Chapter Objectives - Chapter 9

CH6M.DOC 1/19/2018 CHAPTER OBJECTIVES - CHAPTER 6 Residential Financial Analysis

The student who has successfully completed this chapter should be able to perform the following:

Calculate the incremental cost of borrowing additional funds for mortgages with different loan-to-value ratios.

Evaluate whether it is desirable to refinance a mortgage taking into consideration prepayment penalties, origination fees, and other charges.

Calculate the maximum discounts to be offered by a lender in order to induce a borrower’s early repayment (assuming interest rates have risen since the loan’s issuance).

Calculate the market value of an outstanding mortgage loan assuming a rise or fall in market interest rates.

Calculate the total premium which should be added to the sale price of a home offering below market financing or a builder buydown.

Understand the motivation for the use of a wraparound loan and be able to compare a wraparound loan with a second mortgage.

Solutions to Questions - Chapter 6 Residential Financial Analysis

Question 6-1 Why do points increase the effective interest rate for a mortgage loan more if the loan is held for a shorter time period than a longer time period? Points are a one-time charge paid when the loan is obtained. The same dollar amount is paid whether the loan is held to maturity or prepaid. The longer the loan is held, the more these costs are, in effect, spread out over more payments. Conversely, if the loan is held for a shorter period of time, the borrower does not get the full benefit of having paid these up-front costs.

Question 6-2 What factors must be considered when deciding whether to refinance a loan after interest rates have declined? The payment savings resulting from the lower interest rate must be weighed against the costs associated with refinancing such as points on the new loan or prepayment penalties on the loan being refinanced.

Question 6-3 Why might the market value of a loan differ from its outstanding balance? The balance of a loan depends on the original contract rate, whereas the market value of the loan depends on the current market interest rate.

1 CH6M.DOC 1/19/2018 Question 6-4 Why might a borrower be willing to pay a higher price for a home with an assumable loan? An assumable loan allows the borrower to save interest costs if the interest rate is lower than the current market interest rate. The investor may be willing to pay a higher price for the home if the additional price paid is less than the present value of the expected interest savings from the assumable loan.

Question 6-5 What is a buydown loan? What parties are usually involved in this kind of loan? A buydown loan is a loan that has lower payments than a loan that would be made at the current interest rate. The payments are usually lowered for the first one or two years of the loan term. The payments are “bought down” by giving the lender funds in advance that equal the present value of the amount by which the payments have been reduced.

Question 6-6 Why might a wraparound lender provide a wraparound loan at a lower rate than a new first mortgage? Although the wraparound loan is technically a “second mortgage,” the wraparound lender is only required to make payments on the existing mortgage if the borrower makes payments on the wraparound loan. Furthermore, the wraparound lender is typically taking over an existing mortgage that has a below market interest rate. Thus, the wraparound lender is benefiting from the spread between the rate being earned on the wraparound loan and that being paid on the existing loan. This allows the wraparound lender to earn a higher return on the incremental funds being advanced even if the rate on the wraparound loan is less than the rate on a new first mortgage.

Question 6-7 Assuming the borrower is in no danger of default, under what conditions might a lender be willing to accept a lesser amount from a borrower than the outstanding balance of a loan and still consider the loan paid in full? If interest rates have risen significantly, the market value of the loan will be less. Thus, the lender may be willing to accept less than the outstanding balance of the loan, especially if the lender still receives more than the market value of the loan. The lender can then make a new loan at the higher market interest rate.

Question 6-8 Under what conditions might a home with an assumable loan sell for more than comparable homes with no assumable loans available? The home with an assumable loan might be expected to sell for more than comparable homes with no assumable loans available when the contract interest rate on the assumable loan is significantly less than the current market rate on a loan with similar maturity and similar loan-to-value ratio. Note that if the dollar amount of the assumable loan is significantly less than that which could be obtained with a market rate loan, the benefit of the assumable loan is diminished because the borrower may need to make up the difference with a second mortgage.

Question 6-9 What is meant by the incremental cost of borrowing additional funds? The incremental cost of borrowing funds is a measure of what it really costs to obtain additional funds by getting a loan with a higher loan-to-value ratio that has a higher interest rate. This measure is important because the contract rate on the loan with the higher loan-to-value ratio does not take into consideration the fact that this higher rate must be paid on the entire loan - not just the additional funds borrowed. Thus, the borrower should consider the incremental cost of the additional funds to know what it is really costing to borrow the additional funds.

Question 6-10 Is the incremental cost of borrowing additional funds affected significantly by early repayment of the loan? The incremental cost of borrowing additional funds can be affected significantly by early repayment of the loan, especially if additional points were paid to obtain the additional funds. Thus, the borrower should consider how long he or she expects to have the loan when calculating the incremental cost of the additional funds.

