June 20, 2010
June 20, 2010
June 23, 2010
15.924.1 - 15.924.22
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.1,4,5,6 Insofar as the lender is concerned, the four payment plans are identical to the
Here, we explore differences among the four payment plans from both the and the lende perspectives. Sensitivity analyses are performed for the various payment plans and conclusions are drawn regarding the plans that maximize -tax present worth -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 or the lende perspective. Further, the performance of the fourth plan (a lump-sum payment at the end of the loan period) is radically
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.
In the early editions of Principles of Engineering Economy,2 four plans were presented for repaying a $10,000 loan in 10 years with interest at 6%. Plan I consisted of 10 equal annual interest payments of $600 and a $10,000 payment at the end of 10 years. Plan II consisted of 10 equal annual principal payments of $1,000, plus interest payments on the unpaid principal balance. Plan III, the familiar equal-annual-payment plan, consisted of 10 equal annual payments of $1,358.68. Plan IV consisted of a single payment of $17,908.49 after 10 years.
As subsequent editions were published, the interest rate in the example changed to reflect economic conditions at the time of publication. The most recent edition3 uses a rate of 9%. Accompanying the discussion of the example, the present worth of each plan is computed using a range of interest rates; again, the range of rates changed over the years. The point is made that the four plans are equivalent only at the stated interest rate, a rate which we refer to as the equivalent rate.
As we studied the results of the calculations involving a range of interest rates, we noted that the rank ordering of present worth values (from largest to smallest) was Plan IV, Plan I, Plan III, and Plan II when the interest rate was less than the equivalent rate. However, the rank ordering was
White, J., & Case, K., & Pratt, D. (2010, June), On The Differences Among "Equivalent" Loan Payment Plans Paper presented at 2010 Annual Conference & Exposition, Louisville, Kentucky. 10.18260/1-2--15915
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