Solutions to Chapter Questions (2, 3, 4, 5, 9)

A mortgage loan is made to Mr. Jones for $30,000 at 10 percent interest for 20 years. If Mr. Jones has a choice between a CPM and a CAM, which one would result in his paying a greater amount of total interest over the life of the mortgage? Would one of these mortgages be likely to have a higher interest rate than the other? Explain your answer.

A CPM loan reduces the principal balance more slowly. As a result, if Mr. Jones chooses a CPM, he will pay a greater amount of interest over the life of the loan. The initial monthly payments for a CPM are considerably less than those of a CAM. Because of lower initial payments with a CPM, this would reduce borrower default risk associated with a CPM loan. Additionally, lenders receive a greater portion of their return (interest earned) early with a CPM. By decreasing default risk, a CPM may have a lower rate of interest than a CAM.

Distinguish between a mortgage and a note.

A note admits the debt and generally makes the borrower personally liable for the obligation. A mortgage is usually a separate document which pledges the designated property as security for the debt.

What is the sinking-fund factor? How and why is it used?

A sinking-fund factor is the reciprocal of interest factors for compounding annuities. These factors are used to determine the amount of each payment in a series needed to accumulate a specified sum at a given time. To this end, the specified sum is multiplied by the sinking-fund factor.

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 two-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.

Define amortization.

Amortization is the process of loan principal repayment over the loan term. Types of amortization are fully, partially, zero or negative rates of amortization.

Why do adjustable rate mortgages (ARMs) seem to be a more suitable alternative for mortgage lending than PLAMs?

An ARM provides for adjustments that are more timely for lenders than a PLAM because values for r, p, and f are revised at specific time intervals to reflect market expectations of future values for each component of i between adjustments dates.

What is an annuity? How is it defined? What is the difference between an ordinary annuity and an annuity due?

An annuity is a series of equal deposits or payments. An ordinary annuity assumes payments or receipts occur at the end of a period. An annuity due assumes deposits or payments are made at the beginning of the period.

What is a capitalization rate? What are the different ways of arriving at an overall rate to use for an appraisal?

An overall rate or overall capitalization rate is the rate on the overall property (debt and equity).One way of arriving at an overall rate is to use the band of investment approach. This is based on taking into consideration the investment criteria of both the lender and the equity investor involved in a project. This is done by taking a weighted average of the equity dividend rate expected by the investor and the mortgage loan constant (expressed on an annual basis) required by the lender.Two different ways of arriving at an overall rate are the direct capitalization approach and the present value method.

What does assignment mean and why would a lender want to assign a mortgage loan?

Assignment gives the lender the right to sell or exchange a mortgage loan to another party without the approval of the borrower.

What is the difference between base rent and effective rent?

Base rent reflects rent that will be paid per rentable square foot of leased space. It does not include additional items such as tenant improvement costs, expense pass throughs and other costs that are included when calculating effective rents.

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?

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 which time 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. 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. When both loans are originated at the same rate of interest, the yield to the lender will be the same regardless of when the loans are repaid (i.e. early or at maturity).

What are loan closing costs? How can they be categorized? Which of the categories influence 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. Categories include: statutory costs, third party charges, and additional finance charges. 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.

What does default mean? Does it occur only when borrowers fail to make scheduled loan payments?

Default means that the borrower has failed to (1) make scheduled loan payments or (2) violated any other provision in the note or mortgage.

What are forward rates of interest? How are they determined? What do they have to do with indexes used to adjust ARM payments?

Forward rates are based on future interest rate expectations that are implicit in the yield curve and reveal investor expectations of interest rates between any two maturity periods on the yield curve. For example, the yield for a security maturing one year from now is 8 percent, and the yield for a security that matures two years from now is 9 percent. Based on these two yields, we can compute a forward rate, or rate that an investor who invests in a one- year security can expect to reinvest funds for one additional year. This forward rate will be 10 percent because if investors have the opportunity to invest today in either the one- or the two-year security and are indifferent between the two choices, the investor buying a one-year security must be able to earn 10 percent on funds available for reinvestment at the end of year 1. This information is important and represents a reference point that may help lenders and borrowers when pricing ARMs and calculating expected yields at the time ARMs are made. Additionally, interest rate series, which may include forward rates of interest, comprise the indexes used to adjust ARMs. This is especially true if an index is long term in nature.