2 CH6M.DOC 1/19/2018 Solutions to Problems - Chapter 6 Residential Financial Analysis

INTRODUCTION

The following solutions were obtained using an HP 12C financial calculator. Answers may differ slightly due to rounding or use of the financial tables to approximate the answers. As pointed out in the chapter, there is often more than one way of approaching the solution to the problems in this chapter. Thus “alternative solutions” are shown were appropriate.

Problem 6-1 (a) Because the amount of the loan does not matter in this case, it is easiest to assume some arbitrary dollar amount that is easy to work with. Therefore we will assume that the purchase price of the home is $100,000. Thus the choice is between an 80 percent loan for $80,000 or a 90 percent loan for $90,000. The loan information and calculated payments are as follows:

Alternative Interest rate Loan term Loan Amount Monthly Payments 90% Loan 8.5% 25 yrs. $90,000 $724.70 80% Loan 8.0% 25 yrs. 80,000 617.45 Difference $10,000 $107.25

$107.25 x (MPVIFA, ?%, 25 yrs..) = $10,000

Solving for the interest rate with a financial calculator we obtain an incremental borrowing cost of 12.3 percent. (Note: Be sure to solve for the interest rate assuming monthly payments. With an HP12C you will first solve for the monthly interest rate, then multiply the monthly rate by 12 to obtain the nominal annual rate.)

(b) Alternative Loan Amount Points Net Proceeds Monthly Payments 90% Loan $90,000 $1,800 $88,200 $724.70 80% Loan 80,000 0 80,000 617.45 Difference $8,200 $107.25

$107.25 x (MPVIFA, ?%, 25 yrs..) = $8,200

Solving for the interest rate with a financial calculator we now obtain an incremental borrowing cost of 15.4 percent.

(c) We now need the loan balance after 5 years.

Alternative Loan Amount Monthly payments Loan Balance 90% Loan $90,000 $724.70 $83,508.62 80% Loan 80,000 617.45 73,819.37 Difference $10,000 $107.25 $9,689.37

Note that the net proceeds of the loan is still $8,200 as in Part b. Thus we have: $107.25 x (MPVIFA, ?%, 5 yrs..) + $9,689.37 x (MPVIF, ?%, 5 yrs..) = $8,200

Solving for the interest rate with a financial calculator we now obtain an incremental borrowing cost of 18 percent.

Problem 6-2 (a) For this problem we need to know the effective cost of the $180,000 loan at 9% combined with the $40,000 loan at 13%

Loan Amount Interest rate Loan term Monthly Payments $180,000 9% 20 yrs.. $1619.51 40,000 13% 20 yrs.. 468.63 Combined $220,000 $2,088.14

$2,088.14 x (MPVIFA, ?%, 20 yrs.) = $220,000

3 CH6M.DOC 1/19/2018

Solving for the effective cost of the combined loans we obtain 9.76%. This is greater than the 9.5% rate on the single $220,000 loan. Thus the $220,000 loan is preferable.

(b) We now need the loan balance after 5 years

Loan Amount Interest rate Loan term Monthly Payments Loan Balance $180,000 9% 20 yrs.. $1619.51 $159,672.44 40,000 13% 20 yrs.. 468.63 37,038.81 Combined $220,000 $2,088.14 $122,633.63

$2,088.14 x (MPVIFA, ?%, 5 yrs.) + $122,633.63 x (MPVIF, ?%, 5 yrs.) = $220,000

Solving for the interest rate, which represents the combined cost, we obtain 9.74%. The effective cost of the single $220,000 would still be 9.5% even if it is repaid after 5 years because there were no points or prepayment penalties. Thus the $220,000 loan is still better.

(c) Assuming the loan is held for the full term (to compare with Part a:)

Loan Amount Interest rate Loan term Monthly Payments $180,000 9% 20 yrs.. $1619.51 40,000 13% 10 yrs.. 597.24 Combined $220,000 $2,216.75

The combined payments are made for the first 10 years only. After that, only the payment on the $90,000 loan is made.

$2,216.75 x (MPVIFA, ?%, 10 yrs..) + $1,619.51 x (MPVIFA, ?%, 10 yrs..) x (MPVIF, ?%, 10 yrs..) = $220,000

Note that the payment of $1,619.51 is first discounted as a 10 year annuity (years 11 to 20) and further discounted as a lump sum for 10 years to recognized the fact that the annuity does not start until year 10.

Solving for the cost we obtain 9.49%. This is less than 9.5% rate for the single $220,000 loan. Thus, the combined loans are preferred.

Assuming the loan is held for 5 years (to compare with Part b): We now need the loan balance after 5 years.

