YIELDS, BONUSES, DISCOUNTS, AND

Transcription

1 YIELDS, BONUSES, DISCOUNTS, AND THE SECONDARY MORTGAGE MARKET 7 Introduction: Primary and Secondary Mortgage Markets The market where mortgage loans are initiated and mortgage documents are created is referred to as the primary mortgage market; the market where borrowers and lenders meet. The process whereby a lender and borrower agree to initiate a loan and create the related mortgage documents is referred to as originating a mortgage or mortgage initiation. The lender and borrower agree, at the time a mortgage loan is initiated, to the financial conditions of the loan contract. Agreement is reached as to the loan amount, the contract rate of interest, the compounding and payment frequency, the term of the loan, and the amortization period. From these financial conditions, the magnitude of the required periodic payments and, in the case of many mortgage loans, balloon payments and a final outstanding balances at the end of the term, are determined. These payments are fixed as a result of the contract. From a financial point of view, once the contract is established, the mortgage is essentially a promise, on behalf of the borrower, to make payments according to a specified schedule and to pay off the balance at the end of the contract term. The mortgage contract is essentially a secured promise by the borrower to make payments according to a specified schedule, and to pay off the balance at the end of the contract term, in exchange for the loan of a principal amount of money. The borrower's promise is secured by their entitlements to real property. Once mortgages are created in the primary mortgage market, they may be sold, by the initiating lender, to 1 subsequent investors in what is referred to as the secondary mortgage market. The right to receive payments and a final outstanding balance payment, as specified and fixed in the mortgage contract, is what subsequent purchasers of the mortgage are acquiring. This resale market for mortgages has developed significantly in recent years, prompted in part by the efforts of Canada Mortgage and Housing Corporation to develop an active secondary market for residential mortgages 3 via NHA mortgage-backed securities. A number of large institutions, most notably the pension funds, were encouraged to enter the real estate financing field via the secondary market by making significant acquisitions of mortgage loans initiated by other (primary) lending institutions. Pension funds were initially attracted by the combination of the investment security provided through the use of private and government mortgage insurance, and the yields which were above those historically offered on high quality corporate and public sector bond issues. 1 3 In this context, secondary does not necessarily bear any relationship to the priority of the mortgage against the security of the property. It is unfortunate that the term secondary is commonly used to describe the resale market activities and second mortgage is used to describe a mortgage which is registered second in priority. To avoid confusion, the term junior mortgage will be used to describe mortgages subsequent to the first mortgage charge. A first mortgage, or any junior (subsequent) mortgage, or any other financial interest may be traded in the secondary market. Canada Mortgage and Housing Corporation (CMHC) is a federal crown corporation responsible for administering federal government housing programmes and insured mortgages granted under the National Housing Act. National Housing Act (NHA) mortgage-backed securities are undivided interests in a pool of insured mortgages, guaranteed by CHMC. 7.1

