978-0077861667 Chapter 7 Solution Manual Part 1

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Answers to Chapter 7

Questions:

1. Mortgage markets are examined separately from bond and stock markets for several reasons. First, mortgages are

backed by a specific piece of real property. If the borrower defaults on a mortgage, the financial institution can take

ownership of the property. Only mortgage bonds are backed by a specific piece of property that allows the lender to

take claim in the event of a default. All other corporate bonds and stocks give the holder a general claim to a

borrower’s assets. Second, there is no set denomination for primary mortgages. Rather, the size of each mortgage

2. Four basic categories of mortgages are issued by financial institutions: homes, multifamily dwellings,

commercial, and farms. Home mortgages ($9.86 trillion outstanding in 2013) are used to purchase one- to

four-family dwellings. Multifamily dwelling mortgages ($0.86 trillion outstanding) are used to finance the purchase

of apartment complexes, townhouses, and condominiums. Commercial mortgages ($2.21 trillion outstanding) are

3. A lien is a public record attached to the title of the property that gives the financial institution the right to sell the

property if the mortgage borrower defaults or falls into arrears on his or her payments. The mortgage is secured by

4. Federally insured mortgages are originated by financial institutions, but repayment is guaranteed by either the

Federal Housing Administration (FHA) or the Veterans Administration (VA). In order to qualify, FHA and VA

mortgage loan applicants must meet specific requirements set by these government agencies. Further, the maximum

5. A fixed rate mortgage locks in the borrower=s interest rate and thus required monthly payments over the life of

the mortgage, regardless of how market rates change. In contrast, the interest rate on an adjustable rate mortgage

Mortgage borrowers generally prefer fixed rate loans to ARMs, particularly when interest rates in the

economy are low. In fact if interest rates rise, ARMs may cause borrowers to be unable to meet the promised

payments on the mortgage. In contrast, most mortgage lenders prefer ARMs when interest rates are low. When

6. By refinancing the mortgage at a lower interest rate, the borrower pays less each month—even if the new

mortgage is for the same amount as the current mortgage. Mortgage refinancing involves many of the same details

and steps involved in applying for a new mortgage and can involve many of the same fees and expenses. Mortgages

are most often refinanced when a current mortgage has an interest rate that is higher than the current interest rate. As

7. A borrower pays points on a mortgage up front in exchange for a reduced interest rate and, consequently, reduced

monthly payments. The choice of points (and lower monthly payments) versus no points (and higher monthly

8. Jumbo mortgages are those mortgages that exceed the conventional mortgage conforming limits. Limits are set

by the two government-sponsored enterprises, Fannie Mae and Freddie Mac (discussed below) and are based on the

maximum value of any individual mortgage they will purchase from a mortgage lender. In 2013, the general limit

was $417,000 for most of the U.S. (the limit is set higher in high cost areas of the country). Because the large size

9. Subprime mortgages are mortgages to borrowers that do not qualify for prime mortgages because of weakened

credit histories including payment delinquencies, and possibly more severe problems such as charge-offs,

judgments, and bankruptcies. Subprime borrowers may also display reduced repayment capacity as measured by

It was subprime mortgages and the huge growth in them that was a major instigator of the financial crisis.

The low interest rate environment in the early and mid-2000s led to a dramatic increase in the demand for residential

mortgages, especially among those who had previously been excluded from participating in the market because of

their poor credit ratings, i.e., subprime borrowers. To boost their earnings, FIs began lowering their credit quality

10. Option ARMs, also called pick-a-payment or pay-option ARMs, are 15- or 30-year adjustable rate mortgages

that offer the borrower several monthly payment options. The four major types of payment options include:

Minimum payment option. The minimum payment is the lowest of the four payment options and carries the most

risk. With these option ARMs, the monthly payment is set for 12 months at an initial interest rate. After that, the

payment changes annually, and a payment cap limits how much it can increase or decrease each year (generally 7.5

The minimum payment on most option arm programs is 1percent fully amortized. Every time the borrower

makes the minimum payment, the difference between the minimum payment and the interest-only payment is tacked