Loan Amount Interest rate Loan term Monthly Payments Loan Balance $180,000 9% 20 yrs.. $1619.51 $159,672.68 40,000 13% 10 yrs.. 597.24 26,248.89 Combined $220,000 $2,216.75 $185,921.57

$2,216.75 x (MPVIFA, ?%, 5 yrs..) + $185,921.57 x (MPVIF, ?%, 5 yrs..) = $220,000

We now obtain 9.67%. This is greater than the 9.5% rate for a single loan.

Problem 6-3 Preliminary calculation:

The existing loan is for $95,000 at a 11% interest rate for 30 years (monthly payments). The monthly payment is $904.71. The balance of the loan after 5 years is $92,306.41.

Payment on a new loan for $92,306.41 at a 10% rate with a 25 year term are $838.79.

4 CH6M.DOC 1/19/2018 (a) Alternative Interest rate Loan term Loan amount Monthly Payments Old loan 11% 30 yrs.. $95,000 $904.71 New loan 10% 25 yrs.. 92,306 838.79 Savings $65.92

Cost of refinancing are $2,000 + (.03 x $92,306.41) = $4,769.19. Considering the $4,769.19 as an “investment” necessary to take advantage of the lower payments resulting from refinancing

$65.92 (MPVIFA, ?, 25 yrs..) = $4,769.19

Solving for the rate we obtain 16.30%. It is desirable to refinance if the investor can not get a higher yield than 16.30% on alternative investments.

Alternate solution:

Amount of new loan $92,306.00 Cost of refinancing $4,769.19 Net proceeds $87,536.81

The net proceeds cam be compared with the payment on the new loan to obtain an effective cost of the new loan. We have:

$838.79 (MPVIFA, ?%, 25 yrs..) = $87,536.81

Solving for the effective cost we obtain 10.69%. Because the effective cost is less than the cost of the existing loan (11%) the conclusion is to refinance.

(b) For a 5-year holding period we must also consider the balance of the old and new loan after 5 year. We have:

Alternative Loan Amount Interest rate Loan term Monthly payments Loan Balance Old loan $95,000 11% 30 yrs.. $904.71 $87,648.82* New loan 92,306 10% 25 yrs.. 838.79 86,918.44 65.92 $730.38

* Balance after 5 additional years or 10 years total.

Looking at the refinancing cash outflows as an investment we have:

$65.92 x (MPVIFA, ?%, 5 yrs..) + $730.38 x (MPVIF, ?%, 5 yrs..) = $4,769.19

Solving for the IRR we obtain -0.6%.

The negative return tells you this is a bad investment if paid off so quickly. The reason for the negative return, is that you pay for the refinancing up-front, but do not benefit from the favorable financing for a period of time long enough to cover and/or justify the cost of refinancing.

Alternative solution:

The effective cost is now as follows:

$838.79 x (MPVIFA, ?%, 5 yrs..) + $86,918.44 (MPVIF, ?%, 5 yrs..) = $87,536.81

Solving for the effective cost we obtain 11.4%. The effective cost is now higher than the rate of return on the old loan so refinancing is not desirable.

5 CH6M.DOC 1/19/2018 Problem 6-4 Payments on the $140,000 loan at 10%, 30 years are $1,228.60 per month.

(a) Note that there are 25 years remaining.

The balance after 5 years can be found by discounting the remaining payments as follows: $1,228.60 x (MPVIFA, 10%, 25 yrs.) = $135,204.03

The market value of the loan can be found by discounting the payments of $1,228.60 for 25 years (monthly) using the required rate of 11%. We have: $1,228.60 x (MPVIFA, 11%, 25 yrs.) = $125,400.16

This is lower than the balance of the loan because payments are discounted at a higher rate than the contract rate on the loan.

(b) The balance of the original loan after five additional years (10 years from origination) is $127,313.21.

To calculate the market value assuming the loan is repaid after 5 additional years, we have: PV = $1,228.60 x (MPVIFA, 11%, 5 yrs..) + $127,313.21 x (MPVIF, 11%, 5 yrs..) PV = $130,144.64

Problem 6-5 (a) Alternative 1: Purchase of $150,000 home:

Interest rate Loan Term Loan Amount Monthly Payments First mortgage 10.5% 20 yrs.. $120,000 $1,198.06 or

Alternative 2: Purchase of $160,000 home:

Interest rate Loan Term Loan Amount Monthly Payments Assumption 9% 20 yrs.. $100,000 $899.73 Second mortgage 13% 20 yrs.. 20,000 234.32 $120,000 $1,134.05

The loan amounts are the same under the two alternatives. The second alternative has lower total payments resulting in savings of $64.01 per month ($1,198.06 - $1,134.05), but requires an additional $10,000 cash outflow as an additional down payment.