2 Chapter 7 Note that the terms of the financial mortgage the loan amount, the interest rate, and the amortization period are used to determine the size of the periodic payments and the outstanding balance at the end of the term. Once the contract is established, it is the promise to make these payments that is of value. The loan amount is imbedded in the payments, and is no longer of direct significance; the mortgage contract does not require that the lender advance the face amount to the borrower nor does it ensure that the lender will receive the face amount if the mortgage is sold to a subsequent investor. This creates, in both the primary and secondary mortgage markets, the potential for situations introducing what is called a bonus or a discount on a mortgage loan. Bonuses and Discounts in the Primary Mortgage Market In the primary market, the effect of a mortgage contract alone is not to contractually oblige the lender to advance the face value of the loan. In fact, in many mortgage loans, less than the full face amount of the loan is advanced to the borrower. In many cases, the difference is the result of appraisal, survey, and legal fees connected with consummating the contract. Such items represent costs paid by the lender on behalf of the borrower in arranging the loan. Other fees often connected with originating a mortgage include a lender bonus and a mortgage brokerage fee. A lender bonus is a fee that may be charged by lenders as a means of increasing their yield on a loan. A brokerage fee is charged by mortgage brokers if their services are rendered in arranging a mortgage loan. Whenever the amount advanced to a borrower is less than the face value of the mortgage (that is, whenever a bonus is charged), the loan is referred to as a bonused mortgage. Bonused mortgages are, under certain circumstances, subject to specific legal requirements under provincial or federal legislation. The fees connected with originating a mortgage are normally paid by the borrower. Either by convention or choice, the fees may be deducted from the loan advance or added to the fact value of the loan. When a fee is deducted from the loan advance, it is referred to as a discount. A discount does not change the face value of the loan. When a fee is added to the face value of a loan, it is referred to as a bonus. Independent of the justification for the additional cost, the effect on the borrower is the same: to reduce the amount actually received relative to the loan amount and, as a result, to increase the real interest rate paid for the funds actually received. In this context, the rate of interest stated in the contract is, to the borrower, of secondary importance. The most relevant measure of the cost of borrowing (lender's yield) is the rate of interest which equates the contracted payments to the funds actually received (advanced). 4 Bonused loan origination is common in the United States, where it is referred to as points up front or front-end loading. In Canada, bonusing at the time a loan is initiated is a common arrangement among both commercial and residential mortgage lenders in two general situations: C C In a case where a mortgage broker adds a bonus to the mortgage as a part of the brokerage fee. For example, the borrower arranges a loan for $1, to be advanced, but signs for a face amount of $13, where the $3, represents a brokerage fee. In cases where a private lender extends funds and, for whatever reason, demands (and the borrower agrees) compensation in excess of the contractual rate. 4 Points up front represents a payment made at the beginning of the loan period that may be set in terms of a percentage of the loan amount and is discussed in Chapter 8. 7.

3 Yields, Bonuses, Discounts, and the Secondary Mortgage Market Bonuses and Discounts in the Secondary Mortgage Market The terms bonus and discount also arise quite naturally in association with mortgages purchased in the secondary market. If a mortgage (or agreement for sale or some other financial instrument) is purchased for more than the current outstanding balance (or book value), a bonus is involved. In this situation, the bonus is defined as the difference between the purchase price and the current outstanding balance, providing the difference is positive. Similarly, a discount is involved whenever a mortgage (or other instrument) is purchased for less than the current outstanding balance. The dollar amount of the discount is the amount by which the current outstanding balance exceeds the purchase price, providing the amount is positive. Consider a situation where a mortgage is sold in the secondary market. The term bonus is used if the amount received on sale minus the outstanding balance on the mortgage at the time of sale is greater than zero. The term discount is used if the amount received on sale minus the outstanding balance on the mortgage at the time of sale is less than zero. In the case of a newly initiated mortgage loan, the amount of the discount is simply the difference between the face value (or principal amount) of the loan and the amount realized on the sale. In the case of existing mortgage loans, the dollar amount of the discount is the difference between the outstanding balance on the loan at the time it is sold and the amount which is received on the sale. If the mortgage is sold at a price equal to the outstanding balance at the time of the sale, neither a bonus nor a discount is involved. The sale is said to occur at par value. There are two common situations where bonuses and discounts occur in the secondary market. The first is the result of changes in market interest rates. If interest rates increase during the period between the initiation of a mortgage and its subsequent sale in the secondary market, the purchaser will be willing to offer somewhat less to the original lender than the principal balance outstanding on the loan at the time the loan is sold (that is, the purchase will be made at a discount). Discounting is the way that the purchaser increases the yield on the investment (purchase price) over the initial contract rate. If interest rates fall over the period of time between initiation and sale of the mortgage, the purchaser may be willing to pay more than the current outstanding balance, that is, the purchaser will pay a bonus in order to acquire the relatively high rate mortgage. The second situation occurs when interest rates are deliberately set below market when mortgage loans are initiated, primarily as a result of vendor financing. In cases where a property vendor offers to finance a portion of the sale price of the property with a loan at less than market rates, the vendor hopes to achieve a (apparently) higher sales price by offering cheaper loans. For example, a vendor offers a property for sale at $, and offers to provide a vendor mortgage of $15, at % less than market rates. If the vendor attempts to sell the mortgage, it will be sold at a discount so that subsequent investors realize the current market rates. This topic is discussed in detail in the next chapter. In this context, it may be noted that real estate representatives should exercise particular care in offering advice to vendor clients where the client is offering financing to prospective purchasers to facilitate the sale of their property. Where a vendor is not made aware of the fact that providing a mortgage at an interest rate less than that prevalent in the market will decrease the cash-equivalent price of the mortgage (i.e., the mortgage will sell at a discount), the vendor may seek damages from the representative. Calculations involving vendor financing are covered in the next chapter. 7.3