What does deficiency judgment mean?

If a default occurs leading to a judicial foreclosure and the property is sold, and if the dollars from the sale are not enough to pay off the loan balance, the borrower is personally liable for the difference.

When might a borrower want to have another party assume his liability under a mortgage loan?

If the loan was made with a favorable interest rate, the seller of the property may want to include this low rate loan as an additional incentive to sell the property.

An expected inflation premium is said to be part of the interest rate, what does this mean?

In general, the nominal interest rates for a specified period (say 10 years) is said to be a composite of three things; (a) real return-such as the growth rate in real GDP (underlying economic growth in the economy, (b) expected inflation , and (c) premium for risk. For example, if a lender quotes a 6% rate on a mortgage loan at a time when 10 year U.S. government bonds are yielding 3.6%, then the risk premium would be 2.4%. If at that same time growth in real GDP is 2.0% and is expected to continue at that rate for 10 years, then expected inflation can be estimated to be 1.6% (or 6%-2.4%-2.0% = 1.6%). Alternatively, if 10 year U.S. Government Bonds that are indexed for inflation (TIPs) are currently yielding 2.0% and 10 year Treasuries not indexed for inflation are yielding 3.6%, the difference, or 3.6%-2.0%, or 1.6% is an estimate of expected inflation.

List each of the main terms likely to be negotiated in an ARM. What does pricing an ARM using these terms mean?

Initial interest rate, index, adjustment interval, margin, composite rate, interest rate caps, negative amortization, floors, assumability, discount points, prepayment privilege. Anytime the process of risk bearing is analyzed, individual borrowers and lenders differ in the degree to which they are willing to assume risk. Consequently, the market for ARMs contains a large set of mortgage instruments that differ with respect to how risk is to be shared between borrowers and lenders. The terms listed above are features that might be used in pricing an ARM and establishing the bearing of risk.

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 means that the risk of default will generally increase to the lender, thereby reducing some of the benefits gained from shifting interest rate risk to borrowers.

What is an tenant estoppel? Why is it used?

It is a legal document used in many circumstances. In real estate, it is used by prospective investors to determine factual information about existing tenants, such as the amount of any rent owed, improvements promised by the current owners, etc.

What is meant by judicial foreclosure of a mortgage, and what alternatives are there to such action?

Judicial foreclosure involves the sale of real property by the courts to satisfy the unpaid debt that is secured by the mortgage. Alternatives: 1. Restructuring the mortgage loan 2. Transfer of the mortgage to a new owner 3. Voluntary conveyance of the title to the mortgagee 4. A "friendly" foreclosure 5. A prepackaged bankruptcy

Question 9-1. How does the use of leases shift the risk of rising operating expenses from the Lessor to the Lessee?

Leases determine how much risk will be borne by the lessor versus the lessee. Future increases in market rent might be compensated for by including an inflationary adjustment, such as a CPI adjustment. In the case of a CPI adjustment, the risk is shifted to the lessee, because the change in rents is not known in advance. If the lessee is responsible for any unexpected increases in the level of inflation, the lessor is insured that the real value of the lease will be preserved. The lessor can shift additional risk to the lessee by including net lease or expense stop provisions in the lease. It is important to note, however, that we would expect the lessor to accept a lower base rent as the burden of risk from inflation and property expense costs are shifted to the lessee.

Why do lenders charge origination fees, especially loan discount fees?

Lenders usually charge these costs to borrowers when the loan is made, or "closed", rather than charging higher interest rates. They do this because if the loan is repaid soon after closing, the additional interest earned by the lender as of the repayment date may not be enough to offset the fixed costs of loan origination.

What is meant by "loss to lease"?