$64.01 x (MPVIFA, ?%, 20 yrs..) = $10,000

The IRR is 4.64%. This does not make sense if the investor can earn more than this on the $10,000. This appears to be too low to justify the additional $10,000 equity - especially with mortgage interest rates at 10.5%. Note that the borrower could take the $150,000 home and use the extra $10,000 to borrow less money, e.g. $110,000 instead of $120,000 which results in interest savings of 10.5% (the rate on the loan).

The point is that the investor’s opportunity cost is 10.5%, which is higher than the 4.64% that would be earned by taking the second alternative.

Note to instructors: It is informative to calculate exactly how much more the borrower could pay for alternative 2. This is found by discounting the payment savings at 10.5%. We have: PV = $64.01 x (MPVIFA, 10.5%, 20 yrs..) = $6,411

Thus, the borrower would be indifferent between alternative 1 and 2 if the price of the home for alternative 2 was $156,411.

6 CH6M.DOC 1/19/2018 (b) With the homeowner providing the second mortgage for the additional $20,000 (purchase money mortgage) we have:

Alternative 2: Purchase of $160,000 home:

Savings are now $1,198.06 - $1,079.68 = $118.38 per month. An additional down payment of $10,000 is still required.

$118.38 (MPVIFA, ?%, 2- yrs.) = $10,000

The IRR is now 13.17%

(c) Alternative 2: Purchase of $160,000 home:

The savings are now $1,198.06 - $1,169.65 or $28.41 per month. Because of the additional amount of the second mortgage, there is no additional down payment even though $10,000 more is paid for the home. Thus, the borrower saves $28.41 under alternative 2 with no additional cash outlay- which is clearly desirable.

Problem 6-6 Loan Amount Payment Term Wraparound $150,000 $1,800.25 15 yrs. Existing 100,000 1,100.25 15 yrs. (remaining) Difference $50,000 $700.25

$700.25 x (MPVIFA, ?%, 15 yrs..) = $50,000

Solving for the IRR we obtain 15.01%. This is the incremental return on the wraparound. Because this is greater than the 14% rate on a second mortgage, the second mortgage is better.

Alternative solution: Loan Amount Payment Term Second mortgage $50,000 $665.87 15 yrs. Existing loan 100,000 1,100.00 15 yrs. (remaining) Difference $150,000 $1765.87

The total payments on the existing loan plus a second mortgage is $1,765.87, which is less than the payments on the wraparound. Furthermore, the effective cost of the combined loans is as follows: $1,765.87 (MPVIFA, ?%, 15 yrs..) = $150,000.

The IRR is 11.64%. Thus, the effective cost of the combined loans is less than the wraparound.

Thus, the combined loans are better. Note: we can only compare payments when the loan terms are the same. However, we can compare effective costs when they differ. As a result, the effective cost is more general than simply comparing payments.

7 CH6M.DOC 1/19/2018 Problem 6-7 (a) Payments on a $100,000 loan at 9% for 25 years is $839.20.

The present value of $839.20 at 9.5% for 25 years is $96,051.64.

The difference between the contract loan amount ($100,000) and the value of the loan ($96,051.64) is $3,948. This must be added on to the home price. Thus, the home would have to be sold for $110,000 + $3,948 or $113,948.

Alternative solution: Payments on a loan for $100,000 at 9.5%: $873.70 Payments on a loan for $100,000 at 9%: 839.20 Savings by getting the loan at 9%: $34.50

Present value of the saving discounted at 10%: PV = $34.50 x (MPVIFA, 9.5%, 25 yrs..) = $3,948.

This is the amount that has to be added to the home as before.

(b) The balance of the $100,000 loan (9%, 25 yrs.) after 10 years is $82,739.23. We now discount the payments on the $100,000 loan which are $839.20 and the balance after 10 years which is 82,739.23. Both are discounted at the market rate of 9.5%. We have: PV = $839.20 x (MPVIFA, 9.5%, 10 yrs..) + $82,739.23 x (MPVIF, 9.5%, 10 yrs..) PV = $96,973

Subtracting this from the loan amount of $100,000 we have $100,000 - $96,973.69 or $3,027. This is the amount that must be added to the home price. Thus, the home price must be $110,000 + $3,027 or $113, 027. Not as much has to be added relative to (a) because the borrower would not have to be given the interest savings for as many years.

Alternative solution: The difference in payments for a $100,000 loan at 9% and $100,000 at 9.5% is $34.50 (same as alternative solution to part a.) We must also consider the difference in loan balances after 10 years.

Balance of $100,000 loan at 9.5% after 10 years: $83,668.75 Balance of $100,000 loan at 9% after 10 years: 82,739.23 Savings $929.52

We now discount the payment savings and the savings after 10 years.