4 Chapter 7 Bonuses and Discounts on Fully Amortized Loans Illustration 7.1 A borrower has obtained a mortgage loan having a face value of $5,. The loan is written at an interest rate of 13.5%, compounded semi-annually, and is to be fully amortized by constant monthly payments over a 15-year amortization period. The face value of the mortgage is inclusive of a $1, bonus. Therefore, only $49, is advanced to the borrower (the $5, face value, less the $49, actually advanced, equals the $1, bonus). The original lender does not wish to assume the risks involved in administering this mortgage. Immediately upon initiation of the loan, the lender sold the mortgage contract to a third party investor for $49,5. The loan was, therefore, sold at a $75 discount. Statement of Problem: (a) Calculate the rate of interest per month paid by the borrower on funds actually advanced. (b) Calculate the monthly rate of interest earned by the investor. (c) Calculate the original lender's gross profit. Analysis: Data Original Loan Face Value: $5, Funds advanced: $49, Term and Amortization: 15 years or 18 months Contract Rate: j =13.5% Sold For: $49,5 Solution: There are three elements to the preceding transaction: the mortgage contract, the funds actually advanced, and the subsequent sale of the contract to an investor. Each of these will be considered, starting with the mortgage contract. Part One: The Contractual Terms of the Mortgage The individual has arranged a mortgage loan with a face value of $5,, which will be fully amortized over 15 years with level monthly payments at a contract rate of 13.5% per annum, compounded semiannually. The borrower is, by contract, agreeing to make a stream of constant regular monthly payments. The first step in the analysis is to find the nominal rate with monthly compounding and then determine the size of the required monthly payments. Analysis: PV = PMT a Ún,j á $5, = PMT a Ú18, j = %á 7.4

5 Yields, Bonuses, Discounts, and the Secondary Mortgage Market CALCULATION Comments 13.5 P/YR P/YR N 5 PV FV , j Enter amortization period Enter loan amount PMT Calculate payment %/& PMT N Revised amortization period 179 N 179 FV %/& PV PMT 1 N 1 FV Final payment 5 Thus, the mortgage would call for 179 monthly payments of $637.8 each and a final payment of $ Part Two: The Bonused Mortgage Loan The mortgage under consideration has a $5, face value: the borrower is contractually obliged to repay $5, at 13.5% per annum, compounded semi-annually. The face value of the loan and the contract rate of interest are used to determine that the borrower is, in effect, promising to make 179 monthly payments of $637.8 plus a final payment. Such a payment stream is sufficient to repay $5, at 13.5% per annum, compounded semi-annually. It is, however, also sufficient to repay $4,718.7 at 18% per annum, compounded semi-annually; $75,85.91 at 6% per annum, compounded semi-annually and an infinite number of other loan amounts at other interest rates. In the case at hand, although the face value of the loan is $5,, this amount includes a bonus of $1, as a fee to the lender. The borrower actually receives $49, in exchange for a promise to repay $ As the monthly payment has been rounded up to $637.8, the actual payment stream would consist of 179 monthly payments of $637.8 and a 18th payment of $635.8 to offset the rounding of each monthly payment. 7.5

