(Practice Problems) FRM and ARM

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University Of Georgia *

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5100

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Apr 3, 2024

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1) What are the major differences between the CAM, and CPM loans? What are the advantages to borrowers and risks to lenders for each? What elements do each of the loans have in common? CAM - Constant Amortization Mortgage - Payments on constant amortization mortgages are determined first by computing a constant amount of each monthly payment to be applied to principal. Interest is then computed on the monthly loan balance and added to the monthly amount of amortization to determine the total monthly payment. CPM - Constant Payment Mortgage - This payment pattern simply means that a level, or constant, monthly payment is calculated on an original loan amount at a fixed rate of interest for a given term. At the end of the term of the mortgage loan, the original loan amount or principal is completely repaid and the lender has earned a fixed rate of interest on the monthly loan balance. However the amount of amortization varies each month. 2) What are the advantages and disadvantages (for both the borrower and lender) of a GPM, as compared to an otherwise similar CPM? Under what circumstances (economic and property specific) will a GPM be most useful? The GPM is useful not only in inflationary environments in which high interest rates make CPM mortgage payments hard to afford, but also for dealing with loans on income properties that are in turnaround, development, or workout situations, in which their ability to generate net rent is expected to increase over time. GPMs may also be useful for first-time homebuyers, whose incomes can be expected to grow. 3) What are loan closing costs? How do they affect borrowing costs and why? Closing costs are incurred in many types of real estate financing, including residential property, income property, construction, and land development loans. Closing costs that do affect the cost of borrowing are additional finance charges levied by the lender. These charges constitute additional income to the lender and as a result must be included as a part of the cost of borrowing. Lenders refer to these additional charges as loan fees. 4) Does repaying a loan early ever affect the actual or true interest cost to the borrower? It depends. If no additional fees are charged (and no PPP), the true interest rate always equals the contract rate of interest. If additional fees are charged, earlier prepayment increases the effective borrowing cost. 5) A. What are some of the reasons up-front points and fees are so common in the mortgage business? B. What is the major reason for the existence of prepayment penalties?

a. Up-front fees are a way for the loan originator to make some profit while providing some disincentive against early prepayment of the loan by the borrower. These fees can also be used as a trade-off against the level of the regular loan payment: Greater origination fees and discount points allow lower regular loan payments for the same yield (other answers exist as well). b. The main reason for prepayment penalties is that the investors want a certain yield locked in and therefore want to mitigate prepayment risk. 6) What is negative amortization? Negative amortization means that the loan balance owed increases over time because payments are less than interest due. 7) A fully amortizing mortgage loan is made for $80,000 at 6 percent interest for 25 years. Payments are to be made monthly. Calculate: a. Monthly payments b. Interest and principal payments during month 1 c. Total principal and total interest paid over 25 years d. The OLB (RMB) if the loan is repaid at the end of year 10. e. Total monthly interest and principal payments through year 10. f. What would the breakdown of interest and principal be during month 50? (a) Monthly payment (PMT (n,i,PV, FV) = $515.44 Solution: n = 25x12 or 300 i = 6%/12 or .50 PV = $80,000 FV = 0 Solve for payment: PMT = -$515.44 (b) Month 1: interest payment: $80,000 x (6%/12) = $400 principal payment: $515.44 - $400 = $115.44 (c) Entire 25 Year Period: total payments: $515.44 x 300 = $154,632 total principal payment: $80,000 total interest payments: $154,632 - $80,000 = $74,632

(d) Outstanding loan balance if repaid at end of ten years = $61,081.77, as presented below for FV. Solution: n = 120 (pay off period) i = 6%/12 or 0.50 PMT = $515.44 PV = $80,000 Solve for FV: FV = $61,081.77 (e) Trough ten years: total payments: $515.44 x 120 = $61,852.80 total principal payment (principal reduction): $80,000 – 61,081.77* = $18,918.23 *PV of loan at the end of year 10 total interest payment: $61,852.80 - $18,918.23 = $42,934.57 (f) Step 1, Solve for loan balance at the end of month 49: n = 49 i = 6%/12 or 0.50 PMT = $515.44 PV = - $80,000 Solve for loan balance: PV = $73,608.28 Step 2, Solve for the interest payment at month 50: interest payment: $73,608.28 x (.06/12)= $368.04 principal payment: $515.44 - $368.04 = $147.40 8) A fully amortizing mortgage is made for $80,000 for a term of 25 years. Total monthly payments will be $899.86 per month. What is the interest rate on the loan? The interest rate on the loan is 12.96%. Solution: n = 25x12 or 300 PMT = -$899.86 PV = $80,000