PV = $34.5 x (MPVIFA, 9.5%, 10 yrs..) + $929.52 x (MPVIF, 9.5%, 10 yrs..) PV = $3,027

Thus $3,027 must be added to the home price as above.

Problem 6-8 (a) Monthly payment reduction during the first year (50% of $726.96): $363.48 Monthly payment reduction during the second year (25% of 4726.96): $181.74

Discounting the payment reduction at 10%” PV = $363.48 x (MPVIFA, 10%, 1 yr.) + $181,74 x (MPVIFA, 10%, 1 yr.) (MPVIF, 10%, 1 yr.) PV = $6,005.66

Note that the second year payment reduction is an annuity that starts after one year.

Thus, the builder would have to give the bank $6,005.66 up front.

8 CH6M.DOC 1/19/2018 (b) Based on the results from (a), the buydown loan is worth $6,005.66 in present value terms. We would expect the home to sell for $6,005.66 more than a comparable home that did not have this loan available. Thus, if the home could be purchased for $5,000 more, the borrower would gain in present value terms by $6,006 - $5,000 or $1,006.

Problem 6-9 (a) Step 1, Calculate the dollar monthly difference between the two financing options. Original loan payment: PV = -$140,000 I = 7/12 or 0.58 N = 15x12 or 180 FV = 0 Solve for the payment: PMT = $1,258.36

Find present value of the payments at the market rate of 8%

I = 8%/12 N = 15x12 or 180 FV = 0 PMT = $1,258.36 Solve for PV: PV = $131,675.49

This is the market (cash equivalent) value of the loan.

The buyer made a cash down payment of $60,000.

Cash equivalent value of loan $131,675.49 Cash down payment 60,000.00 Cash equivalent value of property $191,675.49

(b) If it is assumed that the buyer only expected to benefit from the favorable financing for five years:

Loan balance after 5 years is $108,378

Find present value of payments for 5 years and loan balance at the end of the 5th year.

I = 8%/12 N = 5x12 or 60 FV = $108,378 PMT = $1,258.36 Solve for PV: PV = $134,804.72

Cash equivalent value of loan $134,804.72 Cash down payment 60,000.00 Cash equivalent value of property $194,804.72

The cash equivalent value is higher because the buyer was not assumed to have discounted the loan by as much.

9 CH6M.DOC 1/19/2018

Chapter 6 Appendix

Problem 6A-1 (a) Loan $100,000, 10% interest, 15 yrs (monthly payments) Monthly payment $1,074.61

Before-tax After-tax Value Month Payment Interest Principal Balance of Deduction AT Payment 0 -100000 -100000 1 1074.61 833.33 241.27 99,759 250.00 824.61 2 1074.61 831.32 243.28 99,515 249.40 825.21 3 1074.61 829.30 245.31 99,270 248.79 825.82 4 1074.61 827.25 247.35 99,023 248.18 826.43 5 1074.61 825.19 249.42 98,773 247.56 827.05 6 1074.61 823.11 251.49 98,522 246.93 827.67 7 1074.61 821.02 253.59 98,268 246.30 828.30 8 1074.61 818.90 255.70 98,013 245.67 828.93 9 1074.61 816.77 257.83 97,755 245.03 829.57 10 1074.61 814.62 259.98 97,495 244.39 830.22 11 1074.61 812.46 262.15 97,233 243.74 830.87 12 1074.61 810.27 264.33 96,968 243.08 831.52 13 1074.61 808.07 266.54 96,702 242.42 832.18 14 1074.61 805.85 268.76 96,433 241.75 832.85 15 1074.61 803.61 271.00 96,162 241.08 833.52 16 1074.61 801.35 273.26 95,889 240.40 834.20 17 1074.61 799.07 275.53 95,613 239.72 834.88 18 1074.61 796.78 277.83 95,335 239.03 835.57 19 1074.61 794.46 280.14 95,055 238.34 836.27 20 1074.61 792.13 282.48 94,773 237.64 836.97 21 1074.61 789.77 284.83 94,488 236.93 837.67 22 1074.61 787.40 287.21 94,201 236.22 838.39 23 1074.61 785.01 289.60 93,911 235.50 839.10 24 1074.61 782.59 292.01 93,619 234.78 839.83 25 1074.61 780.16 294.45 93,325 234.05 840.56 26 1074.61 777.71 296.90 93,028 233.31 841.29 27 1074.61 775.23 299.37 92,728 232.57 842.04 28 1074.61 772.74 301.87 92,427 231.82 842.78 29 1074.61 770.22 304.38 92,122 231.07 843.54 30 1074.61 767.68 306.92 91,815 230.31 844.30 31 1074.61 765.13 309.48 91,506 229.54 845.07 32 1074.61 762.55 312.06 91,194 228.76 845.84 33 1074.61 759.95 314.66 90,879 227.98 846.62 34 1074.61 757.33 317.28 90,562 227.20 847.41 35 1074.61 754.68 319.92 90,242 226.40 848.20 Balance 36 90993.83 752.02 322.59 89,919 225.60 90768.23

