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Chapter 16: Mortgage calculations and decisions

Chapter 16: Mortgage calculations and decisions. Real Estate Principles: A Value Approach Ling and Archer. Outline. Fixed-payment calculations with no prepayment Fixed-payment calculations with prepayment ARM calculations Refinancing. TVM.

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Chapter 16: Mortgage calculations and decisions

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  1. Chapter 16: Mortgage calculations and decisions Real Estate Principles: A Value Approach Ling and Archer

  2. Outline • Fixed-payment calculations with no prepayment • Fixed-payment calculations with prepayment • ARM calculations • Refinancing

  3. TVM • The calculations in this chapter is based on time-value-of-money (TVM), which you learned in BSAD 180, 181, etc. • The financial calculator used in this course is Texas Instruments BAII Plus.

  4. Loan amount = PV • The maximum amount a lender will be willing to loan is the PV of the future payments that it expect to receive. • A 30-year, fixed-rate, LPM mortgage. The quoted interest rate is 6%. The monthly payment is $1,000. What is the loan amount? • 360 N; 0.5 I/Y; 1000 PMT; CPT PV. • The answer is: PV = -166,791.6144.

  5. Monthly loan payments • A 15 fixed-rate mortgage. The loan amount is $300,000. The quoted interest rate is 5.5%. What is the monthly payment? • I/Y = 5.5 / 12 = 0.4583; N = 15 × 12 = 180. • 300000 PV; 180 N; 0.4583 I/Y; CPT PMT. • The answer is: -2,451.1867.

  6. Quoted rate • A 20-year mortgage. The monthly payment is $2,000. The loan amount is $300,000. What is the quoted rate? • 240 N; -2000 PMT; 300000 PV; CPT I/Y. The answer is: I/Y = 0.4268. • Quoted rate = 0.4268 × 12 = 5.1216%.

  7. Loan balance • The remaining balance on a fixed-payment loan is the PV of the remaining payments. • A 30-year mortgage. The monthly payment is $1,000. The quoted rate is 7% (monthly rate = 7% / 12 = 0.5833%). • 360 N; 0.5833 I/Y; 1000 PMT; CPT PV. The answer is -150,307.5679. • What is the loan balance at the end of 5 years? The remaining months = 360 – 60 = 300. • 300 N; 0.5833 I/Y; 1000 PMT; CPT PV. The answer is -141,492.0117.

  8. Discount points • The actual interest payments of a loan to the lender are usually higher than the quoted rate would suggest. • Discount points: advance interest the lender charge at the beginning of the loan contract. • For example, in the previous example, if the lender charges discount points in the amount of $5,307.5676. Then the actual payout to the borrower is $145,000 ($150,307.5676 – $5,307.5676 = $145,000).

  9. Lender’s yield (LY) • Because of discount points, the lender learns a higher yield, called “lender’s yield), than the quoted rate. • 145000 PV; -1000 PMT; 360 N; CPT I/Y. The answer is: I/Y = 0.6133. • The LY = I/Y × 12 = 7.36%.

  10. Effective borrowing cost (EBC) • In addition to quoted rate and discount points, the borrower needs to incur other costs at the closing, called closing costs, such as title insurance, appraisal fee, etc. • Suppose that the closing costs are $2692. Then, the actual loan received by the borrower is $145,000 – $2,692 = $142,308. • 142308 PV; -1000 PMT; 360 N; CPT I/Y. The answer is: I/Y = 0.6292. • EBC = I/Y × 12 = 7.55%.

  11. Usual up-front financing costs • Discount points. • Loan origination fee (e.g., 1% of the loan amount). • Loan application and document fees ($200-$700). • Appraisal ($250-$400). • Credit check ($35-$75). • Title insurance (0.5-1% of the loan). • Mortgage insurance (>2% of the loan if pay up-front). • Recording fee ($40-$200). • Survey costs ($200-$300). • Etc.

  12. Annual percentage rate (APR) • The Trust-in-Lending Act: the lender needs to disclose APR of the loan to the borrower. • APR can be thought as a proxy for EBC. • The expense (closing costs) items to be included in calculating APR may omit a few relevant ones. • The calculation of APR is based on the assumption of no prepayment.

  13. Prepayment • Prepayment is the norm for residential mortgages; households sell their homes frequently. • The calculations of LY and EBC are sensitive to when a prepayment may happen. • Note that the previous LY and EBC calculations are based on the assumption of no prepayment.

  14. LY with prepayment • Prepayment is a major risk that introduces re-investment risk. • However, a prepayment would increase the lender’s return, i.e., LY, as well. • Suppose that the loan is expected to be paid off at the end of 7 years (84 months). Quoted rate is 7% (monthly rate = 7% / 12 = 0.5833%). • The loan balance is: 276 N; 0.5833 I/Y; 1000 PMT; CPT PV  $137,006.1412. • 84 N; -145,000 PV; 1000 PMT; 137006.1412 FV; CPT I/Y  0.6399. • LY = I/Y × 12 = 7.68% > 7.36% (LY w/o prepay).

