of bonds usually average to about 30%.

Tax-Equivalent Yield = Tax-Exempt Interest Rate / (1 – Your Federal Income Tax Rate)

                               = 1.8%/ (1-0.30)

                               = 2.57%

Since there is not much difference between 2.6% and 2.57% (almost same), both the bonds are equally good.

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