The before-tax effective cost is 10 percent, the same as the interest rate on the loan. The after tax effective cost is 7 percent. This can be verified by computing the IRR using the after-tax payment column above. Because there are no points, the answer is also exactly equal to the before-tax effective cost times the complement of the tax rate, i.e. 10% (1 -.3) = 7%

10 CH6M.DOC 1/19/2018 (b)

Before-tax After-tax Value Month Payment Interest Principal Balance of Deduction AT Payment 0 -95000 -96500 1 1074.61 833.33 241.27 94,759 250.00 824.61 2 1074.61 789.66 284.95 94,474 236.90 837.71 3 1074.61 787.28 287.32 94,186 236.18 838.42 4 1074.61 784.89 289.72 93,897 235.47 839.14 5 1074.61 782.47 292.13 93,605 234.74 839.86 6 1074.61 780.04 294.57 93,310 234.01 840.59 7 1074.61 777.58 297.02 93,013 233.28 841.33 8 1074.61 775.11 299.50 92,714 232.53 842.07 9 1074.61 772.61 301.99 92,412 231.78 842.82 10 1074.61 770.10 304.51 92,107 231.03 843.58 11 1074.61 767.56 307.05 91,800 230.27 844.34 12 1074.61 765.00 309.61 91,490 229.50 845.11 13 1074.61 762.42 312.19 91,178 228.73 845.88 14 1074.61 759.82 314.79 90,863 227.95 846.66 15 1074.61 757.19 317.41 90,546 227.16 847.45 16 1074.61 754.55 320.06 90,226 226.36 848.24 17 1074.61 751.88 322.72 89,903 225.56 849.04 18 1074.61 749.19 325.41 89,578 224.76 849.85 19 1074.61 746.48 328.12 89,250 223.94 850.66 20 1074.61 743.75 330.86 88,919 223.12 851.48 21 1074.61 740.99 333.62 88,585 222.30 852.31 22 1074.61 738.21 336.40 88,249 221.46 853.14 23 1074.61 735.41 339.20 87,910 220.62 853.98 24 1074.61 732.58 342.03 87,568 219.77 854.83 25 1074.61 729.73 344.88 87,223 218.92 855.69 26 1074.61 726.86 347.75 86,875 218.06 856.55 27 1074.61 723.96 350.65 86,524 217.19 857.42 28 1074.61 721.04 353.57 86,171 216.31 858.29 29 1074.61 718.09 356.52 85,814 215.43 859.18 30 1074.61 715.12 359.49 85,455 214.54 860.07 31 1074.61 712.12 362.48 85,092 213.64 860.97 32 1074.61 709.10 365.50 84,727 212.73 861.87 33 1074.61 706.06 368.55 84,358 211.82 862.79 34 1074.61 702.99 371.62 83,987 210.90 863.71 35 1074.61 699.89 374.72 83,612 209.97 864.64 Balance 36 90993.83 696.77 377.84 83,234 209.03 90784.80

The after-tax effective cost is 8.56%, found by the IRR of the ATCF column above

(c) The before-tax effective cost is not 12.09%. It is higher than (a) due to the effect of the 5 points. The after-tax effective cost is still approximately the same as the answer that would be found by multiplying the before-tax cost times the complement of the tax rate which is 12.09 x (1 -.3) = 8.46%.

11 CH6M.DOC 1/19/2018 Problem 6A -2 Initial loan amount $100,000 Monthly payment $839.20

Monthly loan schedule

Cumulative Beginning Ending Interest Cumulative Cumulative Deferred Month Balance Payment Interest Principal Balance Deduction Deduction Interest Interest

