ON THE DIFFERENCES AMONG 'EQUIVALENT' LOAN PAYMENT PLANS

摘要

Throughout its many editions, Principles of Engineering Economy, by Eugene L. Grant and, subsequently, in partnership with W. Grant Ireson and Richard S. Leavenworth, provides an example in which a loan can be repaid using one of four different plans: I (interest payments only until the end of the loan period, at which time the principal is repaid); II (equal principal payments, plus interest on the unpaid balance of the loan); III (equal periodic payments); and IV (single payment of principal and accumulated interest at the end of the loan period). These and similar payment plans appear in a number of other books. Insofar as the lender is concerned, the four payment plans are equivalent. However, unless the borrower's time value of money is identical to the lender's interest rate, the four plans are not equivalent for the borrower. Here, we explore differences among the four payment plans from both the borrower's and the lender's perspectives. Sensitivity analyses are performed for the various payment plans and conclusions are drawn regarding the plans that maximize the borrower's after-tax present worth and the lender's after-tax present worth in an inflationary economy. Interestingly, the payment plan that is emphasized in engineering economy courses and found to be most prevalent in practice, a uniform series of loan payments, does not perform as well as other plans when considered from either the borrower's or the lender's perspective. Further, the performance of the fourth plan (a lump-sum payment at the end of the loan period) is radically different from the other plans when the lender's interest rate is greater than the borrower's time value of money. From the analysis, it is evident that neither the borrower nor the lender should be indifferent when choosing a payment plan from among those considered.