Crossover Point The February 1986 AAII Journal featured an article by Alan Pope exploring the concept of the crossover point--the price below which the benefits of holding a stock to long-term and paying lower taxes on the capital gain vanish. The program given below is an adaptation and extension of the ideas given in Mr. Pope's article, which readers should refer to for additional discussion of the issues involved. In determining the crossover point, one calculates the maximum allowable price drop (ADP) that would equate the after-long-term-taxes net profit (if you hold) with the after-short-term-taxes net profit (if you sell now). Then if the actual price drop between now and when the stock goes long-term is smaller than the maximum allowable price drop, your after-taxes net profit if you sell when the stock goes long-term will be greater than if you sell it while still short-term. Unfortunately (and possibly for the sake of simplicity), the calculation of ADP in the Journal article failed to take into account the time value of money--the notion that a sum of money in the present is worth more than that same sum of money in the future. (If offered $1,000 now or $1,000 one year from now, most people would prefer to have the $1,000 now. Why? For one thing, you could use the money now to buy something you just can't wait to have. For another, you could invest the money in a money market fund earning 7%, say, and have $1,070 at the end of the year. Thus, in one sense, $1,000 now is worth $70 more than $1,000 a year from now.) As a corollary to this, it is better to receive benefits sooner rather than later, and to incur costs later rather than sooner. Accordingly, when comparing sums of money at different dates, one must first put them in a common frame of reference. This is usually done by means of discounting all future values to their present values. It could be that, in order to take advantage of the lower long-term capital gains tax rates, it is advantageous to wait until the security goes long-term. On the other hand, postponing the sale also postpones your profit, and future profits must be discounted. Similarly, the relative benefit of paying lower taxes is not felt with full force immediately; rather, it is felt the following year at tax time. Thus, in general, the ADP shrinks when the time value of money is taken into account. But, consider this: Suppose you bought a security after June 30, 1986, implying that it will go long-term after January 1, 1987. Suppose also that the year is still 1986. If you sell now, you will pay taxes on your capital gain in 1987. But if you sell when the security goes long-term, you are putting off the payment of taxes on your capital gain for one additional year, until 1988. In this case, the time value of money factor tends to work in favor of selling long- term. In order to sort out all these different time value of money effects, one should discount all future cash flows to their present values before solving for the time-weighted ADP. The program Crossover Point ("CRSOVR") presented below does this. (For the sake of completeness, but at the expense of added complexity, the program could also take into account dividends and commissions. Analysis suggests that, in general, the impact of these is relatively insignificant--they "come out in the wash"--when compared to the discounting effects.) When you run the program, it asks you for the stock's purchase price, its current price, the date of purchase, and today's date. You must also indicate, by modifying the program code: the most likely month and day of your tax payments, your marginal tax rate, and the short- term, risk-free interest rate. (These last three data items will vary only occasionally. Rather than have you input these values each time you run the program, a better procedure is to have you modify the program code only when changes in one or more of the three variables call for it. Whenever you modify the program in this way, be sure to save the modified version to disk before turning off your computer.) Given these data, the program calculates the date when the stock will go long-term, the allowable price drop (in percent), and the stock's crossover price. Embellishing the example given in the Journal article: Suppose you purchased 100 shares of stock at $100 per share on December 10, 1985, and the price today, March 30, 1986, stands at $140. You are in the 50% tax bracket, you typically pay your taxes on the last day possible (in this case, April 15, 1987), and the going money market rate is 7%. What is the crossover price? First, if you haven't already done so, be sure to modify the following lines of program code (note that there is no need to change line 2120): 2130 T = 50: REM ... 2140 I = 7: REM ... Run the program, and as a reminder, the coded data are displayed: MONTH & DAY OF TAX PAYMENT: 4/15 MARGINAL TAX RATE (%): 50 INTEREST RATE (%): 7 You then answer the following questions: WHAT WAS THE PURCHASE PRICE ($): 100 WHAT IS THE CURRENT PRICE ($): 140 WHAT WAS THE PURCHASE DATE? 12,10,1985 WHAT IS TODAY'S DATE? 3,30,1986 and momentarily the program produces this output: DATE STOCK WILL GO LONG-TERM: 6/11/1986 ALLOWABLE PRICE DROP (%): 8.3 CROSSOVER POINT ($): 128.38 (If you modify the program code by setting I=0, thereby nullifying the time value of money effects, then rerun this example, the program computes a time-neutral ADP of 10.71%, which matches Mr. Pope's results. Note that, as expected, factoring in the time value of money shrinks the ADP and raises the crossover point compared to when you ignore the effects of discounting.) You must now project the course of the stock's price between the present and June 11, 1986, the date when the stock will go long-term. If you expect the price to rise above it current level, hold onto the stock for now. If you expect the price to go into a more or less continual decline, you must decide: Is it likely to be above or below the crossover price, $128.38, on the date when it goes long-term? If below, then sell now. If above, then hold (and pray that your price projection is accurate). Even if the price declines, but by no more than 8.3%, and thus your before-tax profit will be smaller than if you sell immediately, your after-tax profit will be greater due to your future lower tax charge. And, as Mr. Pope points out, holding onto the stock gives you a "grace period" during which the stock might revert to a rising price trend. What if you lose the bet and the price falls below the crossover point before the stock goes long-term? Then you could determine a new crossover price and decide anew whether to hold or sell; or your could execute a stop-loss order based on the original crossover price. If you hold onto a declining stock in the hope of benefitting from lower capital gains taxes when it goes long-term, you are taking a gamble. The Crossover Point program won't eliminate the risk, but it should help give you a clearer picture of the odds. Robert Osterlund