Interest-only payment: An interest-only option ARM requires the borrower to pay only the interest on the loan

during the initial period of the loan. During this period, no principal must be repaid. After the interest-only period,

the mortgage must amortize so that the mortgage will be paid off by the end of its original term. This means that

Interest-only payment option ARMs carry a great deal of payment-shock risk. Not only do the payments have the

30-year fully amortizing payment: With fully amortizing option ARMs, the borrower pays both principal and interest

15-year fully amortizing payment: This option ARM is similar to the 30-year fully amortizing payment option ARM,

with a full principal and interest payment, but with a larger amount of principal paid each month. This amount

11. The secondary mortgage markets were created by the federal government to help boost U.S. economic activity

during the Great Depression. As borrowers defaulted on mortgages, banks and thrifts found themselves strapped for

cash. To create liquidity in the mortgage markets and to raise levels of home ownership and the availability of

affordable housing, in 1938 the government established the Federal National Mortgage Association (FNMA or

Further, by the late 1960s, fewer veterans were obtaining guaranteed VA loans. As a result, the secondary market for

Mortgage Association (GNMA or Ginnie Mae) and the Federal Home Loan Mortgage Corporation (FHLMC or

12. A mortgage sale occurs when a financial institution originates a mortgage and sells it with or without recourse to

an outside buyer. Mortgage sales usually involve no creation of new types of securities. Securitization of mortgages

13. Mortgage-backed securities allow mortgage issuers to separate the credit risk exposure from the lending process

itself. That is, FIs can assess the creditworthiness of loan applicants, originate loans, fund loans, and even monitor

and service loans without retaining exposure to loss from credit events, such as default or missed payments. This

decoupling of the risk from the lending activity allows the market to efficiently transfer risk across counterparties.

14. Pass-through mortgage securities promise payments of principal and interest on pools of mortgages created by

financial institutions to secondary market participants (mortgage-backed bondholders) holding an interest in these

pools. After a financial institution issues mortgages, they pool them and sell interests in these pools to pass-through

15. The Government National Mortgage Association (GNMA), or Ginnie Mae, began in 1968 when it split off from

the Federal National Mortgage Association (FNMA). GNMA is a government-owned agency with two major

functions: sponsoring mortgage-backed securities programs by financial institutions such as banks, thrifts, and

mortgage bankers and acting as a guarantor to investors in mortgage-backed securities regarding the timely

16. Originally created in 1938, the Federal National Mortgage Association (FNMA or Fannie Mae), is the oldest of

the three mortgage-backed security-sponsoring agencies. It is now a private corporation owned by shareholders with

its common stock traded on the New York Stock Exchange, but in the minds of many investors, it still has implicit

directly to finance those purchases.

Specifically, FNMA creates mortgage-backed securities (MBSs) by purchasing packages of mortgage loans

from banks and thrifts; it finances such purchases by selling MBSs to outside investors such as life insurers or

pension funds. In addition, FNMA engages in swap transactions by which it swaps MBSs with a bank or thrift for

17. Together FNMA and FHLMC represent a huge presence in the financial system as they have over

60 percent of the single-family mortgage pools in the United States. Some regulators and politicians have argued

Also, in the early 2000s, these two agencies came under fire for several reasons. First, in September 2002, Fannie

Mae was criticized for allowing a sharp increase in interest rate risk to exist on its balance sheet. The Office of

Federal Housing Enterprise Oversight (OFHEO), a main regulator of Fannie Mae, required Fannie Mae to submit

weekly reports to the OFHEO on the company’s exposure to interest rate risk. The OFHEO also instructed Fannie

Mae to keep regulators apprised of any challenges associated with returning its interest rate risk measure to more

acceptable levels and warned that additional action would be taken if there were adverse developments with Fannie

Underlying the concerns about the actions of these two GSEs was the widespread perception among investors that

neither would be allowed to fail if they got into trouble. This perception created a subsidy for the agencies and

allowed them to borrow more cheaply than other firms with similar balance sheets. The fear was that the two

agencies used their implicit federal backing to assume more risk and finance expansion through increased debt. Such

actions created a source of systemic risk for the U.S. financial system. These fears and concerns became reality

GSE status, however, enabled them to continue to fund their operations by selling debt securities, because the

market believed that Fannie and Freddie debt was implicitly guaranteed by the government. In July 2008, however,

viability. As a result, the federal government concluded that “the companies cannot continue to operate safely and

soundly and fulfill their critical public mission, without significant action” to address their financial weaknesses.

