Brueggeman17e_Chap06_PPT_accessible.pptx

Real Estate Development and Investment

1. Chapter 6 Mortgages: Additional Concepts, Analysis, and Applications Copyright 2022 © McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill LLC.

2. Incremental Borrowing Cost Assume two borrowing alternatives for purchasing a property for $100,000: 80% C P M for 25 years at 6 percent. 90% C P M for 25 years at 7 percent. Alternative Loan Amount Monthly Payment I @ 6% $80,000 $515.44 II @ 7% $90,000 $636.10 Difference $10,000 $120.66

3. What would be the incremental cost of borrowing the additional $10,000 in Alternative II? n = 25 × 12 = 300. P V = −$10,000. P M T = $120.66. F V = 0. Solve for i = 1.1698% (monthly). Solve for i = 14.04% (annually = 1.1698 × 12).

4. Incremental Borrowing Cost: Early Repayment Assume the loan is repaid after five years instead of being held for the entire loan term. Alternative Loan Amount Monthly Payment Loan Balance After Five Years I @ 6% $80,000 $515.44 $71,945.67 II @ 7% $90,000 $636.10 $82,045.94 Difference $10,000 $120.66 $10,100.27

5. What is the impact of early repayment on the incremental borrowing cost? n = 5 × 12 = 60. P = −$10,000. P M T = $120.66. F V = $10,100.27. Solve for i = 1.2180% (monthly). Solve for i = 14.62% (annually = 1.2180 × 12).

6. Incremental Borrowing Cost: Origination Fees Assume loan origination fees are charged on both loans as follows: Alternative I: 2 points. Alternative II: 3 points. Recall that these fees do not impact the loan amount or monthly payment. Alternative Loan Amount Fees Net Amount Disbursed I @ 6% $80,000 $1,600 $87,300 II @ 7% $90,000 $2,700 $78,400 Difference $10,000 $8,900

7. What is the impact of origination fees on the incremental borrowing cost? n = 25 × 12 = 300. P V = −$8,900. P M T = $120.66. F V = $0. Solve for i = 1.33% (monthly). Solve for i = 15.96% (annually = 1.33 × 12).

8. Incremental Borrowing Cost versus a Second Mortgage The incremental cost of borrowing the additional funds must be competitive with the rate on a second mortgage. Assume that a second mortgage for 10% of the purchase price can be obtained with an effective cost of 20% with a 25-year maturity. Access the text alternative for slide images.

9. Incremental Borrowing Cost and the Loan-to-Value Ratio As the loan-to-value ratio increases, the level of default risk also increases. Incremental borrowing cost should rise with loan-to-value ratio. Access the text alternative for slide images.

10. Incremental Borrowing Cost: Difference in Maturities Assume that the $90,000 alternative has a 30-year maturity in addition to the higher interest rate. Alternative Loan Amount Payments Years 1 to 25 Payments Years 26 to 30 I @ 6% for 25 years $80,000 $515.44 $0 III @ 7% for 30 years $90,000 $598.77 $598.77 Difference $10,000 $83.33 $598.77

11. What is the impact of differences in maturities on the incremental borrowing cost? C F = −$10,000. C F j = $83.33. n j = 25 × 12 = 300. C F j = $598.77. n j = 5 × 12 = 60. Solve for I R R = 0.9386% (monthly). Solve for I R R = 11.26% (annually = 0.9386 × 12).

12. Loan Refinancing Assume a borrower made a mortgage loan five years ago for $80,000 at 6 percent interest for 30 years with a current balance of $74,443.49 and a prepayment penalty of 2%. After five years, interest rates fall, and a new mortgage loan is available at 5 percent for 25 years with a $2,500 origination fee and $25 in closing costs. Cost to refinance: Prepayment penalty $1,488.87 Origination fees 2,500.00 Closing costs 25.00 Total $4,013.87 Monthly savings due to refinancing: Monthly payments on existing loan $479.64 Monthly payments on new loan $435.19 Difference in monthly payments $44.45

13. What would be the rate of return on the investment in refinancing? n = 25 × 12 = 300. P V = −$4,013.87. P M T = $44.45. F V = $0. Solve for i = 1.0607% (monthly). Solve for i = 12.7281% (annually = 1.0607 × 12).

14. Loan Refinancing: Early Repayment Assume the borrower plans to hold the property for only 10 more years after refinancing. Difference in balances: Loan balance after 15 years on existing loan $56,839 Loan balance after 10 years on new loan $57,281 Difference $442

15. Is refinancing still worthwhile given the borrowers plans for early repayment? n = 10 × 12 = 120. P V = −$4,013.87. P M T = $44.45. F V = $442. Solve for i = 0.5984% (monthly). Solve for i = 7.18% (annually = 0.5984 × 12).

