# A discounted cash flow analysis for financing alternatives.

When a home buyer shops for a mortgage, one difficult decision that he or she has to make is whether to pay points to lower the prevailing market interest rate. The term "points" is sometimes used to describe certain charges paid by a borrower to a lender. They are also called loan origination fees, maximum loan charges, or premium charges. If the payment of these charges is only for the use of money, it is prepaid interest. A point is equal to 1% of the amount of loan. Most financing institutions will reduce one-eighth percentage of the interest rate for a thirty-year mortgage. Many accountants probably would advise their clients that the primary factor in making the decision is the estimated time that one intends to live in one's property. This is called the payback period which is the time required to recover the prepaid points. The major weakness of the payback approach is its neglect of the time value of money. A dollar received today is worth more than a dollar received one or two years from today. Therefore, the present cash outflows of prepaid points and future cash inflows of interests savings, before they can be compared, must be converted to a common denominator, which is the present value.This article develops a discounted cash flow model for evaluating two financing alternatives: the first alternative (with the higher interest rate but with lower points or loan origination fees), and the second alternative with the lower interest rate (but with higher points or loan origination fees). Surprisingly, there is no evidence to show any benefits of paying the points to reduce the monthly payments under many circumstances. The model can also be used for comparing the mortgage contracts between two companies. The spreadsheet software used here is LOTUS 1-2-3 for Windows 95, but the application is readily adaptable to other spreadsheet software such as Microsoft Excel.

The Decision Model

The decision model for evaluating financing alternatives entails the following steps:

1. Develop loan amortization schedules for the two financing alternatives. Choose the one with the higher interest rate and the lower financing cost as the first case and the one with the lower interest rate and the higher financing cost as the second case.

2. Compute the difference of financing cost between these two alternatives.

3. Subtract the monthly payment of the second case from the monthly payment of the first case. This is the amount of monthly payment savings for the second case.

4. Select the cost of capital rate or minimum desired rate of return. This rate of return is different from person to person. For example, an aggressive investor who constantly invests in equity mutual funds will have a higher rate of return than a conservative investor who invests in fixed income instruments.

5. Compute the cumulative cost savings by adding up the cash inflows from the monthly payment savings, the difference of the unpaid principal balance between the two financing alternatives, and the initial cash outflows from paying loan origination fees or points. This figure does not consider the time value of money.

6. Obtain the present value of the cumulative cost savings by multiplying the discount factor with the cash inflows and the cash outflows for each period.

7. Choose the minimum period that the borrower intends to hold the mortgage.

8. If the present value of cumulative cost savings is positive at the last period that the borrower intends to hold the mortgage, the second alternative with the lower interest rate but the higher initial financing cost should be accepted. If the amount is negative, the first alternative with the higher interest rate but the lower initial financing cost is desirable.

To illustrate how the electronic spreadsheet can facilitate the computation, an insightful example follows. On December 1, 1997, John Smith considered borrowing $100,000 from Central Mortgage Bank which offered him two alternatives: the first alternative was a thirty-year mortgage at 7.875% with the prepayment of one loan origination fee; the second alternative was a thirty-year mortgage at 7.625% with the prepayment of two points and one loan origination fee. The first payment started on January 1, 1998, and his cost of capital rate was 10 percent. The steps for each cell number used to prepare the comparison schedule are as follows:

1. E1: Enter Alternative Financing Comparison.

2. E2: Enter Discounted Cash Flow Approach.

3. B3: Enter Case I.

4. F3: Enter Case II.

5. A4: Enter Amount of Loan:.

6. C4: Enter 100000; change format to currency with two decimal places.

7. AS: Enter Loan Fees and Points:.

8: C5: Enter 1000; change format to currency with two decimal places.