1 100,000 500.00 750.00 -250.00 100,250 500.00 500.00 750.00 250.00 2 100,250 500.00 751.88 -251.88 100,502 500.00 1000.00 1501.88 501.88 3 100,502 500.00 753.76 -253.76 100,756 500.00 1500.00 2255.64 755.64 4 100,756 500.00 755.67 -255.67 101,011 500.00 2000.00 3011.31 1011.31 5 101,011 500.00 757.58 -257.58 101,269 500.00 2500.00 3768.89 1268.89 6 101,269 500.00 759.52 -259.52 101,528 500.00 3000.00 4528.41 1528.41 7 101,528 500.00 761.46 -261.46 101,790 500.00 3500.00 5289.87 1789.87 8 101,790 500.00 763.42 -263.42 102,053 500.00 4000.00 6053.29 2053.29 9 102,053 500.00 765.40 -265.40 102,319 500.00 4500.00 6818.69 2318.69 10 102,319 500.00 767.39 -267.39 102,586 500.00 5000.00 7586.08 2586.08 11 102,586 500.00 769.40 -269.40 102,855 500.00 5500.00 8355.48 2855.48 12 102,855 500.00 771.42 -271.42 103,127 500.00 6000.00 9126.90 3126.90 13 103,127 875.20 773.45 101.75 103,025 875.20 6875.20 9900.35 3025.15 14 103,025 875.20 772.69 102.51 102,923 875.20 7750.40 10673.04 2922.63 15 102,923 875.20 771.92 103.28 102,819 875.20 8625.60 11444.96 2819.35 16 102,819 875.20 771.15 104.06 102,715 875.20 9500.80 12216.10 2715.30 17 102,715 875.20 770.36 104.84 102,610 875.20 10376.01 12986.47 2610.46 18 102,610 875.20 769.58 105.62 102,505 875.20 11251.21 13756.05 2504.84 19 102,505 875.20 768.79 106.41 102,398 875.20 12126.41 14524.83 2398.42 20 102,398 875.20 767.99 107.21 102,291 875.20 13001.61 15292.82 2291.21 21 102,291 875.20 767.18 108.02 102,183 875.20 13876.81 16060.00 2183.19 22 102,183 875.20 766.37 108.83 102,074 875.20 14752.01 16826.38 2074.37 23 102,074 875.20 765.56 109.64 101,965 875.20 15627.21 17591.94 1964.72 24 101,965 875.20 764.74 110.47 101,854 875.20 16502.41 18356.67 1854.26 a) For the first 12 months the payments are $500 and the actual interest incurred is higher than $500. However, the maximum interest deduction allowed is the amount of cash paid. Thus, the interest deduction in the first year is for the first 12 months the payments are $500 and the actual interest incurred is higher than $500. However, the maximum interest deduction allowed is the amount of cash paid. Thus, the interest deduction in the first year is 12 x $500.00 = 6,000 b) Because only the amount of the cash payment could be deducted and the actual amount of interest paid exceeded the cash paid, the excess interest must be carried forward into year 2. The deferred interest for a given month is defined as the excess of interest on the loan less the actual cash payment made. As seen above the deferred interest at the end of year 1 is $3,127. c) Interest deducted in year 2 is $875.20 x 12 = $10,502

12 CH6M.DOC 1/19/2018 Chapter 6: Residential Financial Analysis Sample Exam Questions

The following are multiple choice.

MC 6-1 A borrower is purchasing a property for $180,000 and can choose between two possible loan alternatives. The first is a 90% loan for 25 years at 9% interest and 1 point and the second is a 95% loan for 25 years at 9.25% interest and 1 point. Assume the loan will be held to maturity, what is the incremental cost of borrowing the extra money.

A. 13.66% B. 13.50% C. 14.34% D. 12.01%

MC 6-2 Use the information in problem 1, except assume that the loan will be repaid in 5 years. What is the incremental cost of borrowing the extra money?

A. 13.95% B. 13.67% C. 14.42% D. 12.39%

MC 6-3 When purchasing a $210,000 house, a borrower is comparing two loan alternatives. The first loan is a 90% loan at 10.5% for 25 years. The second loan is an 85% loan for 9.75% over 15 years. Both have monthly payments and the property is expected to be held over the life of the loan. What is the incremental cost of borrowing the extra money?

A. 20.25% B. 16.17% C. 11.36% D. 12.42%

MC 6-4 A borrower made a mortgage loan 7 years ago for $160,000 at 10.25% interest for 30 years. The loan balance is now $151,806.62 and rates for this amount are currently 9.0% for 23 years. Origination fees and closing costs are $4,500 and closing costs are not financed by the lender. What is the effective cost of refinancing?

A. 9.0% B. 10.85% C. 15.32% D. 9.39%

MC 6-5 Mr. Tramp made a mortgage 5 years ago for $85,000 at 8.25% interest and a 15 year term. Rates have now risen to 10% for an equivalent loan. Mr. Tramp’s lender is willing to discount the loan by $2,000 if he will prepay the loan. What rate of return would Mr. Tramp receive by prepaying the loan?

A. 10.24% B. 8.95% C. 14.32% D. 9.14%

13 CH6M.DOC 1/19/2018 MC 6-6 A loan was made 10 years ago for $140,000 at 10.5% for a 30 year term. Rates are currently 9.25%. What is the market value of the loan?

A. $128,271 B. $147,600 C. $139,828 D. $151,395

MC 6-7 Bud is offering a house for sale for $180,000 with an assumable loan which was made 5 years ago for $140,000 at 8.75% over 30 years. Kelsey is interested in buying the property and can make a $20,000 down payment. A second mortgage can be obtained for the balance at 12.5% for 25 years. What is the effective cost of the combined loans, if Kelsey would like to compare this financing alternative to obtaining a first mortgage for the full amount?

