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Subject:  Discounting YTMs Date:  7/22/2011  4:20 PM
Author:  charliebonds Number:  33115 of 37023

The Dutch auction of Zion Bankcorp's 5-year, 5%, triple-BBBs closes on 07/27. At the current, market-clearing price of 97.000, the bond would offer a nominal 5.70% to maturity. Is this a good deal? On the surface, it would seem to be, given their current yield-curve below (where price includes a commish of a $1 a bond and the YTMs are as E*Trade calculates them):

Cpn Due Price YTM
5.000 11/07/12 103.861 1.92%
5.650 05/15/14 104.100 4.08%
7.750 09/23/14 109.950 4.34%
6.000 09/15/15 104.100 4.89%
5.500 11/16/15 103.600 4.57%
5.500 11/16/15 101.615 5.08%
5.500 05/10/16 101.972 2.94%(YTC)

However, taxes have to be paid on gains, and inflation will erode returns. So let’s run the numbers. Excel’s YIELD formula asks for the following facts: Settlement, Maturity, Coupon_Rate, Purchase_Price Remption_ Price, Coupon_Frequency, and (optionally) Year_Type, as below:


If one’s marginal tax-rate on ordinary-income is 25% and on cap-gains, 15%, then the coupon degrades to .035 and the redemption to 97.450. When those numbers are used in the formula, the YTM becomes 3.69%. But the situation is worse. If inflation is assumed to be 5%, then the coupon is further degraded and becomes .031 and the redemption degrades to 78.297. The net-effect is that buying the bond at 97 would result in an annual loss of purchasing-power of about 47 bps, aka, a tax-and-inflation-adjusted YTM of (0.47%) That’s tolerable, but it probably wasn’t what was intended, nor what will be achieved, because it is probable that the bond will be sold at a higher price than the current bid. Some fussing in Excel suggests that a price of 94.935 would put a buyer even, and anything less would begin to appreciate capital.

Why run these kinds of exercises? So that one's bond-shopping can be done efficiently, 500 bonds at time, to find the very few that merit a further look.
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