REAL 4100: Real Estate Finance & Investment Analysis

Present Value: Discounting future cash flows to the present What is the value today of $2,000 you will receive in year 3 if the interest rate is 8% compounded monthly?

$1,574,51

Class problem one: Calc PV

(need to complete)

Class problem two: Calc Rate

(need to complete)

The maximum monthly mortgage payment that you can afford is $930. You can put down $12,000 on a house and interest rates are 7.5% on a 30-year mortgage. What is the maximum purchase price that you can afford?

(need to complete)

You have a 25 year, $172,500 mortgage at 8.8% interest. You plan to sell the house in 4 years. What is the loan balance owed to the lender at the end of 4 years?

(need to complete)

Things to keep in mind about AMRS

- ARMs do not eliminate interest rate risk - The longer the adjustment interval, the more interest rate risk the lender will take on. - As the lender assumes less interest rate risk by putting it onto the borrower, the lender should expect to receive a lower yield than she would otherwise receive with a fixed rate mortgage.

Why would a borrower take an ARM?

- FRM payments are initially > ARM payments -- FRM interest rates are tied to long-term interest rates, which include a premium to compensate the lender for tying up their money longer and for inflation -- So, ARM payments initially appear to be more affordable - Borrowers with low credit ratings may be less sensitive to risk because of lower cost of default (already have bad credit) - Finally, studies suggest that borrower financial literacy may affect mortgage choice -- Borrowers who choose ARMs appear more likely to underestimate or not understand how changes in interest rates would affect their loans -- Systematic differences in levels of financial literacy among borrowers with different credit scores

Teaser Rate on ARMS

- Lenders compete by offering an initial "teaser" rate that is later adjusted - It is not clear whether all borrowers comprehend or appropriately price the inherent risks in ARMs - Lender's sell the loans off to investment banks, who securitize them and sell them to investors

The Federal Housing Administration (FHA) Fannie Mae and Freddie Mac

- Offer guarantees that made 30-year loans possible. - A conventional mortgage, meeting Fannie and Freddie standards, requires prime credit and 20% down. - If you have less than that, you buy private mortgage insurance - rather expensive

Financial Crisis of 2007-2008

- Predatory lending targeting low-income homebuyers - Excessive risk-taking by global financial institutions - Bursting of the United States housing bubble The Perfect Storm

The Federal Housing Administration (FHA)

- The FHA will accept a 3.5% down payment! It will also accept near-prime (not subprime) credit scores. - Borrowers still have to pay an FHA insurance fee. - FHA-guaranteed loans are a sizeable portion of the mortgage-backed securities market - The FHA lost market share in the lead-up to the 2007-2009 crisis as lending standards dropped and private lenders began pushing subprime, adjustable rate mortgages

Ready to Finance? 8 Steps for success

1: Identify your objectives 2.) refresh old paperwork 3.) Crunch the Numbers 4.) Shop around 5.) Submit your application 6.) Pick your loan 7.) get an appraisal 8.) Be prepared to wait

Risk Premiums, Interest Rate Risk, and Default Risk

As more interest rate risk is assumed by the lender, the lender will demand a higher risk premium.When interest rate risk assumed by the borrower increases, default risk assumed by the lender increases.

Variations: 3/1m 5/1, and 7/1 'Hybrid Loans'

Assume a $100,000 3/1 hybrid with a 30-year maturity and an initial rate of 6 percent. Calculate the payments for the first three years. Initial payment = $599.55 n = 30 × 12 = 360 i = 6%/12 = 0.50 PV = $100,000 FV = $0

Variations: Interest-Only ARM and Floating Rate Loans

Assume a $100,000 interest-only ARM with a 30-year maturity and an initial rate of 6 percent. Calculate the payment for the first year. If at the reset date the index has increased and the new interest rate becomes 8 percent, what is the new monthly payment? 100,000 * (.08%12) = 666.67

Incremental Borrowing Cost: Difference in Maturities

Assume that the $90,000 alternative has a 30-year maturity in addition to the higher interest rate.