The Housing and Economic Recovery Act of 2008, enacted July 30, 2008, gave the authority for the government’s

takeover of the GSEs. The act created a new GSE regulator, the Federal Housing Finance Agency (FHFA), with the

authority to take control of either GSE to restore it to a sound financial condition. The act also gave the Treasury

The takeover of Fannie and Freddie, and specifically the commitment to meet all of the firms’ obligations to debt

holders, exposes the U.S. government to a potentially large financial risk. At the time the FHFA took over, debt

issued or guaranteed by the GSEs totaled more than $5 trillion. The risks of not acting, however, clearly appeared

In February 2011, the Obama administration recommended phasing out the GSEs and gradually reducing the

government’s involvement in the mortgage market. In the proposal, any dismantling of Fannie and Freddie would

Complicating these efforts, as the U.S. economy and housing market slowly recovered, so did the GSEs. In 2012,

FNMA and Freddie Mac reported net income of $17.2 billion and $11.0 billion, respectively, the best year ever for

both companies. By mid-2013 the companies’ stocks were trading at $4.08 and $3.75, respectively, up from

18. A CMO can be viewed as a multiclass pass-through with a number of different bondholder classes or tranches.

Unlike a pass-through which has no guaranteed annual “coupon,” each bondholder class has a different guaranteed

coupon just as a regular T-bond has, but more importantly, the allocation of any excess cash flows over and above

CMOs can be created either by packaging and securitizing whole mortgage loans or, more usually, re-securitizing

19. MBBs differ from pass-throughs and CMOs in two key dimensions. First, while pass-throughs and CMOs help

cash flows on the bond instrument issued. By contrast, the relationship for MBBs is one of collateralization; the cash

20. Figure 7–8 shows the distribution of mortgages outstanding in 1992, 2007, and 2010 by type of mortgage holder

—the ultimate investor. Notice in Figure 7–8 the growth in the importance of mortgage securitization pools over the

period (40.42 percent of all mortgages outstanding in 1992 versus 55.35 percent in 2007 and 60.01 percent in 2013).

Actual holdings of mortgages by specialized mortgage companies (such as Sierra Pacific Mortgage Company and

Blue Water Mortgage Corp. of New Hampshire) are small (1.49 percent in 1992, 3.65 percent in 2007, and 1.33

percent in 2013). Mortgage companies, or mortgage bankers, are financial institutions 9 that originate mortgages and

collect payments on them. Unlike banks or thrifts, mortgage companies typically do not hold on to the mortgages

they originate. Instead, they sell the mortgages they originate but continue to service the mortgages by collecting

Problems:

1. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $20,000

(0.20 x $100,000) at closing and borrow $80,000 through the mortgage.

a. For your mortgage:

Thus, your monthly payment is $601.01.

c. The 225th payment of $601.01 is split as follows: $364.32 to interest and $236.69 to principal.

2. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $35,000

(0.20 x $175,000) at closing and borrow $140,000 through the mortgage.

Thus, your monthly payment is $1,317.79.

b. The 60th payment of $1,317.79 is split as follows: $713.07 to interest and $604.72 to principal.

c. The 180th payment of $1,317.79 is split as follows: $8.46 to interest and $1,309.33 to principal.

d. The total payments over the life of the mortgage amount to payments of $237,201.48 ($1,317.786 x 15 x 12):

$140,000 to the repayment of principal and $97,201.48 to the payment of interest.

3. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $16,000

(0.20 x $80,000) at closing and borrow $64,000 through the mortgage.

a. For your mortgage:

$64,000 = PMT{[1 – (1/(1 + 0.08/12)15(12))]/(0.08/12)}

or PMT = $64,000/{[1 – (1/(1 + 0.08/12)15(12))]/(0.08/12)}

therefore PMT = $64,000/104.6406 = $611.617

Thus, your monthly payment is $611.62.

b. The 127th payment of $611.62 is split as follows: $184.39 to interest and $427.23 to principal.

c. The 159th payment of $611.62 is split as follows: $83.17 to interest and $528.45 to principal.

d. The total payments over the life of the mortgage amount to payments of $110,091.60 ($611.62 x 15 x 12):

$62,000 to the repayment of principal and $46,091.60 to the payment of interest.

4. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $30,000

(0.20 x $150,000) at closing and borrow $120,000 through the mortgage.

a. For your mortgage: $120,000 = PMT{[1 – (1/(1 + 0.0525/12)15(12))]/(0.0525/12)}

or PMT = $120,000/{[1 – (1/(1 + 0.0525/12)15(12))]/(0.0525/12)}

therefore PMT = $120,000/124.3970 = $964.65

Thus, your monthly payment is $964.65.

b. Amortization Schedule for first 6 payments (months)

Beginning Ending

Loan Loan

Month Balance Payment Interest Principal Balance

1 $120,000.00 $964.65 $525.00 $439.65 $119,560.35

2 119,560.35 964.65 523.08 441.57 119,118.78

3 119,118.78 964.65 521.14 443.51 118,675.27

4 118,675.27 964.65 519.20 445.45 118,229.82

5 118,229.82 964.65 517.26 447.39 117,782.43

6 117,782.43 964.65 515.30 449.35 117,333.08

5. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of $40,000

(0.20 x $200,000) at closing and borrow $160,000 through the mortgage.

a. For your mortgage: $160,000 = PMT{[1 – (1/(1 + 0.0650/12)30(12))]/(0.0650/12)}

or PMT = $160,000/{[1 – (1/(1 + 0.0650/12)30(12))]/(0.0650/12)}

therefore PMT = $160,000/158.2108 = $1,011.31

Thus, your monthly payment is $1,011.31.

b. Amortization Schedule for first 6 payments (months)

Beginning Ending

Loan Loan

Month Balance Payment Interest Principal Balance

1 $160,000.00 $1,011.31 $866.67 $144.64 $159,855.36

2 159,855.36 1,011.31 865.88 145.43 159,709.93

3 159,709.93 1,011.31 865.10 146.21 159,563.72

4 159,563.72 1,011.31 864.30 147.01 159,416.71

5 159,416.71 1,011.31 863.51 147.80 159,268.91

6 159,268.91 1,011.31 862.71 148.60 159,120.31

6. EXCEL Problem: Payment = $1,245.62

Payment = $1,286.13

Payment = $1,390.52

Payment = $1,521.40

7. EXCEL Problem: Payment = $875.36

Payment = $923.58

Payment = $1,048.82

Payment = $1,206.93

8. For the either mortgage, you will make a down payment of 20 percent of the purchase price: or a down payment

of $40,000 (0.20 x $200,000) at closing and borrow $160,000 through the mortgage.

a. Total payments on the 15-year mortgage are $250,878.60, of which $90,878.60 is interest. This compares to

interest of $232,932.80 on the 30-year mortgage (a difference of $142,054.20, disregarding time value of money).

The mortgage borrower’s interest payments are reduced significantly with the 15-year mortgage relative to the

30-year mortgage.

b. For the 30-year mortgage: $160,000 = PMT{[1 – (1/(1 + 0.0725/12)30(12))]/(0.0725/12)}

or PMT = $160,000/{[1 – (1/(1 + 0.0725/12)30(12))]/(0.0725/12)}

therefore PMT = $160,000/146.5897 = $1,091.48

For the 15-year mortgage: $160,000 = PMT{[1 – (1/(1 + 0.0650/12)15(12))]/(0.0650/12)}

or PMT = $160,000/{[1 – (1/(1 + 0.0650/12)15(12))]/(0.0650/12)}

therefore PMT = $160,000/114.7964 = $1,393.77

The borrower must pay $1,393.77 per month with the 15-year mortgage compared to $1,091.48 with the 30-year

mortgage, a difference of $302.29 per month. This may be difficult if the borrower’s income level is not very high.