6 Chapter 7 per month for 179 months plus a final payment. The central concern is to find the rate of interest that equates the payments to a present value of $49,. This rate more accurately reflects the actual position of the borrower. The procedure to find the cost of funds advanced to the borrower (the rate of interest paid on the amount of the loan net of the bonus) is of exactly the same form as that used to solve for the size of the monthly payments. The following equation represents the financial arrangement from the mortgagor's perspective: PV = [PMT a Ún,já] + Final (1 + i) -(n+1) and j $49, = [$637.8 a Ú179, já] + $635.8(1 + m ) -18 m where j% is the rate of interest at which the monthly payments have a present value of $49, and n is the number of FULL payments required on this loan. In this and similar cases, where the payments are rounded up to the next higher whole cent, the final payment differs little from the rounded payment ($637.8! = $1.8). Moreover this difference does not occur until the 18th month, and the effect today (present value) is insignificant. As a consequence, most analysts simply ignore the minor impact of the rounded payment and elect to proceed with payments of $ Hence $49, = $637.8 a Ú , j á The monthly rate of interest that the borrower is actually paying is j = ( % per month), not the j = % ( % per month) specified in the contract. This can be directly compared to the contract rate by converting the actual monthly rate to its equivalent semi-annual rate (j ). 5 PV 5, FV CALCULATION (continued) Comments I/YR and P/YR already stored %/& PMT Actual payments N Recalculate N based on PMT of $ PV 49, Funds actually advanced I/YR j rate on funds advanced j 1 P/YR j 7.6

7 Yields, Bonuses, Discounts, and the Secondary Mortgage Market Expressed as a nominal rate with semi-annual compounding, the borrower is paying interest at a rate of % for the funds advanced. For purposes of comparison with the contract rate, the equivalent nominal rate with semi-annual compounding is % higher than the 13.5% stated in the contract. This simplification will give an exact answer in this case but will not always provide exact answers. For example, the rate of interest the borrower pays, based on the simplified calculation, is % per annum, compounded monthly. CALCULATION Comments P/YR j %/& PMT N FV 179 PV 6M 48, , FV 18 N %/& FV PMT PV M% RM , Hence, in this case, the error based on the use of the simplified form of analysis is $.481. Readers are cautioned that any rounding of payments will have an effect on the amount of the final payment. As a consequence, most fully amortized loans become partially amortized loans in as much as an unusual final payment is involved. Part Three: The Discounted Mortgage Loan The original lender immediately sold the right to receive the payments to a third party for $49,5. Consequently, the loan is sold at a discount of $75 (since the face value is $5,). 7.7

8 Chapter 7 To determine the rate realized by the investor, one now has to solve for a rate of interest that equates the future payments to a present value of $49,5. Analyzing the transaction from the investor's perspective: the investor is paying $49,5 for the right to receive the terms of the contract (i.e., monthly payments of $637.8). PV = PMT a Ún,já $49,5 = $637.8 a Ú , já CALCULATION Comments I/YR From interest rate conversion of j =13.5% P/YR 18 N 18 FV 5 PV 5, PMT %/& PMT N PV 49,5 Amount issued I/YR j on funds invested P/YR j Thus, the investor should expect a yield of % per year, compounded monthly on the $49,5 invested. Finally, to make the expression of the interest rate earned comparable to the contract rate, the equivalent nominal rate with semi-annual compounding is %. Part Four: Summary A review of this illustration demonstrates that the series of payments resulting from the interaction of the face value of the contract ($5,) and the contract rate of interest (j = 13.5%) do not always fully explain the nature of the financial relationships. According to the Terms of the Contract: Face Value: $5, Rate of Interest: 13.5% per annum, compounded semi-annually Amortization Period: 15 years or 18 monthly payments Result: Monthly Payments of $637.8, N =