Examples of recent rates: Investments

Bank savings account, insured 0.10%• Money market fund 0.30% • 3-year certificate of deposit 0.50% • 5-year junk bonds 4.00% • Stock index fund (S&P 500) 10.40%

When interest rates go up, lenders would like ______.

Borrowers to repay their loans

Your interest rate and your number of time periods must match up!

If you are making monthly payments your interest rate must be a monthly interest rate If considering a mortgage and trying to compute the monthly payments, remember that the annual interest rate that is quoted must be converted to a monthly rate in determining the amount of the monthly payment.

ARM: Yields

In normal times, an ARM is made when expected benefit of shifting interest rate risk to borrower > expected losses from higher default risk. -- Otherwise, FRM is preferred

Increasing a first mortgage or adding a second mortgage will both (increase/decrease) the loan-to-value ratio.

Increase

Another word for the marginal cost of borrowing is the ______ cost of borrowing

Incremental

ARMS and Floating Rate Loans: Other Characteristics

Index - the interest rate series agreed on by both the borrower and the lender and over which the lender has no control Margin (Spread) - a premium in addition to the index chosen Composite Rate - the sum of the interest rate based on the index chosen plus the margin used to establish the new rate of interest on each reset date. Reset Date - the point in time when payments will be adjusted. Negative Amortization - when additions to the outstanding loan balance are allowed in the loan agreement Caps - maximum increases allowed in payments, interest rates, maturity extensions, and negative amortization on reset dates. Floors - maximum reductions in payments or interest rates Assumability - the ability of the borrower to allow a subsequent purchaser to assume a loan under the existing terms.

Interest Rate and risk

Interest rates ("discount rates") reflect the risk inherent in an investment or a loan. The more risky an investment the higher the risk, the higher the interest rate.

The "effective" interest rate under annual compounding(or "APR"): Compounded annually

Invest $100 on Jan 1 at 5% compounded annually • At the end of the year, earn $5 in interest The contract or nominal rate of interest is 5%,

The "effective" interest rate under annual compounding(or "APR"): Compounded Semi-annually

Invest $100 on Jan 1 at 5% compounded semi-annually • On July 1, earn $2.50 in interest (=$100 x 5%/2) • Earn interest on the $102.50 for the second 6-month period. • $102.50 x 5%/2 = $2.56 • Total interest earned over the year: $2.50 + $2.56 = $5.06 The effective annual rate of interest is 5.06%

For low loan-to-value ratios, the incremental borrowing cost:

Is the same

Incremental borrowing cost increases as the

LTV increases

Under what interest rate condition might a lender pay borrowers to repay a loan early?

Large Increase

Under an adjustable rate mortgage, who bears interest rate risk?

Lenders and Borrowers

Early Loan Repayment: Lender Inducements

Lenders will, at times, give a borrower an inducement to prepay their loan. • Part of a plan which is now collapsed except for a few loans • Lenders can gain personal compensation for new loan • Lenders wish to keep a borrower

Loan Closing Costs

Loan origination fees Loan discount fees (points) "Buying down the interest rate"

The borrower benefits by having a _______ amortization period.

Longer

A second mortgage is preferred to a larger single mortgage if the rate of the second mortgage is (higher/lower) than the incremental cost.

Lower

If below-market financing is not transferable, the premium a buyer would pay for a below-market-interest-rate loan will be:

Lower

If interest rates are expected to fall, the premium a buyer would pay for a below-market-interest-rate loan will be:

Lower

With a buydown loan, the seller pays to _____ the interest rate on the loan.

Lower

The amount a new lender is willing to pay to purchase a mortgage is called:

Market Value

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 PV = $80,000i = 6%/12 = 0.50% FV = $0 Solve for PMT = $479.60 Biweekly Payments (26)$479.60 ÷ 2 = $239.80

Lenders targeted minorities with subprime, adjustable rate loans

Mortgage brokers received incentives to offer subprime ARM's even to those with credit ratings that merited a conforming (i.e., non-subprime) loan. Blacks and Latinos were more than twice as likely as comparable whites to receive such high-cost loans.