Many leases reflect market conditions and rents that existed when the lease was executed. Many financial statements estimate gross rental revenue based on (1) all rental space re-leased today at prevailing rents and compare that amount to (2) actual rental revenue based on leases that have been executed at various times in the past. The difference between (1) and (2) is "loss to lease", or the difference between current market rents and rents actually collected based on lease terms with each tenant.

How can mechanics' liens achieve priority over first mortgages that were recorded prior to the mechanics' lien?

Mechanics' liens are permitted to be recorded after the fact. State laws generally give contractors, laborers, or suppliers of materials a certain period of time following the completion of work or delivery of materials during which to file their lien. When the lien is filed it relates back and takes priority over all liens filed after the time when materials were first delivered or work was first performed on real estate.

How do inflationary expectations influence interest rates on mortgage loans?

Most savings institutions had been making constant payment mortgage loans with relatively long maturities, and the yields on those mortgages did not keep pace with the cost of deposits. These problems prompted savings institutions (lenders) to change the mortgage instruments to now make more mortgages with adjustable interest rate features that will allow adjustments in both interest rates and payments so that the yields on mortgage assets will change in relation to the cost of deposits.

What is negative amortization?

Negative amortization means that the loan balance increases over time because payments are less than the interest due.

In the absence of loan fees, does repaying a loan early ever affect the actual or true interest cost to the borrower?

No, the effective interest rate will equal the contract rate of interest.

Can borrowers pay off part or all of a loan anytime that they desire?

No. In general, prepayment is a privilege not a right. In cases of residential/consumer loans made by federally related lenders, this option is usually provided to borrowers. In commercial real estate loans it is usually not.

Is a cap rate the same as an IRR? Which is generally greater? Why?

No. The cap rate is the relationship between the current NOI and present value. The IRR is the return on all future cash flows from the operation and sale of the property. Usually the IRR is greater than the cap rate.

How does the price level adjusted mortgage (PLAM) address the problem of uncertainty in inflationary expectations? What are some of the practical limitations in implementing a PLAM program?

One concept that has been discussed as a remedy to the imbalance problems for savings institutions is the price level adjusted mortgage (PLAM). To help reduce interest rate risk, or the uncertainty of inflation and its effect on interest rates, it has been suggested that lenders should originate mortgages at interest rates that reflect expectations of the real interest rate plus a risk premium for the likelihood of loss due to default on a given mortgage loan. Problems with PLAM: a. Should prices of other goods, represented in the CPI increase faster than housing prices, indexing loan balances to the CPI could result in loan balances increasing faster than property values. If this occurred, borrowers would have an incentive to default. b. A second problem with PLAMs has to do with the relationship between mortgage payments and borrower incomes. Should inflation increase sharply, it is not likely that borrower incomes would increase at the same rate in the short run. During short periods, the payment burden may increase, and households may find it more difficult to make mortgage payments. c. A third problem with PLAMs is that the price level chosen for indexation is usually measured on a historical basis. In other words, the index is based on data collected in the previous period but published currently.

Distinguish between the initial rate of interest and expected yield on an ARM. What is the general relationship between the two? How do they generally reflect ARM terms?

One important issue in ARMs is the yield to lenders, or cost to borrowers, for each category of loan. Given the changes in interest rates, payments, and loan balances, it is not obvious what these yields (costs) will be. This means that the costs of each category of loan will be added to the initial interest rate, thus producing an expected yield.

What is partial amortization?

Partial amortization occurs when payments exceed the accrued interest due but not by enough to reduce the amount owed to zero at maturity.

What are pass through expenses, recoverable expenses and common area expenses? Give examples of each.

Pass throughs are expenses such as electricity, insurance, and property taxes that are billed directly to tenants on the basis of the rentable area that they occupy. Recoverables are expenses incurred by owners for specific expenses identified in a lease such as security, maintenance, utilities, etc. and are pro-rated and billed to tenants. Common areas include mall open areas, parking areas, lobbies, and hallways. Expenses related to these areas are referred to as common area expenses.

What is meant by a "purchase money" mortgage loan? When could a loan not be a purchase money mortgage?

