Reverse Mortgages: Practice Problems and Solutions for Real Estate Finance Students - Prof | Assignments Real Estate Management

RE 611 / Fin 611 – Real Estate Finance

Reverse Mortgages

Practice Problems  Solutions

Dr. Stanley D. Longhofer

1) Your grandmother owns a house worth $155,000 and would like to use some of her

equity while she lives in the house. She is considering a reverse annuity mortgage

(RAM) with a 10-year term, 60 percent maximum loan-to-value (LTV) ratio, and

monthly payments at 7.125 percent interest. She will pay a 2 point origination fee on

this loan; this amount will be added to her principal balance at the origination of the

loan.

a) How large of payments will she receive from her lender?

The key with a RAM, is that the LTV ratio is used to determine the maximum

loan balance that will accrue. This value will be the balance due at the end of

the loan term (FV). FV = 155,000  0.60 =  93,000, P/Y = 12, N = 120,

I = 7.125, PV = 0.02  93,000 = 1,860  PMT = $511.91.

Notice that the points are treated as a cash inflow. This is because the lender is

implicitly giving you $1,860 that you use to pay your closing costs. Just as

with the monthly payment, this amount is added to your outstanding principal

balance that you will have to repay at the end of the loan’s term.

b) What will happen at the end of the loan’s term?

In principle, the property will be sold at the end of the loan term in order to pay

off the outstanding principal balance. Many RAMs, however, allow the

borrower to keep the property until they die or sell the home. The monthly

payments on the loan stop, but interest continues to accrue until the loan is

repaid.

c) What will be your grandmother’s effective borrowing cost (EBC) on this

mortgage?

Simply trace the actual cash flows. She will be receiving payments of $511.91

per month for 120 months. At the end of that time she will repay $93,000.

Notice, however, that although two points are paid at the beginning of the

loan, this is not a cash flow item for her; it is simply added to her principal

balance.

P/Y = 12, N = 120, PMT = 511.91, FV =  93,000, PV = 0  I = EBC = 7.87%.

2) Suppose that Jacob owns a house worth $325,000. He would like to tap the equity in

this house to pay general monthly expenses for the next 15 years, at which time he

expects to sell his house.

a) AllStar Mortgage Corporation is willing to offer Jacob a 15-year, 60% LTV RAM

at 8.0% interest with monthly payments. How much will Jacob receive every

month from this mortgage?

N = 180, I = 8.0, PV = 0, FV =  325,000  0.60 =  195,000  PMT = $563.52

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RE 611 / Fin 611 – Real Estate Finance

Reverse Mortgages Practice Problems  Solutions Dr. Stanley D. Longhofer

Your grandmother owns a house worth $155,000 and would like to use some of her equity while she lives in the house. She is considering a reverse annuity mortgage (RAM) with a 10-year term, 60 percent maximum loan-to-value (LTV) ratio, and monthly payments at 7.125 percent interest. She will pay a 2 point origination fee on this loan; this amount will be added to her principal balance at the origination of the loan. a) How large of payments will she receive from her lender? The key with a RAM, is that the LTV ratio is used to determine the maximum loan balance that will accrue. This value will be the balance due at the end of the loan term (FV). FV = 155,000  0.60 =  93,000, P/Y = 12, N = 120, I = 7.125, PV = 0.02  93,000 = 1,860  PMT = $511.91. Notice that the points are treated as a cash inflow. This is because the lender is implicitly giving you $1,860 that you use to pay your closing costs. Just as with the monthly payment, this amount is added to your outstanding principal balance that you will have to repay at the end of the loan’s term. b) What will happen at the end of the loan’s term? In principle, the property will be sold at the end of the loan term in order to pay off the outstanding principal balance. Many RAMs, however, allow the borrower to keep the property until they die or sell the home. The monthly payments on the loan stop, but interest continues to accrue until the loan is repaid. c) What will be your grandmother’s effective borrowing cost (EBC) on this mortgage? Simply trace the actual cash flows. She will be receiving payments of $511. per month for 120 months. At the end of that time she will repay $93,000. Notice, however, that although two points are paid at the beginning of the loan, this is not a cash flow item for her; it is simply added to her principal balance. P/Y = 12, N = 120, PMT = 511.91, FV =  93,000, PV = 0  I = EBC = 7.87%.
Suppose that Jacob owns a house worth $325,000. He would like to tap the equity in this house to pay general monthly expenses for the next 15 years, at which time he expects to sell his house. a) AllStar Mortgage Corporation is willing to offer Jacob a 15-year, 60% LTV RAM at 8.0% interest with monthly payments. How much will Jacob receive every month from this mortgage? N = 180, I = 8.0, PV = 0, FV =  325,000  0.60 =  195,000  PMT = $563. 1

b) If AllStar Mortgage wants to make sure that it earns 8.5% on this RAM, how much must it charge Jacob in up-front fees? I = 8.5  PV =  $2,490.96.

Maureen’s home is currently worth $185,000. Her current mortgage has an outstanding balance of $28,000. She is considering taking out a reverse mortgage. Her lender has offered her a 70 percent LTV reverse mortgage at 7.00 percent interest with a 15-year term; Maureen will incur closing costs of $1,500 in association with this loan; these costs will be rolled into the loan. a) Based on this information, how large are the monthly payments that Maureen will receive from this loan? The initial principal balance of Maureen’s new reverse mortgage will be the current balance on her existing mortgage plus the closing costs she incurs: PV = 28,000 + 1,500 = 29,500. This is entered as a positive number, because it represents value that Maureen will receive. The LTV ratio is used to calculate the FV of the loan at the end of 20 years, so enter FV =  185,000  0.70 =  129,500. This is entered as a negative number because it is the amount Maureen (or her heirs) will have to pay at the end of 15 years. Finally, enter P/Y = 12, N = 15  12 = 180, I = 7 and solve for PMT = 143.41. The positive number here indicates that Maureen can receive $143.41 per month from the lender. b) How much will Maureen owe on this loan at the end of 10 years? Enter N = 10  12 = 120 and solve for FV =  84,107.38. c) If Maureen expects to be in this home for 10 more years, what is her EBC on this loan? Think about the actual cash flows here. Although her initial loan amount is $29,500, Maureen only received $28,000 in cash (that she used to pay off her old mortgage); the rest was a fee charged by the new lender. Thus, enter PV = 28,000 and solve for I = 7.42%. Notice that the EBC is larger than the nominal interest rate (this is one way to check your answer). d) How will the outstanding loan balance ultimately be repaid? When Maureen dies, sells the house, or permanently moves out of the house (into a nursing home?), the loan must be repaid. Typically, the home is sold and the proceeds used to pay off the loan. 2

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RE 611 / Fin 611 – Real Estate Finance