Expected Yields on ARMs: Summary Observations

Moving from an ARM with no caps or limitations (ARM I) to an ARM with payment caps and negative amortization (ARM II) to an ARM with interest rate caps (ARM III), interest rate risk to the lender increases. As interest rate risk increases to the lender, default risk for the borrower declines.

=nper(

NPER, is very rarely used in this class. It returns the number of compounding periods: m x n NPER is n x 12; depending on what you are solving for, n could be the year to maturity or the years until the house is sold and the mortgage balance repaid.

The effective cost of refinancing includes which of the following?

New monthly payments Prepayment penalty points

If the borrower instead wishes to make payments which will fully amortize the loan balance over the remaining term, what will be the new payment?

New payment = -$739.95 n = 29 × 12 = 348 i = 8%/12 = 0.6667 PV = $100,000 FV = $0

If your current mortgage of $55,000 has a rate of 4% and you have an investment opportunity with an expected return of 7%, should the borrower repay the loan early?

No over 6%?

When (PV,FV)

Now or in the future? The amount now is the present value and the amount in the future is typically referred to as the future value

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% PV = $80,000PMT = -$239.80 FV = $0 Solve for n = 637 Number of years to maturity 637/26 = 24.5 Total interest savings Total monthly payments = $172,671 Total biweekly payments = $152,821 Difference: $19,850

How often (PMKT = payment amount)

One payment is often referred to a lump sum A series of payments is typically referred to as an annuity.

=PMT(

PMT, this calculates a payment (annuity), such as a monthly mortgage payment PMT is a constant monthly mortgage payment

Let's buy a house Price of the house: $282,000 10% down, meaning we need a 90% loan-to-value (LTV) Two loan offers: 30 year fixed-rate mortgage of 4.125%b) 15 year fixed-rate mortgage of 3.375% How do you think the interest rate on a 5-year fixed rate mortgage will compare to the above interest rates? A. More than 4.125% B. Between 4.125% and 3.375% C. Less than 3.375%

PV = $282,000 * 90% = @253,800 i = 4.125% n = 30 m = 12 FV = 0 <--After 30 years the loan will be fully amortized =pmt(4.125%/12,30*12,-253800,0) = $1,230.04 Do this for both to find both monthly pmts

Future Value Formula

PV(1+r)^n (not sure which is right)

=pv(

PV, a very commonly used function, calculates the current value of future cash flows. These cash flows could be rent collected on a property or payments made on a mortgage loan. With mortgages, the PV can give you the original loan amount. PV is an original loan amount (money the borrower receives from the lender upfront to purchase the house)

The financing _______ is the value of assuming a loan when purchasing a property.

Premium

The Price Level Adjusted Mortgage (PLAM)

Price level adjusted mortgage (PLAM) - an ARM where the loan balance would be adjusted up or down by a price index

Effect of origination fees on IBR: Rate

Pv = -$8,900 n = 300 pmt $120.66 FV = 0 SOLVE FOR I = 1.33% (monthly) SOLVE FOR I = 15.96 (Annually = 1.33 x 12)

=rate(

RATE calculates the interest rate. i is an interest rate. For now, assume it is the contract rate of interest (a.k.a. "the nominal interest rate" or "the annual interest rate"); must be divided by 12.

Why are fixed rate mortgages not always ideal?

Recall, what goes into the lender's contract rate of interest decision for fixed rate loans: -- i n = rn + pn + f --- rn = expected real interest rate --- pn = risk premium --- fn = anticipated inflation premium - With a fixed rate mortgage, lenders take on all the risk that market rates will later increase (due to an unanticipated increase in rn , pn or fn) - What if market rates decline? Then, do lenders win? - Risk bearing is not symmetric!