9 Yields, Bonuses, Discounts, and the Secondary Mortgage Market From the Mortgagor's Perspective: Monthly Payment: $637.8 Number of Payments: 18 ( ) Funds Actually Received: $49, Result: Interest Paid on Funds Actually Received: % per annum, compounded semi-annually. From the Investor's Perspective: Monthly Payments: $637.8 Number of Payments: 18 ( ) Funds Invested: $49,5 Result: Interest Earned on Funds Invested: % per annum, compounded semi-annually. From the Original Lender's Perspective: Cash Received $49,5 (from investor)! Cash Paid Out! $49, (to mortgagor) = Gross Profit: $ 5 (to broker) The gross profit to the original lender can be seen as compensation for costs and services involved in arranging and subsequently selling this mortgage loan. Example 7.1 A borrower has arranged a second mortgage which has a face value of $9,54.39 and a contract rate of % per annum, compounded semi-annually. The loan, according to the terms of the contract, is to be fully amortized with constant monthly payments of $34 over 35 months. The borrower receives only $7, The $, difference between the face value of the loan and the amount advanced to the borrower represents a bonus to the lender. Statement of Problem: Calculate the rate of interest paid by the borrower on the funds actually received. Express this rate as a nominal rate with semi-annual compounding. Solution: j = % j = % 7.9

10 Chapter 7 Example 7. An investor has purchased a newly created mortgage where he will receive monthly payments of $65 for months. The purchase price was based on the assumptions that the mortgage was written at j =13% and the investor would earn a yield of 15% per annum, compounded semi-annually. As the mortgage is fully amortized, the monthly payments will serve to extinguish the borrower's financial obligation no outstanding balance (or balloon) payment is required. Statement of Problem: Determine the following from the information given: (a) The face value of the loan. (b) The discounted value of the loan (the price paid by the investor). (c) The size of the discount necessary to increase the yield from 13% to 15%, both compounded semiannually. Solution: (a) $4,44.77 (use j = % equivalent to j =13%) (b) $39,47.1 (use j = % equivalent to j =15%) (c) $3,17.56 ($4,44.77! $39,47.1) Example 7.3 A mortgagor has signed a second mortgage contract where the loan amount is specified to be $,5, the contractual rate of interest is 9% per annum compounded annually, and the loan is to be fully amortized with monthly payments over 5 years. As a result of a bonus arrangement, the borrower is advanced only $11,5. The mortgage lender, immediately after receiving the 6th monthly payment, sells the right to receive the remaining payments to an investor. The investor plans to realize a yield of 7% per annum, compounded semiannually. Statement of Problem: 7.1 Given the information above, calculate: (a) The size of the contractual monthly payment (round to the next higher cent). (b) The rate of interest paid by the borrower on the funds actually advanced. Express this as a monthly rate and as an equivalent annual rate with semi-annual compounding. (c) The outstanding balance immediately after the sixth monthly payment. (d) The price paid by the investor assuming the yield is to be j = 7%. (e) The discount necessary to decrease the yield from j 1 = 9% to j = 7%. Solution: (a) PMT = $57.36, N = months (b) i mo = % j = %

11 Yields, Bonuses, Discounts, and the Secondary Mortgage Market (c) OSB 6 = $11, (d) j = % N = months PV = $11,917.3 (e) Discount = $ Bonuses and Discounts on Partially Amortized Loans The calculations for bonuses and discounts are slightly modified in cases where either the mortgage loans are not fully amortized or the impact of rounding payments is such as to influence significantly the amount of the final payment. While the principles involved are not changed, the calculations are made slightly more complex since the outstanding balance on the mortgage must be explicitly considered. Illustration 7. The details of this illustration are similar to Illustration 7.1 except that the loan is assumed to have a five-year contractual term (partially amortized mortgage). Statement of Problem: Given the inclusion of a five-year contractual term, calculate the cost of funds advanced (i.e., the rate paid by the borrower on funds actually advanced $49,) and the yield earned by the investor on the ($49,5) discounted mortgage investment. Analysis: Data Summarizing the details from Illustration 7.1, one finds that the following conditions prevail: Mortgage Contract: Face Value: $5, Interest Rate: j = 13.5% per annum compounded semi-annually j = % Payments: $637.8 Outstanding Balance Due after 6 monthly payments (OSB 6) =? Funds Advanced: $49, Mortgage Investor's Purchase Price: $49,5 Solution: Part One: The Mortgage Contract As a first step, it is necessary to calculate the outstanding balance at the end of the term of the loan. 7.11