A. 10.63% B. 9.39% C. 9.04% D. 11.27%

MC 6-8 A house is sold with an assumable $156,000 below-market loan at 8.5% for a remaining term of 15 years. Current rates are 9.75% for 15 year mortgages. If the house sold for $240,000, what is the cash-equivalent value of the house.

A. $250,834.82 B. $229,165.18 C. $260,660.40 D. $219,339.60

MC 6-9 Ms. Madison has an existing loan with payments of $782.34. The interest rate on the loan is 10.5% and the remaining loan term is 10 years. The current balance of the loan is $57,978.99. The home is now worth $120,000 and Ms. Madison would like to borrow an additional $30,000 through a wraparound loan which would increase the debt to 487,978.99. Terms of the wraparound loan are 12.25% interest with monthly payments for 10 years. What is the incremental cost of borrowing the extra $30,000 through a wraparound loan?

A. 15.47% B. 11.38% C. 12.96% D. 13.41%

MC 6-10 Mr. Fisher has built several houses and is offering buyers mortgage rates of 10% with 15 year term. Current rates are 10.75%. Fourth National Bank will provide the loans, if Mr. Fisher pays an equivalent amount up front to buy down the interest rate. If a house is sold for $290,000 with a 90% loan, how much would Mr. Fisher have to pay to buy down the loan?

A. $1,957.50 B. $11,989.34 C. $11,250.25 D. $10,790.41

14 CH6M.DOC 1/19/2018

MC 6-11 When calculating the cash equivalent value of an assumable loan, you find the present value of the payments using the

A. Contract interest rate B. Incremental borrowing cost C. Market interest rate D. Discount rate

MC 6-12 Which of the following is TRUE concerning Wraparound Loans:

A. The borrower makes payments on existing loan B. The lender makes payments on existing loan C. The lender only makes payments on the second mortgage D. The borrower only makes payments on the second mortgage

MC 6-13 Which of the following is FALSE concerning Buydown Loans:

A. They are often used during periods of high inflation B. They always lower the rate on the loan for the borrower for the entire loan term C. Help borrowers qualify for a loan D. They can be offered by home builders

MC 6-14 Which of the following is TRUE regarding the incremental Cost of Borrowing :

A. It should be less than the rate for a first mortgage B. It should be compared to the cost of obtaining a second mortgage C. It is used to calculate the APR for the loan D. It is independent of Loan-to-Value Ratio

MC 6-15 The Market Value of a loan is:

A. The loan balance times one minus the market rate B. The loan balance times one minus the original rate C. The future value of the remaining payments D. The present value of the remaining payments

The following questions are true-false.

TF 6-16 A borrower finds that the incremental cost of borrowing an extra $10,000 is 14%. The borrower can earn 12% on alternative investments of comparable risk so he would be better off by not borrowing the extra 14%. TF 6-17 A borrower finds that the incremental cost of borrowing an extra $10,000 is 14%. A second loan can be obtained at 15% so the borrower would be better off by borrowing with the smaller loan and a second mortgage. TF 6-18 The cash equivalent value of a house that sold with favorable financing is usually less than its sale price. TF 6-19 The effective cost of a wraparound loan should be comparable to the cost of a second mortgage with the same loan-to-value ratio. TF 6-20 A borrower is considering refinancing and finds that the return, considering refinancing charges and lower payments, is 10%. The borrower can earn 12% on alternative investments so the property should be refinanced. TF 6-21 Homeowners should not borrow refinancing costs because the effective rate of refinancing will be higher. TF 6-22 If interest rates decrease, the market value of a loan previously make will increase.

15 CH6M.DOC 1/19/2018 TF 6-23 A house that is financed with a below-market loan is available for sale. The value of the house will be higher than similar properties regardless of the other terms of the loan. TF 6-24 A potential buyer is interested in purchasing a home that has an assumable below-market loan. The buyer determines that the financing premium associated with the below-market loan is worth $4,300. If similar houses sell for $100,000, the buyer should be willing to pay $104,300 or more for the property. TF 6-25 Buydown loans are advantageous to borrowers because the effective cost of the loan is always less than the market.

16 CH6M.DOC 1/19/2018

SOLUTIONS TO CHAPTER 6

Multiple Choice

6.1 A 6.2 A 6.3 D 6.4 D 6.5 B 6.6 C 6.7 B 6.8 B 6.9 A 6.10 D 6.11 C 6.12 B 6.13 B 6.14 B 6.15 D

True/False

6.16 T 6.17 F 6.18 T 6.19 T 6.20 F 6.21 F 6.22 T 6.23 F 6.24 F 6.25 F