By extending the term (maturity), the monthly payment can be

Reduced Car costs $22,000. Two loan options: • $453 a month for 6 years = 72 months • $512 a month for 5 years = 60 months

Legislative Risk

Refers to changes in the regulatory environment in which markets operate Law passed that is going to make something harder for you

If interest rates rise over time, borrowers with a fixed rate mortgage will not:

Refinance

Default Risk

Risk that borrowers will default o obligations to repay interest and principal (wont pay)

If a buyer does not have enough cash, an option may be a ______ mortgage.

Second

Who provides financing with a purchase money mortgage?

Seller

Home Equity Lines of Credit (HELOC)

Similar to consumer credit loans (credit cards) • Second liens, but not lump sum • Pay like credit cards based on the amount outstanding • Usually like ARM rates (index + margin) • Often have early terminations/inactivity fees • Still lower interest rates than other consumer credit loans

Below-Market Financing & 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 will sell for $100,000, and a loan for $70,000 can be obtained at a market rate of 11 percent with a 15-year term.

Perceptions of Credit Risk

TED spread is the difference between the three-month Treasury bill and the three-month LIBOR based in U.S. dollars. To put it another way, the TED spread is the difference between the interest rate on short-term U.S. government debt and the interest rate on interbank loans. - Investopedia

IBR is?

The IRR on the "marginal" or "incremental" cash flows

The initial loan terms will reflect the net effect of

The amount of interest rate risk assumed by the lender as determined by the index chosen, adjustment period, any caps or negative amortization and The amount of default risk assumed by the lender as determined by the amount of interest rate risk shifted to a specific borrower

accrual rate

The frequency at which a loan requires interest to be accrued is calculated as i/m

Market Value

The market value of a loan (if the loan were sold on the secondary mortgage market) is the PV of the remaining stream of payments discounted at the prevailing market rate.

Time periods:* Don't get tripped up

The number of time periods is associated with the number of payments to be made or received. • A 30 year mortgage involves 360 time periods. • A 5 year car loan involves 60 time periods.

Negative Amortizing

The pay rate will be less than the accrual rate Payment is less than meeting the minimum on interest By end of loan you owe more

Interest Only ("zero amortizing")

The pay rate will equal the accrual rate

Fully Amortizing

The pay rate will exceed the accural rate

Partially Amortizing

The pay rate will result in a payment that will exceed accured interest but not by as much as the payment for the fully amortizing loan

"Buying down the interest rate"

The practice of charging borrowers loan discount points instead of raising the interest rate.

Pay Rate

The ratio of the loan payments to the loan amount (which is not necessarily equal to the referral rate)

Prepayment Risk

The risk that the loan will be repaid when interest rates fall below the contract rate

With a wraparound loan, who makes payments on the original loan?

The wraparound lender

Mortgages are like annuities

They have level cash flow streams (monthly payments) Terminates at some data in the future (when the loan has been fully amortized)

T/F: On a mortgage with a 12% annual interest rate (or "contract rate of interest"), the borrower pays 1% interest each month on the outstanding loan balance?

True

True or false: The buydown amount is likely added into the price of the property.

True

The important factors for a TVM problem

When (PV, FV) How often (PMKT = payment amount) How long (m = number of periods per year x n = number of years) How much (i = Interest rate)

If your current mortgage of $55,000 has a rate of 8% and you have an investment opportunity with an expected return of 5%, should the borrower repay the loan early?

Yes

Which mortgage is used for single family properties

adjustable rate mortgage

The financing premium is the value of ________ a loan when purchasing a property.

assuming

Which of the following loans allows the seller to pay the lender a fee to lower the interest rate?

buy down loan

If market rate > contract rate, the loan will be sold at a ___________

discount (less than face value)

The cost of making a new loan after taking fees and other costs into account is often called the ______.

effective cost of refinancing

A biweekly payment schedule is

every two weeks

Which mortgage is used for commercial properties

floating rate mortgage

A borrower would take a second mortgage if ______.

it was a better economic outcome than getting a new first mortgage for the new balance