9. A6: Enter Years of Financing:

10. C6: Enter 30.

11. A7: Enter Interest Rate.

12 C7: Enter .07875; change format to percentage with three decimal places.

13. A8: Enter Monthly Payment:.

14. C8: Enter @Round(@PMT(C4, C7/12,C6(*)12),2); change format to currency with two decimal places.

15. A9: Enter Cost of Capital Rate:.

16. C9: Enter .10; change format to percentage with three decimal places.

17. E4: Enter Amount of Loan:.

18. G4: Enter 100000; change format to currency with two decimal places.

19. ES: Enter Loan Fees and Points:.

20. GS: Enter 3000; change format to currency with two decimal places.

21. E6: Enter Years of Financing:.

22. G6: Enter 30.

23. E7: Enter Interest Rate:.

24. G7: Enter .07625; change format to percentage with three decimal places.

25. E8: Enter Monthly Payment:.

26. G8: Enter @Round(@PMT(G4, G7/12, G6* 12), 2); change format to currency with two decimal places.

27. E8: Enter Monthly Payment Savings:.

28. G9: Enter +C8-G8; change format to currency with two decimal places.

29. B11: Enter Loan Amortization for Case I.

30. A13: Enter "Period.

31. B13: Enter "Interest.

32. C13: Enter "Principal.

33. D13: Enter "Unpaid.

34. B14: Enter "Paid.

35. C14: Enter "Paid.

36. D14: Enter "Principal.

37. A17: Enter O; change format to general.

38. D17: Enter +C4; change format to currency with two decimal places.

39. A18: Enter +A16+1; change format to general.

40. B18: Enter @Run(+D17*$C$7/12,2); change format to comma with two decimal places.

41. C18: Enter $C$8-B18; change format to comma with two decimal places.

42. D18: Enter +D 17-C18; change format to comma with two decimal places.

43. F11: Loan Amortization for Case II

44. E13: Enter "Period.

45. F13: Enter "Interest.

46. G13: Enter "Principal.

47. H13: Enter "Unpaid.

48. F14: Enter "Paid.

49. G14: Enter "Paid.

50. H14: Enter "Principal.

51. E17: Enter 0; change format to general.

52. H17: Enter G4; change format to currency with two decimal places.

53. E18: Enter E17+1; change format to general.

54. F18: Enter @Run(H17*$G$7/12,2); change format to comma with two decimal places.

55. G18: Enter $G$8-F18; change format to comma with two decimal places.

56. H18: Enter +H 17-G 18; change format to comma with two decimal places.

57. I12: Enter "Unpaid.

58. I13: Enter "Principal.

59. I14: Enter "Savings.

60. J13: Enter "Interest.

61. J14: Enter "Savings.

62. K12: Enter "Cumulative.

63. K13: Enter "Cost.

64. K14: Enter "Savings.

65. L12: Enter "Present Value.

66. L13: Enter "of Cumulative.

67. L14: Enter "Cost Savings.

68. I16: Enter Initial Cost Difference:.

69. K16: Enter $C$5-$G$5; change format to currency with two decimal places. This figure represents the additional points or loan origination fees for Case II.

70. K17: Copy form K16 to K17.

71. I18. Enter +D18-H18. This figure represents the additional principal payments for Case II. The figure will be relevant when one pays off the loan.

72. J18: Enter +B18-F18; change format to comma with two decimal places. This figure represents the monthly interest savings for Case II.

73. K18: Enter +KI+J1; change format to comma with two decimal places. This figure represents the cumulative cost savings of Case II. The figure does not consider any time value of money.

74. L16..L17: Copy K16..K17 to L16..L17.

75. L18: Enter +$L$17+@PV($G$9,$C $9/12,A18)+I18/(l+$C$9/12)^A18; change format to comma with two decimal places.

This figure represents the present value of the cumulative cost savings of Case II. The first item in the cell formula is the additional points for Case II. The second item is the present value of cumulative payment savings up to the current period. The third item is the present value of extra principal payments of Case II. This item will be relevant when one decides to pay off the loan. Both the second and the third item are discounted at the cost of capital rate.

