# Calculating the cost basis on a tax free Zero Coupon Bond

A tax free zero coupon bond is issued with a yield to maturity of 3.5%. After some time, an investor buys the bond at 50. ( 50 cents on the dollar ). When he buys the bond, the bond has a yield to maturity of 3.4%. After some time, he sells the bond for 80 cents on the dollar. In computing his cost basis in the bond, for tax purposes, should he use the 3.4% interest rate or the 3.5% interest rate? I believe he should use the 3.5% interest rate which will save him tax money.

The investor is in the United States.

• Do you believe that because it would save tax money? I'm not a tax expert but I've never seen cost basis based on prices before an asset is acquired. There are ways that cost bases can be adjusted after it's acquired but the yield at issuance should be irrelevant. Also, if this is a tax free bond, what difference does it make what the cost basis is? Jul 7 at 21:17
• In other words, why do you think that the 3.5% interest rate should be used? What price does that yield correspond to? A higher yield would mean a lower price and thus a lower cost basis, which would mean more tax, not less. Jul 7 at 21:35
• @DStanley There maybe capital gain when the bond is sold. Therefore, when the bond is sold you need to compute the cost basis of the bond. In computing the cost basis of the bond you add in the accrued interest.
– Bob
Jul 7 at 21:49
• @DStanley By using a higher interest rate you recognize more interest. This results in a higher cost basis. A higher cost basis means less profit which means less tax.
– Bob
Jul 7 at 21:50
• @DStanley I am thinking ( guessing ) you use the 3.5% rate because that was the rate at which the bond was issued at.
– Bob
Jul 8 at 2:45

Yield to maturity is a derived value based on price, and vice versa. In calculating calculating capital gain for tax purposes, your cost basis is 50 (50 cents on the dollar), your exit price is 80 (80 cents on the dollar) so your capital gain per dollar of face value is 30 cents.

You can't "choose" a yield to maturity to use for your cost basis. If you calculated YTM on the 50 cent zero coupon to be 3.4%, that's what yield to maturity (or interest rate, you seem to use them interchangeably) would be stated as your cost basis.

"Changing" the interest rate on a zero coupon bond, by definition, involves changing it's present value, or price. If in your example you have no intention of restating at the purchase price of your bond and your entry price is still 50% of par, then your yield to maturity has to be 3.4%. The only way the yield to maturity used for your cost basis could be 3.5% is if the purchase price on the bond was restated to something below 50% par, say 45% par.

• I do not understand what you mean by: restating at the purchase price
– Bob
Jul 15 at 18:57
• My capital gain would not be 30 cents per bond because you need to add in the accrued interest to the cost basis.
– Bob
Jul 15 at 19:00
• Hah...you said this is a zero coupon bond, no? No accrued interest on a zero coupon bond :-) Interest rate = yield to maturity. Yield to maturity and price are inversely related, if one goes up the other goes down. Your original question was "what interest rate should I choose". What I am saying is there is no "choice" to be made. The price of the bond at purchase: 50% par = yield to maturity 3.4%. The price of the bond at sale: 80% par = yield to maturity 3.0% (something less than 3.4). Jul 16 at 2:10