Loan Refinancing: Effect of early repayment

n = 10 × 12 = 120 PV = -$4,013.87 PMT = $44.45FV = $1,807 Solve for i = 10.0841%

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 PV = $74,443.49 PMT = -$458.65FV = $0 Solve for i = 0.4611% (monthly) Solve for i = 5.53% (annually)

A wraparound loan allows a borrower to _____________ while keeping an existing loan in place.

obtain additional financing

A price level adjusted mortgage adjusts the loan balance by what? Multiple choice question.

price index

Home Equity Loans

provide lump sum based on second mortgage lien on property • Riskier -> higher interest rates • Interest rates may be fixed or adjustable • Periodic payments • Typically require 80% LTV

Effect from Loan-to-Value (LTV): Incremental borrowing cost Deff

return that lenders require at the margin for lending additional funds e.g., to borrow an extra $20k, the lender charges 6% instead of 5.5%, and earns a 10% yield on the extra Reflects return required to compensate the lender for the additional default risk associated with a higher LTV

Liquidity Risk

securities that can be easily sold and resold in well-established markets will require lower premiums than those that are more difficult to sell

Book Value

the PV of the remaining stream of payments discounted at the contract rate.

Loan Amount

the amount borrowed and what the borrower is legally required to repay

If market rate < contract rate, the loan will be sold at a ___________

the bonds will sell for more than their face amount

Loan Maturity Date

the date by which the loan must be fully repaid

Equivalent Nominal Annual Rate (ENAR)

the rate of interest before adjustment for inflation (in contrast with the real interest rate); or, for interest rates "as stated" without adjustment for the full effect of compounding; also referred to as the nominal annual rate. ENAR = [(1+EAY)^1/m -1]*m

Interest Rate Risk

the uncertainty about what interest rate to charge when a loan is made

Loan discount fees (points)

to adjust the yield on a mortgage loan Payments made on the contracted loan amount

By making biweekly mortgage payments, what may occur?

total interest paid decreases the loan is repaid earlier

The market _______ market , Correct Unavailable value of a loan is the amount that a new investor is willing to pay to receive the remaining payments.

value

Below market loans have

value to the buyer

A ______ loan allows a borrower to obtain additional financing while keeping an existing loan in place.

wraparound

Present Value: Discounting future cash flows to the present What is the value today of $112.16 you will receive in year 3 if the interest rate is 3.9% compounded annually?

$100

ARM Example

- $60,000 30-year loan, initial interest rate is 10%, - Interest resets after 1 year based on a market index (given in the excel). - Margin on the index (e.g. LIBOR) is always 2%. - What will be your payment the first year? - What will be your payment after the first reset (the second year)? - What is the yield assuming sale at the end of year 5?

ARM Yields are a Function of:

- Initial intrest rate - Index to which interest rate is tied - Margin (premium or "spread" over index rate) - Caps or floors on the interest rate, payments, or loan balances -Any discount points or organization fees charged - Frequency of payment adjustments

Compounding example #2

Christopher Columbus deposited $100 in a bank account pay 10% interest in October 1492 when he landed in the New World. How much would be in the Columbus account in 2014? Not compounded: Columbus earns $10 in interest each year on his initial $100. After 522 years, he would have $5,320. If compounded annually: After 522 years, Columbus would have $405 sextillion in his account.

Compounding example #1

Compounding Example 1: 12% interest compounded monthly on a $100 investment During the first month, you earn $1 in interest (1% of your initial $100 investment) During the second month, you again earn $1 in interest on your initial investment, but you also earn an additional 1 cent of interest because you earn 1% interest on the $1 of interest you earned in the first month: $1.01 in interest.

Fixed Rate Mortgages are commonly referred as

Constant Payment Mortgages (CPMS)

Teaser Rate on ARMS Example

During the first year, interest will accrue at 6% despite payments being based on a 1.5% teaser rate -- [Accrual rate - Teaser rate] gets added to loan balance and then accrues interest negative amortization -- On reset, payment is calculated based on the initial loan + the accrued interest "payment shock" -- Negative amortization + higher interest rate increases the probability of default

A buydown will make it ____ for a borrower to qualify for a loan.