16. Loan Refinancing: Effective Cost of Refinancing What is the effective cost of refinancing? Refinancing proceeds are equal to existing loan balance less refinancing costs. n = 25 × 12 = 300. P V = $74,443.49. P M T = −$458.65. F V = $0. Solve for i = 0.4611% (monthly). Solve for i = 5.53% (annually = 0.4611 × 12).

17. Loan Refinancing: Borrowing the Refinancing Costs Assume that the borrower also borrows the refinancing costs. Refinancing proceeds would then be equal to the existing loan balance. n = 25 × 12 = 300. P V = $74,443.49. P M T = − $482.10. F V = $0. Solve for i = 0.5045% (monthly). Solve for i = 6.05% (annually = 0.5045 × 12).

18. Loan Refinancing: Biweekly Payment Patterns Assume a borrower makes a fully amortizing $80,000 loan at 6 percent for 30 years. What would be the monthly payment? What would be the biweekly payment? Monthly Payments (360). n = 30 × 12 = 360. P V = $80,000. i = 6%/12 = 0.50%. F V = $0. Solve for P M T = $479.60. Biweekly Payments (26). $479.60 ÷ 2 = $239.80.

19. Assuming biweekly payments: How many payments are needed to repay the loan? What are the approximate number of years to maturity? What is the approximate total interest savings over the life of the loan? Number of payments. i = 6%/26 = 0.2308%. P V = $80,000. P M T = −$239.80. F V = $0. Solve for n = 637. Number of years to maturity. 637/26 = 24.5. Total interest savings. Total monthly payments = $172,656. Total biweekly payments = $152,752. Difference: $19,904.

20. Loan Refinancing: Early Loan Payoffs Assume a borrower makes a fully amortizing loan for $80,000 at 6 percent interest for 30 years. After five years the borrower is able to repay the entire loan balance early. Should the borrower repay early? Total remaining payments ($479.64 × 300) $143,892 Current loan balance $74,443 Potential interest savings $69,449

21. Early Loan Repayment: Lender Inducements Assume a borrower has a loan that was made 10 years ago. The original loan amount was $75,000 to be amortized over 15 years at 8 percent interest. The balance of the loan is $35,348 and the payments are $716.74 per month.

22. If the lender discounts the loan by $2,000, is this attractive to the borrower? n = 5 × 12 = 60. P V = −$33,348. P M T = $716.74. F V = $0. Solve for i = 0.8748 (monthly). Solve for i = 10.50% (annually = 0.8748 × 12).

23. Market Value of a Loan Assume that a loan was made five years ago for $80,000 with an interest rate of 6 percent and monthly payments over a 20-year loan term. Payments on the loan are $573.14 per month.

24. What is the market value of the loan? Step 1: Calculate the present value of the remaining payments at the market interest rate n = 15 × 12 = 180. i = 8%/12 = 0.6667%. P M T = −$573.14. F V = $0. Solve for P V = $59,973.71. Step 2: Calculate the loan balance n = 15 × 12 = 180. i = 6%/12 = 0.50%. P M T = − $573.14. F V = $0. Solve for P V = $67,919.10. The loan is selling at a discount of $7,945.39 ($67,919.10 − $59,973.71).

25. Effective Cost of Two or More Loans Assume that a seller bought a $100,000 property and made a mortgage loan five years ago for $80,000 at 10% interest for 25 years. Assume the market value of the property has risen to $115,000 and the buyer will assume the existing mortgage. Cash required for purchase: Purchase price $115,000 Seller’s mortgage balance 75,331 Cash required $39,669

26. Should the buyer finance the transaction with a new 80% loan at 12% for 20 years or assume the existing mortgage and take out a second mortgage for $16,669 at 14% for 20 years? Effective cost of combined loans. n = 20 × 12 = 240. P V = $92,000. P M T = − $934.24. F V = $0. Solve for i = 0.8961 (monthly). Solve for i = 10.75% (annually = 0.8961 × 12). Monthly payments Assumed loan $726.96 Second mortgage $207.28 Total $934.24

27. If a five-year term were available on a second mortgage loan at 14 percent interest, would the borrower still be better off by assuming the existing mortgage and taking a second mortgage? Effective cost. C F = $92,000. C F j = − $1,114.82. n j = 5 × 12 = 60. C F j = − $726.96. n j = 15 × 12 = 180. Solve for I R R = 0.8573% (monthly). Solve for I R R = 10.28% (annually = 0.8573 × 12). Monthly payments Assumed loan $726.96 Second mortgage $387.86 Total $1,114.82

28. Effect of Below-Market Financing on Property Prices Suppose that property can be purchased for $105,000 subject to an assumable loan at a 9 percent interest rate with a 15-year remaining term, a balance of $70,000, and payments of $709.99 per month. A comparable property without any special financing costs $100,000, and a loan for $70,000 can be obtained at a market rate of 11 percent with a 15-year term.