12 Chapter 7 CALCULATION Comments I/YR j from interest rate conversion calculation P/YR 5 PV %/& PMT 5, Face value Actual payment FV N Actual amortization period th 6 N FV -4, Calculate balance after 6 payment Part Two: The Bonused Mortgage Calculate the rate paid by the borrower on funds actually advanced. The determination of the rate, in this case, rests with identifying the rate of interest that equates the sum of the present values of the two elements of the cash flow to the amount actually advanced. Thus, the present value of the 6 payments of $637.8 plus the present value of the outstanding balance payment of $4,44.64 to be made in 6 months must equal $49, (the amount received). The task is to determine the interest rate at which this occurs. As the borrower has two forms of payments to make (monthly payments and the outstanding balance), the analysis must take into account both components: PV = PV (payments) + PV (outstanding balance) $49, = [$637.8 a Ú6,i á] + $4,44.64 (1 + i ) mo -6 mo The two parts of the borrower's obligation (an ordinary simple annuity of 6 payments of $637.8 and a single lump sum payment of $4,44.64 sixty months in the future) both affect the rate of interest to be calculated. Most, but not all, financial calculators can handle the two types of cash flows simultaneously provided that the number of payments (in this case, 6) is identical to the number of periods the lump sum is outstanding. The mortgage contract calls for $5, to be repaid by 6 monthly payments of $637.8 plus the outstanding balance of $4,44.64 to be repaid 6 months in the future. The contract rate of interest (j = 13.5% or j = % or imo = %) is the interest rate at which the present value of the stream of monthly payments and the present value of the outstanding balance equal the face value of the loan: -6 $5, = $637.8 a Ú6, i mo = %á + $4,44.64 ( ) 7.

13 Yields, Bonuses, Discounts, and the Secondary Mortgage Market As only $49, is actually advanced, and as the amount and timing of the payments and outstanding balance remain unchanged, the rate of interest paid on the funds advanced must be higher than the contract rate of % per month. However, as the bonus is relatively small in comparison to the amount advanced, the rate paid on funds actually advanced will not be substantially above the contract rate. The interest rate is calculated as follows: CALCULATION (continued) Comments I/YR and P/YR already stored 6 N 6 Number of compounding periods %/& PMT Payment per period %/& FV -4,44.64 Outstanding balance to be paid in the future 49 PV 49, Funds advanced I/YR j rate j rate P/YR j At j = %, the sum of the present values of the stream of required monthly payments and the outstanding balance is equal to the amount of the funds advanced. Thus, j = % is the rate of interest that the borrower is paying on the funds actually received (cost of funds advanced). Note that this rate of interest is higher than that calculated for the similar fully amortized loan (j = % in Illustration 7.1). This higher rate results from the fact that the $1, bonus is being amortized over 5 years on this mortgage rather than the 15 years on the fully amortized loan. Part Three: The Discounted Mortgage Loan In solving for the investor's expected yield rate, a similar process is used. The problem reduces to identifying the interest rate that equates the two elements of the cash flow to a present value of $49,5. PV = PV (payments) + PV (outstanding balance) $49,5 = [$637.8 a Ú6,i á] + $4,44.64 (1 + i ) mo 1-6 mo Note that as the mortgage contract specifies the amount and timing of payments (including the outstanding balance), these elements remain unchanged during the entire analysis. The only changes for the analysis of a discounted mortgage are the present value ($49,5) and the resultant yield rate. 7.13

14 Chapter 7 P/YR CALCULATION Comments j from interest rate conversion 6 N 6 Number of compounding periods %/& PMT Payment %/& FV -4,44.64 Outstanding balance to be paid in future 495 PV 49,5 Paid by investor I/YR j P/YR j The investor expects to earn % per annum, compounded monthly or j = % on the partially amortized loan. This can be compared to the j = % on a similar, but fully amortized, loan. The impact of the shorter contractual term on the yield to the investor is significantly magnified when larger bonuses and/or discounts exist. Contract SUMMARY TABLE Fully Amortized Partially Amortized Face value $5, $5, Rate j = 13.5% j = 13.5% Amortization Period 15 years 15 years Term 15 years 5 years Payments $637.8 $637.8 Outstanding balance $4,44.64 Final payment $635.8 Bonused Mortgage Funds Advanced $49, $49, Cost of funds advanced j = % j = % Discounted Mortgage Funds Paid $49,5 $49,5 Investor's Yield j = % j = % Broker's Gross Profit $5 $5 7.14