Easier

Effect From Early Repayment Assume the loan is paid after five years instead of being help for the entire loan term

Effect from Early Repayment - Part 2 Impact of early repayment on the incremental borrowing cost n = 5 × 12 = 60 PV = -$10,000 PMT = $120.66 FV = $10,100.27 Solve for i = 1.2180% (monthly) Solve for i = 14.62% (annually = 1.2180 × 12)

=fv(

FV calculates the future value, such as the balance on a mortgage years in the future. FV is a mortgage balance at some date in the future; equals zero when the loan is fully amortized (at maturity)

The IRR and the years held after refinancing have a linear relationship.

False

True or false: The IRR from savings following refinancing is increasing at an increasing rate with the number of years held after refinancing.

False The IRR from savings following refinancing is increasing at a decreasing rate with the number of years held after refinancing.

ARM Payment Mechanics: Payment Caps and Negative Amortization

First year payment = -$252.96 First year mortgage balance = $58,747 Second year payment = -$265.61 Second year mortgage balance = $57,894

ARM Payment Mechanics: No Caps or Limitations

First year payment = -$252.96 First year mortgage balance = $58,748 Second year payment = -$285.50 Second year mortgage balance = $57,651

Types of amortization

Fully Amortizing Partially Amortizing Interest only (Zero - Amortizing) Negative Amortizing

Constant payment mortgages

Fully amortizing loan Ordinary annuities The payment is always the same and always due at month-end, the loan balance can change Loan term or maturity...

If your interest rate is high when getting a car:

Get a co-signer with a good credit score, and the interest rate will drop to 3.5% Payment will also go down, from $453 per month to $339 per month.

A buydown loan is used during periods of ____ interest rates to help borrowers qualify for financing.

High

The price of a property with a purchase money mortgage will typically be ______, relative to a traditional mortgage, all else equal.

Higher

Types of Second Mortgages

Home Equity Loans Home Equity Lines of Credit (HELOC)

How long (m = number of periods per year x n = number of years)

How many time periods are involved? e.g., you need to borrow $1,000 now, and an acquaintance offers to loan you the money if you repay $100 per month. What if you have to pay a $100 per month for 11 months? Well, now there's some interest involved, the effective rate on that loan would be 19.5%

Loan origination fees

are intended to cover expenses incurred by the lender for processing and underwriting loan applications preparation of loan documentation and amortizations schedules, obtaining credit reports, and any other expenses that the lender believes should be recovered from the borrower.

Which of the following are mortgage loans where interest rates may change with market conditions?

floating rate mortgage adjustable rate mortgage

With a fixed rate mortgage, the ----- bears the interest rate risk.

lender

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 PV = $74,443.49 PMT = -$482.10FV = $0 Solve for i = 0.5045% (monthly) Solve for i = 6.05% (annually = 0.5045 × 12)

Rate of return on the investment in refinancing

n = 25 × 12 = 300 PV = -$4,013.87 PMT = $44.45FV = $0 Solve for i = 1.0607% (monthly) Solve for i = 12.7285% (annually = 1.0607 × 12)

Which of the following determine whether to refinance a mortgage?

new loan terms being considered prepayment penalties

The effective cost of refinancing includes which of the following?

new monthly payments Points prepayment penalty

Adjustable Rate Mortgages (ARMs)

- The interest rate, used to amortize the loan, adjusts over time - The ARM contract rate of interest is: -- in = index + margin -- Index: standard indices (an interest rate that the lender does not control): --- US Treasury securities --- Average Cost of Funds Index (COFI) from the Federal Home Loan Bank --- London Interbank Offered Rate (LIBOR --- Any index that quickly adjusts for changes in inflation and general market risk -- Margin: --- Set in advance (e.g., 2 percentage points over LIBOR) --- premium added to the index to account for risk associated with that particular borrower or loan type/horizon

With a biweekly mortgage, there are ______ periods per year.

26

If a wraparound mortgage is for $100,000, and the initial loan has a balance of $70,000, the borrower will receive _______ in cash.