  15. EBC with prepayment • Similarly, a prepayment would increase the EBC. • The loan balance is $137,006.1412. • The actual proceed received by the borrowers after discount points and closing costs is $142,308. • 84 N; -142,308 PV; 1000 PMT; 137006.1412 FV; CPT I/Y  0.6695. • EBC = I/Y × 12 = 8.03% > 7.55% (EBC w/o prepay).

  16. ARMs • One of the most popular ARMs is 1-year ARM based on a 30-year amortization; that is, the initial contract rate remains in effect for 1 year and adjusts annually thereafter. • Periodic cap: the cap that limits change in the interest rate from one change date to the next. • Overall cap: the cap that limits interest rate change over the life of the loan. • Teaser rate: many ARM loans are marketed with a temporarily reduced interest rate.

  17. ARM example, I • A 1-year $100,000 ARM with a 30-year amortization. The index rate is 1-year T-bill rate, which is 3.25% now. The margin is 2.75%. The teaser rate is 4.5%, though. • The monthly interest rate for the 1st year: 4.5 / 12 = 0.375%. • The monthly payment for the 1st year: 360 N; 0.375 I/Y; 100,000 PV; CPT PMT  -506.6853.

  18. ARM example, II • The balance after 1 year is: 348 N; 0.375 I/Y; 506.6853 PMT; CPT PV  -98,386.7714. • Suppose that the index rate remains at 3.25% after 1 year. • The interest rate for the 2nd year: 3.25 + 2.75 = 6%. Monthly rate is 0.5%. • The monthly payment for the 2nd year: 348 N; 0.5 I/Y; 98386.7714 PV; CPT PMT  -597.2122 (vs. 506.6853 for 1st year).

  19. ARM example, III • The balance after 2 years: 336 N; 0.5 I/Y; 597.2122 PMT; CPT PV  -97,088.0967.

  20. Refinancing • The borrower may refinance after interest rate falls. • Whether to refinance is a very complex investment decision because refinancing is not a one-time decision. • You can refinance later (say, 1 year later) when interest rate could be lower, instead of doing it today even though doing it today seems to be a good deal compared with the existing loan. • Timing option.

  21. Refinancing example, I • Suppose that Alan has an existing loan with a remaining term of 15 years, a remaining balance of $100,000, and an interest rate of 7%. The existing monthly payment is $898.83. • Alan can refinance the loan for $100,000, the same 15 years, for 5%. But the up-front refinancing costs (fees) are 5% (usually 3-9%) of the loan amount, i.e., $5,000.

  22. Refinancing example, II • If refinancing, the monthly rate is 5 / 12 = 0.4167%. • Suppose the $5000 fee is not amortized. The monthly payment is: 180 N; 0.4167 I/Y; 100000 PV; CPT PMT  -790.81. • The reduction in monthly payment: 898.83 – 790.81 = $108.02. • Suppose that Alan can earn 6% on the $108.02 saving. • If Alan expects to sell his house in 8 years, the PV of the expected benefits of refinancing is: 96 N; 0.5 I/Y; 108.02 PMT; CPT PV  -8,219.8055.

  23. Refinancing example, III • The up-front refinancing costs (fees) are 5% (usually 4-9%) of the loan amount, i.e., $5,000. • Suppose that Alan has a 20% marginal income tax rate. • The NPV of refinancing after tax is: (8219.8055 × (1 – 20%)) – 5000 = $1,575.884. • NPV > 0, so refinancing is not a bad idea. • We focus on NPV after tax because mortgage interest payments are tax deductible; the existing loan has higher interest expense and higher tax benefits than the new (refinancing) one.

  24. Refinancing example, IV • Suppose that Alan also expects that the interest rate will drop from 5% to 4% in 1 month. • In 1 month, the existing loan has a remaining term of 14 years and 11 months. The interest rate on the existing loan is 7%. The existing monthly payment is $898.83. • Thus, the remaining balance in 1 month is: 179 N; 0.5833 I/Y; 898.83 PMT; CPT PV  -99,687.1661.

  25. Refinancing example, V • The new monthly payment is: 179 N; 0.3333 I/Y; 99,687.1661 PV; CPT PMT  -740.36. • The reduction in monthly payment: 898.83 – 740.36 = $158.47. • Alan can earn 6% on the saving and expect to sell his house in 7 years and 11 months. • The PV of the expected benefits of refinancing is: 95 N; 0.5 I/Y; 158.47 PMT; CPT PV  -11,960.63.

  26. Refinancing example, VI • The NPV of refinancing after tax is: (11960.63× (1 – 20%)) – 5000 = $4,568.50. • This NPV is higher than that of financing now ($1,575.884). • Thus, Alan will prefer to wait even though the NPV for acting today is positive. • Is it optimal for Alan to refinance twice: now and 1 month later?

  27. Rule of thumb • A widely used rule of thumb by practitioners and news media is that: refinance when the interest rate spread between existing loan and a new loan reaches about 2%. • Of course, this rule of thumb is very rough.

  28. Fee paying options • 3 main options for paying refinancing fees: (1) pay the fees up front, (2) opt for a higher mortgage rate instead of paying the fees, and (3) have the fees tacked on to the principal of the mortgage.

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