15 Yields, Bonuses, Discounts, and the Secondary Mortgage Market Note that the higher rate paid by the borrower on the funds advanced and the higher rate earned by the third party investor on the purchase price, each using the partially amortized loan, are solely the result of paying the $1, bonus and receiving the $5 discount, respectively, over 5 years on the partially amortized loan rather than the 15 years on the fully amortized loan. The Impact of Partial Amortization on Interest Rates and Yields on Bonused Mortgage Loans With reference to Illustration 7., it is extremely important to note that the rate charged to the borrower on funds advanced for the partially amortized loan (j = %) is higher than the rate which would apply if the loan was fully amortized (j = %). The difference, slightly more than 1/5 of one percent, is solely the result of the change in the contractual term of the loan. On the fully amortized loan, the bonus of $1, is paid by the borrower for the use of funds over a 15 year period. Reducing this period to 5 years, without decreasing the size of the bonus or brokerage fee, increases the effective cost of borrowing. With a bonus of any given size, and all other things being held equal, the effective rate paid by the borrower on funds advanced will increase dramatically as the term of the loan is progressively shortened. This relationship is illustrated graphically in Figure 1 below: Figure 1 The Impact of Partial Amortization on Rates Paid on Funds Advanced on Bonused Mortgage Loans The shorter the term of the loan contract, given that all other factors are unchanged, the greater the rate of interest paid by the borrower on bonused or discounted mortgage loans. Loans with very short contractual terms (for example one year) may result in the borrower being charged rates of interest that are significantly greater than the contract rate. The foregoing is one reason why public regulatory agencies introduced the requirements for disclosure statements, a topic discussed in detail in the next chapter. Borrowers, even when they are aware of the general implications of brokerage fees and lender bonuses, generally do not possess sufficient knowledge to ascertain the true impact of brokerage fees on the cost of borrowing: for example, very few borrowers are aware of the dramatic impact on the cost of borrowing created by varying the term of the contract when bonuses are charged. 7.15

16 Chapter 7 Given that the only change in the two illustrations reviewed in this chapter is a variation of the contractual term, the importance of the duration of the term in bonused mortgage loans should be readily apparent. The borrower in these circumstances should be aware of the rate of interest on funds advanced, which implies acknowledging the contractual term. One final point must be made on the topic of rates paid by borrowers on bonused mortgage loans (or yields earned by investors on discounted loans). Borrowers frequently wish to repay the remaining balance on a mortgage loan prior to the maturity date of the loan (i.e., prior to the end of the contractual term). This is particularly true when borrowers have an opportunity to refinance the outstanding balance at a lower rate of interest. With bonused mortgage loans, such prepayment will have the effect of increasing the rate of interest on borrowed funds over that rate based on the assumption that the loan will run to maturity. The impact of prepayment on bonused mortgages is discussed in the next chapter. The rate of interest paid by the borrower on funds actually advanced is a true reflection of the actual cost of borrowing only in those circumstances where funds remain outstanding for the full term of the loan. As lenders and brokers cannot be expected to know when or if prepayment will occur, analysis and decisions, including the disclosure of the effective rate, are based on the premise that the loan will run to maturity. The financial analysis presented in this chapter has reviewed: C C C the impact of bonuses and/or brokerage fees on the cost of borrowing the implications of partial amortization on bonused mortgage loan rates the effect of prepayment on rates of interest on bonused mortgage loans An understanding of these relationships is a fundamental ingredient to real estate financing and mortgage brokerage in Canada. The following examples are designed to reinforce these points. Example 7.4 A real estate investment firm has arranged a mortgage loan with the following terms: Face value: $137, Contract rate: 5.5% per annum, compounded annually Term: 1 years Amortization: years Payment frequency: Annual payments, rounded to the next higher ten dollars At the time the contract was drawn, the lender and borrower agreed to a bonus of $3,, such that only $134, was actually advanced. Statement of Problem: Given the above, determine the following: (a) The size of the annual payments and outstanding balance as dictated by the terms of the contract. (b) The effective annual rate paid by the borrower on funds actually advanced (cost of funds advanced). 7.16