30,000

A loan of $125,000 with 3 points has a loan origination fee of how much?

3750 125000*.03

(75,000/90,000) x 4% + (15,000/90,000) x 4.9% = % (round to the nearest whole number)

4%

Examples of recent rates: Loans

5 year fixed-rate mortgage loan 3.38% • 30 year fixed-rate mortgage loan 4.13% • Home equity loan (2nd mortgage) 4.24% • Unsecured bank loan 6-29%

Number of compounding periods (m) affects the

APR Thus, APR can be used to compare loan offers with different compounding periods. Luckily, mortgages are typically monthly. So, no need.

Which provides for a more timely adjustment for lenders? SLAM ARM PLAM HAM

ARM

ARM Payment Mechanics: Payment Caps and Negative Amortization

Assume a $60,000 loan with a 30-year term and a 3% initial interest rate and 2 discount points where the ARM interest rate will be adjusted annually based on the index of one-year U.S. Treasury securities plus a 2 percent margin with a 5% payment cap, no interest rate cap and negative amortization.If the index is expected to be 2, 3, 4, and 2 percent for the next four years, what would be the payment adjustments and loan balances each year?

ARM Payment Mechanics: No Caps or Limitations

Assume a $60,000 loan with a 30-year term and an 3% initial interest rate and 2 discount points where the ARM interest rate will be adjusted annually based on the index of one-year U.S. Treasury securities plus a 2 percent margin with no payment or interest caps or negative amortization.If the index is expected to be 2, 3, 4, and 2 percent for the next four years, what would be the payment adjustments and loan balances each year?

Loan Refinancing Example

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.

ARMS and Floating Rate Loans: Payment Basics

Assume an ARM for $60,000 with an initial interest rate of 6% with a term of 30 years with payments reset at the end of each year based on an index. Initial payment = $359.73 n = 30 × 12 = 360 i = 6%/12 = 0.50 PV = $60,000 FV = $0

Effect of Origination Fees on IBR

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.

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.

PLAM: Payment Mechanics

Assume that a mortgage is made for $60,000 for 30 years at an interest rate of 4 percent and the loan balance will be indexed to the consumer price index (CPI) and adjusted annually with annual inflation at 6 percent.

Expected Yield Relationships and Interest Rate Risk

At origination, the expected yield on an ARM should be less than the expected yield on an FRM. Adjustable rate mortgages tied to short-term indexes are generally riskier to borrowers than ARMs tied to long-term indexes. ARMs with shorter time intervals between adjustments in payments are generally riskier to borrowers than those with longer time periods. To the extent ARMs contain maximum caps on interest rate adjustments, the interest rate risk incurred by borrowers will be lower. If an ARM has negative amortization due to a payment cap, the effect of changes in interest rates will not materially reduce interest rate risk to borrowers.

How much (i = interest rate)

At what rate can I borrow money? e.g., you sign a $300,000 mortgage loan. This is a 30 year mortgage, so you will make a total of 360 monthly payments. How much are your monthly payments? If the interest rate is 4%, then the monthly payment is $1,432. If the interest rate is 18% (what mortgage rates were in 1980), then the monthly payment is $4,521.

A purchase money mortgage typically has:

Below market rate

The Market Value of a Loan

Book value Market Value

How do you solve for the monthly investment you would need to make to accumulate $10,000 by the end of a 5-year period. Assume your investment earns 3% annual interest, compounded monthly? a) =PMT(i=3%, nper=5*12, PV=0, FV=10000) b) =PMT(i=3%/12, nper=5*12, PV=10000, FV=0) c) =PMT(i=3%/12, nper=5*12, PV=0, FV=10000)

C

Impact of mortgage loan maturity: Difference in Maturities

CF0 = -$10,000 CFj = $83.33 nj = 25 × 12 = 300 CFj = $598.77 nj = 5 × 12 = 60 Solve for IRR = 0.9386% (monthly) Solve for IRR = 11.26% (annually = 0.9386 × 12)