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Car-Buying Advice Uses Faulty Logic

September 29, 1985

There are certainly times when getting a loan is a useful stratagem, but the case cited in S. J. Diamond's "For What It's Worth" column ("Credit or Cash? The Difference Can Add Up," Sept. 23) is not one of them. In this case, since poor advice is being offered to people who might suffer from following it, it seems appropriate to provide a demurrer.

In brief, Geoffrey Keppel of Berkeley concluded that buying a car on time was better than paying cash for it and Diamond agreed with him. The conclusion reached is simply not correct, at least under the conditions described. The following explains why this is so.

The borrower, whom I will call "B", has $8,239.05 on hand to cover the balance due on the car (no mention is made of a down payment, but presumably B and also the cash customer, known to his friends as "C", have enough money to cover it also) but he chooses instead to finance the car at 14.2% per annum, and to invest the money at 8% per annum. The loan of $8,239.05 requires 48 payments of $225.97 per month, and thus the cost of the contract is $10,846.56, of which $2,607.51 is interest.

On the other hand, $8,239.05 invested at 8% compounded monthly for 48 months yields $11,334.18, of which $3,095.13 is interest. Thus B appears to walk away with a gain because of the interest differential of $487.62. This paltry return (less than 1.5% per annum on the original investment) pleases B mightily, especially since he observes that C has accrued no such differential.

Unfortunately, B has overlooked one point: B is obliged to pay $225.97 per month for 48 months, while C is not. To see what this implies, let us have C invest $225.97 per month, at 8% compounded monthly. Now the two cases are more nearly alike, in that both B and C spend $8,239.05 initially (along with the unspecified down payment), and they each spend $225.97 per month for four years. At the end of the period C's savings plan gives him $12,733.39. B's savings plan gave him $11,334.18, as we saw, or $1,399.21 less than C's.

Another way of looking at it is that B's taxable income is $487.62, while C's is $1,886.83. The net after taxes may vary according to B's and C's tax brackets, but will always represent a considerable net advantage for C. Even if C gets only 6% on his savings, he still ends up $890.30 better than the clever Mr. B.

Diamond generalizes the case under the name "Sperling's Rule," which incorporates the same error--forgetting that the money needed to repay the loan is available to the cash customer for investment, or, flexibly, for any other useful purpose that may arise. The correct generalization I shall call "Webber's Rule" (although it has been known and followed at least as long as bankers have existed)--"If you have the money, borrow only when the rate of interest you pay is less than the rate of interest you can receive by investing the money." Simple and obvious? Yes, of course, but with the virtue of being true.


Sherman Oaks

The preceding three letters, along with more than 100 others received by The Times, are correct. S. J. Diamond will address the issue further in her column Monday.--Editor

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