17 Yields, Bonuses, Discounts, and the Secondary Mortgage Market Solution: (a) PMT = $11, PMT = $11,47 (rounded) OSB 1 = $86, (b) i a = % Example 7.5 A mortgage broker has proposed a mortgage loan whereby the prospective borrower will make quarterly payments of $,5 to repay the $7, principal amount. The rate upon which the contract will be based is % per annum, compounded semi-annually. The broker plans to sell the right to receive the required payments to a private investor immediately after the contract is initiated. Statement of Problem: Given the information above, calculate: (a) The nominal rate, compounded quarterly for the contract rate and the number of full quarterly payments required. (b) The actual amortization period. (c) The maximum price an investor would be willing to pay to earn.5% per annum, compounded quarterly. (Hint! Use the full amortization period of the loan when calculating the maximum price.) (d) The nominal rate, with quarterly compounding, anticipated by investors who paid $68, for the right to receive the required payments. Solution: (a) j = %; 6 payments 4 (b) quarters (c) $67,517.9 (d) j =.96699% 4 Summary This chapter introduces the nature and methods of analysis for bonused and discounted financing arrangements. It opens with an introduction to bonused and discounted mortgage loans in general. Following this, the methods of analysis applicable to both bonused and discounted fully amortized loans are presented in detail. The focus then moves to the analysis of bonuses and discounts in the context of partially amortized loans. Here it becomes apparent that consideration of the duration of the contractual term of a financial arrangement is fundamental to the analysis of bonused and discounted transactions. Finally, just as the duration of the term is of critical importance, readers are made aware of the impact of prepayment on borrowing costs and yields. 7.17

18 Chapter 7 The financial analysis presented in this chapter has reviewed: C C C the impact of bonuses and/or brokerage fees on the cost of borrowing the implications of partial amortization on bonused mortgage loan rates the effect of prepayment on rates of interest on bonused mortgage loans An understanding of these relationships is a fundamental ingredient to real estate financing and mortgage brokerage in Canada. 7.18

19 Yields, Bonuses, Discounts, and the Secondary Mortgage Market APPENDIX 1 Calculator Steps for Selected Examples Example 7.1 CALCULATION PV 35 N FV 7, %/& PMT -34 P/YR I/YR P/YR Example 7. (a) CALCULATION 13 P/YR P/YR N FV %/& PMT -65 PV 4,

20 Chapter 7 (b) CALCULATION continued PV 4, P/YR P/YR PV 39,47.13 (c) CALCULATION continued ! = 3,17.56 Example 7.3 (a) CALCULATION P/YR 1 9 P/YR PV,5 6 N 6 FV PMT %/& PMT N

21 Yields, Bonuses, Discounts, and the Secondary Mortgage Market (b) CALCULATION continued 115 PV 11,5 I/YR.6518 = = P/YR (c) CALCULATION P/YR 1 9 P/YR PV,5 6 N 6 FV PMT %/& PMT INPUT AMORT PER 6-6 = = = 11,

22 Chapter 7 (d) CALCULATION 7 P/YR P/YR N %/& PMT FV PV 11, (e) CALCULATION 9 P/YR %/& PMT FV N PV 11, =

23 Yields, Bonuses, Discounts, and the Secondary Mortgage Market Example 7.4 (a) CALCULATION P/YR PV 137, N FV PMT -11, %/& PMT -11,47 1 INPUT AMORT PER 1-1 = -6, = -5, = 86, (b) CALCULATION continued %/& FV -86, N PV 134, I/YR

24 Chapter 7 Example 7.5 (a) CALCULATION P/YR 4 P/YR %/& PMT -,5 FV 7 PV 7, N (c) CALCULATION continued P/YR 4 PV 67, (d) CALCULATION continued PV 68, I/YR