76. A19 through L377: Copy from A18.. L18 to E19..L377.

Discussion

Exhibit I illustrates a portion of the comparison schedule between Case I, the financing alternative with the higher interest rate, but the lower points or loan [TABULAR DATA FOR EXHIBIT I OMITTED] origination fee, and Case II, the financing alternative with the lower interest rate, but the higher points or loan origination fees. If we use the traditional payback method without considering the time value of money, the payback period will be $2000/$17.28 or 115.74 months. If we consider the additional principal payments of Case II, the payback period will be 95 months. If we discounted the future cash savings of Case II at the cost of capital rate of 10%, the additional points or fees will never be paid back. This is because the break-even point is at the cost of capital rate of 9.815 percent. If the cost of capital rate is the average money market mutual fund return in recent years, the payback period is 134 months. This indicates that even the most conservative borrowers will not be able to recover the additional points and loan origination fees, because the average life of a home mortgage is about 7 years. Since the points and loan origination fees are excellent profits for financing companies, one should always negotiate the mortgage down to no points or loan origination fees, if at all possible.

One may argue that the loan origination fees and the points of a loan that are used to buy a main home are deductible in the year paid under the current tax law. This will provide the additional cash inflow for the borrower. However, the additional interest payments for the financing alternative with the higher interest rate and the lower points are also deductive throughout [TABULAR DATA FOR TABLE II OMITTED] the life of the loan. Exhibit II illustrates the impact of a tax benefit at the 28% tax bracket. Again, no benefits are shown at all over the entire life of the loan. Indeed, after the 190th payment, the cumulative present value with the higher interest deduction will outweigh the benefit of an initial points deduction. Furthermore, once a taxpayer's adjusted gross income exceeds $117,950, his or her deductible amount of points and home mortgage interest are gradually reduced to only 20 percent. The benefit of paying additional points is further compromised. Therefore, one can completely ignore the income tax effect in making the decision.

To construct a comparison schedule for Exhibit II which considers the tax effect, one needs to modify the cell formula of K18 to +K18+J18*.28 and the cell formula of L18 to +L17+@PV ($G$9,$C$9/[12,A18)+I18/(1+$C$9/12)^A18-@PV ($G$9,$C$9/12,A17)-I17/(1+ $C$9/12)^A17-.28*J18/(1+$C$9/12)^A18, where .28 is the tax bracket for the taxpayer. The first item of the cell formula of L18 is the present value of cumulative cost savings up to the previous period; the second item is the present value of an ordinary annuity of monthly payment savings for Case II; the third item is the present value of the additional principal payments for Case II; the fourth and the fifth item removes the cumulative effect of the second and the third item because they are also accumulated into the first item; the sixth item is the tax savings of Case I (which will be a negative cash flow for Case II), because the additional interest payment for Case I is deductible. Care must be taken that if one's adjusted gross income is over $117,950 one cannot use Exhibit II for evaluation.

Conclusion

This article has demonstrated that paying the points to reduce the interest rate of a loan is, never a wise decision except for a very conservative investor who intends to hold the mortgage for more than eleven and half years. The speed and accuracy of constructing a comparison schedule for two financing alternatives can be significantly improved by using a spreadsheet to perform computations. Once the first spreadsheet is prepared, the decision maker can simply change the parameters in the spreadsheet for further calculations, without being forced to redo the entire spreadsheet. This process can be completed in several minutes instead of a few hours. The decision maker can efficiently apply the discounted cash flow approach instead of a rough-and-ready model such as the payback approach.

Richard C. Chen, PhD, CPA, is an associate professor of accounting at Eastern Kentucky University. He has published numerous articles in professional and academic journals and holds a CPA certificate from Texas.

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Author: | Chen, Richard C. |
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Publication: | The National Public Accountant |

Date: | Jul 1, 1998 |

Words: | 2247 |

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