29. Which alternative is best for the buyer? n = 15 × 12 = 180. P V = − $5,000. P M T = $85.63. F V = $0. Solve for i = 1.6177 (monthly). Solve for i = 19.41% (annually = 1.6177 × 12). Down Payment Monthly Payment Market rate loan $30,000 $795.62 Loan assumption $35,000 $709.99 Difference $5,000 $85.63

30. Assume the balance on the assumable loan is only $50,000 and monthly payments are $507.13 and the buyer can obtain a second mortgage for $20,000 for 15 years at a 14 percent interest rate. n = 15 × 12 = 180. P V = − $5,000. P M T = $22.14. F V = $0. Solve for i = − 0.2417% (monthly). Solve for i = − 2.90% (annually = − 0.2417 × 12). Down Payment Monthly Payment Market rate loan $30,000 $795.62 Loan assumption + second mortgage $35,000 $773.48 Difference $5,000 $22.14

31. Cash Equivalency How much more than $100,000 could the buyer pay if he or she chose to assume the 9 percent loan and still be as well off as if the property were purchased for $100,000 and financed with an 11 percent loan?

32. How much more should the buyer pay for below-market financing? Step 1: Find the cash equivalent value of the total loan payments. n = 15 × 12 = 180. i = 11%/12 = 0.91666%. P M T = − $709.99. F V = $0. Solve for P V = $62,466.30. Step 2: Find the premium for the benefit of below-market financing. Financing premium: Financing value $70,000.00 Cash equivalent value $62,466.30 Financing premium $7,533.70

33. Cash Equivalency: Smaller Loan Balance Assume that the balance of the assumable loan is only $50,000 and the buyer would have to borrow an additional $20,000 through a second mortgage to obtain the $70,000 needed. Assume also that the second mortgage could be obtained at a 14 percent rate for a 15-year term and that a $70,000 new first mortgage could be obtained at an 11 percent rate with a 15-year term.

34. How much could the buyer pay for the property and be indifferent to the two methods of financing? Step 1: Find the cash equivalent value of the total loan payments. n = 15 × 12 = 180. i = 11%/12 = 0.91666%. P M T = − ($507.13 + $266.35) = − $773.48. F V = $0. Solve for P V = $68,052.27. Step 2: Find the premium for the benefit of below-market financing. Financing premium: Financing value $70,000.00 Cash equivalent value $68,052.27 Financing premium $1,947.73

35. Cash Equivalency: Concluding Comments If the below-market financing is not transferable to a subsequent buyer, this would impact the financing premium. Even if below-market loans were always assumable by subsequent buyers, the value of this financing depends on the market rate of interest at the time of subsequent sales. The value of below-market financing is reduced by the “option” to refinance if interest rates fall.

36. Wraparound Loans Assume: A property owner has an existing loan with a balance of $90,000 and monthly payments of $860.09 The interest rate on the loan is 8 percent and the remaining loan term is 15 years. The property has risen in value to $150,000. The current loan balance is 60 percent of the current value of the property. The owner would like to borrow an additional $30,000. The current effective interest rate on a first mortgage with an 80 percent L T V is 1.5 percent with a term of 15 years. The current effective interest rate on a second mortgage for an additional 20 percent of value would be 15.5 percent for a term of 15 years. A new lender is willing to make a wraparound loan for $120,000 at a 10 percent rate for a 15-year term for $1,289.53 per month.

37. Is the wraparound loan a desirable alternative for the property owner to obtain an additional $30,000? Find the incremental borrowing cost: n = 15 × 12 = 180. P V = $ 30 ,000. P M T = − ($1,289.53 − $860.09) = $429.44. F V = $0. Solve for i = 1.2886 (monthly). Solve for i = 15.46% (annually = 1.2886 × 12). The incremental borrowing cost is roughly the same rate as that for a second mortgage. The wraparound loan rate is a weighted average of the rate on the existing loan and the rate on a second mortgage.

38. Buydown Loans Assume: Interest rates are currently 15 percent and a buyer can only qualify for a loan at a 13 percent fixed rate. The loan will be for $75,000 with monthly amortization based on a 30-year term. Payments at 15 percent would be $948.33 per month. Payments at 13 percent would be $829.65 per month.

39. How could the seller buy down the interest rate to lower the payments for the first five years and enable the bank to make the loan? The seller would have to make up the difference in payments. $948.33 − $829.65 = $118.68. n = 5 × 12 = 60. i = 15%/12 = 1.25%. P M T = $118.68. F V = $0. Solve for P V = $4,988.67.

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