9. For the either mortgage, you will make a down payment of 20 percent of the purchase price: or a down payment

of $48,000 (0.20 x $240,000) at closing and borrow $192,000 through the mortgage.

a. Total payments on the 15-year mortgage are $273,297.60, of which $81,279.60 is interest. This compares to

interest of $211,365.60 on the 30-year mortgage (a difference of $130,068.00, disregarding time value of money).

The mortgage borrower’s interest payments are reduced significantly with the 15-year mortgage relative to the

30-year mortgage.

b. For the 30-year mortgage: $192,000 = PMT{[1 – (1/(1 + 0.0575/12)30(12))]/(0.0575/12)}

or PMT = $192,000/{[1 – (1/(1 + 0.0575/12)30(12))]/(0.0575/12)}

therefore PMT = $192,000/171.3582 = $1,120.46

For the 15-year mortgage: $192,000 = PMT{[1 – (1/(1 + 0.0500/12)15(12))]/(0.0500/12)}

or PMT = $192,000/{[1 – (1/(1 + 0.0500/12)15(12))]/(0.0500/12)}

therefore PMT = $192,000/114.7964 = $1,518.32

The borrower must pay $1,518.32 per month with the 15-year mortgage compared to $1,120.46 with the 30-year

mortgage, a difference of $397.86 per month. This may be difficult if the borrower’s income level is not very high.

10. You will make a down payment of 20 percent of the purchase price, or you will make a down payment of

$23,000 (0.20 x $115,000) at closing and borrow $92,000 through the mortgage.

a. If Option 2 is chosen you pay $92,000 x 0.02 = $1,840 in points and receive $90,160 at closing ($92,000 –

$1,840), although the mortgage principal is $92,000. To determine the best option, we first calculate the monthly

payments for both options as follows

Option 1: $92,000 = PMT {[1 – (1/(1 + 0.0900/12)30(12))]/(0.0900/12)} => PMT = $740.25

Option 2: $92,000 = PMT {[1 – (1/(1 + 0.0885/12)30(12))]/(0.0885/12)} => PMT = $730.35

In exchange for $1,840 up front, Option 2 reduces your monthly mortgage payments by $9.90. The present value of

these savings (evaluated at 8.85 percent) over the 30 years is

PV = $9.90 {[1 – (1/(1 + 0.0885/12)30(12))]/(0.0885/12)} = $1,248.06

Option 1 is the better choice. The present value of the monthly savings, $1,248.06, is less than the points paid up

front, $1,840.

b. If Option 1 is chosen you pay $92,000 x 0.01 = $920 in points and receive $91,080 at closing ($92,000 – $920),

although the mortgage principal is $92,000. If Option 2 is chosen you pay $92,000 x 0.025 = $2,300 in points and

receive $89,700 at closing ($92,000 – $2,300). The difference in savings on the points is $1,380.

To determine the best option, we calculate the monthly payments for both options as follows

Option 1: $92,000 = PMT {[1 – (1/(1 + 0.1025/12)30(12))]/(0.1025/12)} => PMT = $824.413

Option 2: $92,000 = PMT {[1 – (1/(1 + 0.1000/12)30(12))]/(0.1000/12)} => PMT = $807.366

In exchange for $1,380 up front, Option 2 reduces your monthly mortgage payments by $17.047. The present value

of these savings (evaluated at 10.00 percent) over the 30 years is

PV = $17.047 {[1 – (1/(1 + 0.1000/12)30(12))]/(0.1000/12)} = $1,942.52

Option 2 is the better choice. The present value of the monthly savings, $1,942.52, is less than the points paid up

front, $1,380.