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FV = 0 Solve for the annual interest rate: i = 1.08 (x12) or 12.96% 9) What is the effective borrowing cost of the loan from the previous question if the borrower pays two points up front to get the loan? n = 25x12 or 300 PMT = -$899.86 PV = $78,400 FV = 0 Solve for the annual interest rate: i = 1.11 (x12) or 13.26% * * “I” is actually a little lower than 1.11 (calculator reports 1.11 even though the number it stores is lower) 10) What is the effective borrowing from the previous problem if the borrower pays two points up front to get the loan, and holds the loan for 5 years? RMB at end of 5 years? n = 60 PMT = -899.86 PV = 80,000 I = 12.96 / 12 = 1.08 CPT FV = -$76,994.79 Solve for EBC using cash flows n = 60 PMT = -899.86 PV = 78,400 FV = -76994.79 CPT I = 1.13 (x 12) = 13.52* * “I” is actually a little higher than 1.13 (calculator reports 1.13 even though the number it stores is lower) 11) A lender is considering what terms to allow on a loan. Current market terms are 8 percent interest for 25 years for a fully amortizing loan. The borrower, Rich, has requested a loan of $100,000. The lender believes that extra credit analysis and careful loan control will have to be exercised because Rich has never borrowed such a large sum before. In addition, the lender

expects that market rates will moved upward very soon, perhaps even before the loan is closed. To be on the safe side, the lender decides to extend to Rich a CPM loan commitment for $95,000 at 9 percent interest for 25 years; however, the lender wants to charge a loan origination fee to make the mortgage loan yield 10 percent. What origination fee should the lender charge? What fee should be charged if it is expected that the loan will be repaid after 10 years? Monthly payments PMT (n,i,PV,FV): n = 300 i = 9%  12 PV = -$95,000 FV = $0 Solve for monthly payments: PMT = $797.24 PV (n,i,PMT,FV) of 300 payments of $797.24 discounted at 10% = $87,733.67 Subtracting $87,733.67 from $95,000.00, we get $7,266.33 The loan origination fee should be $7,266.33 if the loan is to be repaid after 25 years and the lender requires a 10% yield. The lender should charge $7,266.33/$95,000 = 7.65% or 7.65 points to achieve a 10% yield. If the loan is expected to be repaid after 10 years, the loan balance at the end of 10 years must be determined: n = 120 i = 9%/12 PMT = $797.24 PV = -$95,000 Solve for FV: FV = $78,602.27 Loan balance after 10 years = $78,602.27 Discounting $797.24 monthly for 120 months and $78,602.27 at the end of the 120 th month by the desired yield of 10% gives: Present value = $89,364.04