Purchase money means funds from the loan will be used to purchase a property. It will not provide funds for other uses such as could be the case with a refinancing.

What does it mean when a lender accelerates on a note? What is meant by forbearance?

The acceleration clause gives the lender the right or option to demand the loan balance owed if a default occurs. Forbearance by the lender allows the borrower time to cure a deficiency without the lender giving up the right to foreclose at a future time.

What is the accrual rate and payment rate on a mortgage loan?

The accrual rate is usually the nominal rate divided by the number of periods within a year that will be used to calculate interest. For example, if interest is to be accrued monthly, the nominal rate is divided by 12; if daily, the nominal rate is divided by 365. The payment rate, or "pay rate", is the % of the loan to be paid at time intervals specified in the loan agreement. This rate is used to calculate payments which are usually made monthly (but could be quarterly, semi-annual, etc.) If the pay rate exceeds the accrual rate, this indicates that some loan repayment (amortization) is occurring. When it is equal to the accrual rate, amortization is not occurring. If the accrual rate is lower than the interest rate there will be negative amortization.

What does non-recourse financing mean?

The borrower is not personally liable on the note. The lender may look only to the property (security) to satisfy the loan in the event of a default.

What is the essential concept in understanding compound interest?

The concept of earning interest on interest is the essential idea that must be understood in the compounding process and is the cornerstone of all financial tables and concepts in the mathematics of finance.

How does discounting, as used in determining present value, relate to compounding, as used in determining future value? How would present value ever be used?

The discounting process is a process that is the opposite of compounding. To find the present value of any investment is simply to compound in a "reverse" sense. This is done by taking the reciprocal of the interest factor for the compound value of $1 at the interest rate, multiplying it by the future value of the investment to find its present value. Present value is used to find how much should be paid for a particular investment with a certain future value at a given interest rate.

If an ARM is priced with an initial interest rate of 8 percent and a margin of 2 percent (when the ARM index is also 8 percent at origination) and a fixed rate mortgage with constant payment is available at 11 percent: a. what does this imply about inflation and the forward rates in the yield curve at the time of origination? b. What is implied if a fixed rate mortgage were available at 10 percent? 12 percent?

The initial interest rate and expected yield for all ARMs should be lower than that of a fixed rate mortgage on the day of origination. The extent which the initial rate and expected yield on an ARM will be lower than that on a fixed rate mortgage or another ARM, depends on the terms relative to payments, caps, etc. One would expect the difference between interest rates at the point of origination to reflect expectations of inflation and forward rates as well. As a fixed rate mortgage's interest rate increases from 11 percent to 10 percent and 12 percent, greater inflation and/or greater uncertainty with respect to inflation is implied.

What is an internal rate of return (IRR)? How is it used? How does it relate to the concept of compound interest?

The internal rate of return integrates the concepts of compounding and present value. It represents a way of measuring a return on investment over the entire investment period, expressed as a compound rate of interest. It tells the investor what compound interest rate the return on an investment being considered is equivalent to.

What special advantages does a mortgagee have in bidding at the foreclosure sale where the mortgagee is the foreclosing party? How much will the mortgagee normally bid at the sale?

The mortgagee can use its claims as a medium of exchange in the purchase, except for costs, which must be paid in cash. Others must pay cash for their purchases or by obtaining a new loan. Lenders will normally bid the full amount of their claim only where it is less than or equal to the market value of the security, less foreclosure, resale, and holding costs.

What dangers are encountered by mortgagees and unreleased mortgagors when property is sold "subject to" a mortgage?

The mortgagor will be responsible if the person acquiring the property subject to the mortgage defaults. In turn, if the original mortgagor then defaults, the bank will have to foreclose on the property which may not be worth what is left to pay on the mortgage.

What are the risks to the lender if a borrower declares bankruptcy?

The probability of default or bankruptcy by a borrower and the legal alternatives available to each party affect the expected return to a lender from the loan. Lenders may find that their security is tied up for years during the reorganization of the debtor's financial affairs and that they are unable to foreclose on their liens where such a foreclosure would interfere with the debtor's plan of reorganization. Lastly, lenders may not be able to accelerate balances or raise interest rates because borrowers have the right to cure default in bankruptcy and reinstate the mortgage.