Subtracting $89,364.04 from $95,000.00, we get $5,635.96. The loan origination fee should be $5,635.96 if the loan is to be repaid after 10 years, and the lender requires a yield of 10%. The lender should charge $5,635.96/$95,000 = 5.93 % or 5.93 points at origination to achieve 10% yield (note that the points the lender needs to charge to achieve the same yield, 10%, are lower if the lender expects the borrower to pay the loan off earlier). 12) Relative to a FRM, how is interest rate risk shared between borrowers and lenders on an ARM? When might an ARM be attractive to a borrower? The borrower bears more interest rate risk while the lender bears less risk. With an ARM, the lender still bears some interest rate risk as the rate typically only adjusts once or twice each year. An ARM might be attractive to a borrower for many reasons, but here are a couple: If the borrower expects interest rates to decrease If the borrower only plans to hold onto the loan for a short period of time If the spread between fixed rate mortgages and ARM interest rates is high 13) What is the difference between interest rate risk and default risk? How do combinations of terms in ARMs affect the allocation of risk between borrowers and lenders? Interest rate risk is the risk that the interest rate will change at some time during the life of the loan. Default risk is the risk to the lender that the borrower will not carry out the full terms of the loan agreement. The fact that ARMs shift all or part of the interest rate risk to the borrower, the risk of default will generally increase to the lender, thereby reducing some of the benefits gained from shifting interest rate risk to borrowers. 14) Which of the following two ARMs is likely to be priced higher, that is, offered with a higher initial interest rate? ARM A has a margin of 3 percent and is tied to a three-year index with payments adjustable every two years; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points will be allowed. ARM B has a margin of 3 percent and is tied to a one-year index with payments to be adjusted each year; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points are allowed. ARM A is likely to be priced higher, because it has a longer-term index and adjustment period. Subsequently, the lender bears more risk and can expect a higher return.

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15) A borrower has been analyzing different adjustable rate mortgage (ARM) alternatives for the purchase of a property. The borrower anticipates owning the property for five years. The lender first offers a $150,000, 30 year fully amortizing ARM with the following terms: Initial Interest rate = 6% Index = 1 year treasuries Payments reset each year Margin = 2% Interest rate cap = None Payment cap = None Negative amortization = Not allowed Origination fees = $3,000 Based on estimated forward rates, the index to which the arm is tied is forecasted as follows: Beginning of year (BOY) 2 = 7%; (BOY) 3 = 8.5%; (BOY) 4 = 9.5%; (BOY) 5 = 11%. Compute the payments, loan balances, and yield (EBC) for the unrestricted arm assuming a five year holding period. (1) (2) (3) (4) (8) EOY Balance (1) - (7) Annual Interes t Rate Monthly Interest Rate (2)/12 BOY Balance Year Payments 0 1 $150,000 6.00% 0.50% $899.33 $148,158 2 148,158 9.00% 0.75% $1,200.31 $147,043 3 147,043 10.50% 0.88% $1,359.42 $146,126 4 146,126 11.50% 0.96% $1,467.12 $145,282 5 145,282 13.00% 1.08% $1,630.42 $144,562

IRR(CF1, CF2, ….CFn) CF j n j -$147,000 899.33 n = 12 1200.31 n = 12 1359.42 n = 12 1467.12 n = 12 1630.42 n = 11 1630.42 + 144,562 n = 1 Solve for the IRR: = 0.85% x 12 = 10.16% (annual rate, compounded monthly) 16) As a borrower, which of the following two 25-year, $100,000, monthly payment loans would you choose if you had a 15-year expected prepayment horizon: 6% interest with four points, or 6.75% interest with one-half point? 6% 4 pt option Get payment N=300 FV=0 I/Y = 6/12 PV =-100,000 CPT PMT = 644.30 RMB at 180

N = 180 CPT FV = 58,034.45 EBC with CFs N = 180 PMT = 644.30 FV = 58,034.45 PV = -96,000 CPT I/Y = 6.49 (the calculation is multiplied by 12) Option 2 Get pmt N=300 FV = 0 I/Y = 6.75 / 12 PV = -100,000 CPT PMT = 690.91 RMB N=180 FV = 60,171.29 EBC with CFs N=180 Pmt = 690.91 FV = 60,171.29 PV = -99,500 CPT I/Y = 6.81 Choose the 6%, 4 point option

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17) Explain intuitively why the low rate, high fee option was better in the previous problem. It makes sense to pay a lot up front to get the lower interest rate (and payments) because you are holding onto the loan for a long period of time. 18) The London Interbank Offered Rate (LIBOR) was the most popular index for floating rate debt. There has been a move to using the Secured Overnight Financing Rate (SOFR) in recent times. What was the problem with LIBOR? LIBOR was based on survey data rather than actual market data. Basically financial institutions were asked what rate they would charge to lend to the highest grade customers, and an average was taken over the financial institutions. The problem is that those same financial institutions can manipulate their answer to the survey question in an attempt to move rates in a direction that is favorable to the financial institution.