What is the economic rationale for the sales comparison approach? What information is necessary to use this approach? What does it mean for a property to be comparable?

The rationale for the market approach (otherwise known as the sales comparison approach), lies in the principle that an informed investor would never pay more for a property than what other investors have recently paid for comparable properties. The sales comparison approach to valuation is based on data provided from recent sales of properties highly comparable to the property being appraised.For a property to be comparable, the sale must be an "arm's-length" transaction or a sale between unrelated individuals. Sales should represent normal market transactions with no unusual circumstances, such as foreclosure, sales involving public entities, and so on.

Question 10-1. What is the economic rationale for the cost approach? Under what conditions would the cost approach tend to give the best value estimate?

The rationale for using the cost approach to valuing (appraising) properties is that any informed buyer of real estate would not pay more for a property than what it would cost to buy the land and build the structure. The cost approach is most reliable where the structure is relatively new and depreciation does not present serious complications.

Why do the monthly payments in the beginning months of a CPM loan contain a higher proportion of interest than principal repayment?

The reason for such a high interest component in each monthly payment is that the lender earns an annual percentage return on the outstanding monthly loan balance. Because the loan is being repaid over a long period of time, the loan balance is reduced only very slightly at first and monthly interest charges are correspondingly high.

What are CAM charges?

These are expenses related to common area maintenance of hallways, lobbies, etc. that are usually prorated and passed on to tenants.

Question 5-1 In the previous chapter, significant problems regarding the ability of borrowers to meet mortgage payments and the evolution of fixed interest rate mortgages with various payment patterns were discussed. Why didn't this evolution address problems faced by lenders? What have lenders done in recent years to overcome these problems?

These inadequacies stem from the fact that although payment patterns can be altered to suit borrowers as expectations change, the CPM, CAM, and GPM are all originated in fixed interest rates and all have predetermined payment patterns. Neither the interest rate nor the payment patterns will change, regardless of economic conditions. A variety of mortgages are now made with either adjustable interest rates or with variable payment provisions that change with economic conditions.

What is the effective borrowing cost (rate)?

This differs from the contract rate because it includes financing fees (points, origination). It differs from the APR because the latter is calculated assuming that the loan is repaid at maturity. When calculating the effective cost, the expected repayment or payoff date must be used. The latter is usually sooner than the maturity date.

What is meant by the "nominal rate" on a mortgage loan?

This rate is usually quoted as an annual rate, however the time intervals used to accrue interest is generally not quoted explicitly. Further, the rate generally does not specify the extent of any origination fees and/or discount points.

What does the time value of money mean?

Time value simply means that if an investor is offered the choice between receiving $1 today or receiving $1 in the future, the proper choice will always be to receive the $1 today, because that $1 can be invested in some opportunity that will earn interest. Present value introduces the problem of knowing the future cash receipts for an investment and trying to determine how much should be paid for the investment at present. When determining how much should be paid today for an investment that is expected to produce income in the future, we must apply an adjustment called discounting to income received in the future to reflect the time value of money.

What is the connection between the Truth-in-Lending Act and the annual percentage rate (APR)?

Truth-in-Lending Act: The lender must disclose to the borrower the annual percentage rate being charged on the loan. The APR reflects origination fees and discount points and treats them as additional income or yield to the lender regardless of what costs the fees are intended to cover. The APR is always calculated assuming that the loan is repaid at maturity.

What is meant by usable vs. rentable space?

Usable space is the area actually occupied by the tenant. Rentable space is usable space plus a share of common area in a property which is included in the load factor.

What general rule can be developed concerning maximum values and compounding intervals within a year? What is an equivalent annual yield?

Whenever the nominal annual interest rates offered on two investments are equal, the investment with the more frequent compounding interval within the year will always result in a higher effective annual yield. An equivalent annual yield is a single, annualized discount rate that captures the effects of compounding (and if applicable, interest rate changes).