Solutions to Questions - Chapter 6Residential Financial Analysis

Question 6-1Why 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 6-2What 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 6-3Why 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.

Question 6-4Why 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 6-5What 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 firstone 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 6-6Why 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.

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Question 6-7Assuming 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 6-8Under 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 dollaramount 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.

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Question 6-9What 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 ratiothat 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 6-10Is 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 werepaid 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.

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Solutions to Problems - Chapter 6Residential Financial Analysis

INTRODUCTION

The following solutions were obtained using an HP 12C financial calculator. Answersmay 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 assumesome 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 AmountMonthly Payments

90% Loan 8.5% 25 yrs. $90,000 $724.7080% Loan 8.0% 25 yrs. 80,000 617.45Difference $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 Payments90% Loan $90,000 $1,800 $88,200 $724.7080% Loan 80,000 0 80,000 617.45Difference $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 paymentsLoan Balance90% Loan $90,000 $724.70 $83,508.6280% Loan 80,000 617.45 73,819.37

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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.

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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 rateLoan term Monthly Payments$180,000 9% 20 yrs.. $1619.5140,000 13% 20 yrs.. 468.63

Combined $220,000 $2,088.14

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

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) REVWe now need the loan balance after 5 years

Loan Amount Interest rateLoan termMonthly Payments Loan Balance$180,000 9% 20 yrs.. $1619.51 $159,672.4440,000 13% 20 yrs.. 468.63 37,038.81

Combined $220,000 $2,088.14 $196,711.25

$2,088.14 x (MPVIFA, ?%, 5 yrs.) + $196,711.25 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 rateLoan term Monthly Payments$180,000 9% 20 yrs.. $1619.5140,000 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 paymenton 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.

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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 rateLoan termMonthly Payments Loan Balance$180,000 9% 20 yrs.. $1619.51 $159,672.6840,000 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.

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Problem 6-3Preliminary 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.

(a)Alternative Interest rate Loan term Loan amount

Monthly PaymentsOld loan 11% 30 yrs.. $95,000 $904.71New loan 10% 25 yrs.. 92,306 838.79Savings $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 investorcan not get a higher yield than 16.30% on alternative investments.

Alternate solution:

Amount of new loan $92,306.00Cost of refinancing $4,769.19Net 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 lessthan 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 Monthlypayments

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

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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 donot benefit from the favorable financing for a period of time long enough to cover and/or justify the cost of refinancing.

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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.

Problem 6-4Payments 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 PaymentsFirst 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 PaymentsAssumption 9% 20 yrs.. $100,000 $899.73Second mortgage 13% 20 yrs.. 20,000 234.32

$120,000 $1,134.056-10

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. $110,000instead of $120,000 which results in interest savings of 10.5% (the rate on the loan).

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The point is that the investor’s opportunity cost is 10.5%, which is higher than the4.64% 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.

(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:

Interest rate Loan Term Loan Amount Monthly PaymentsAssumption 9% 20 yrs.. $100,000 $899.73Second mortgage 9% 20 yrs.. 20,000 179.95

$120,000 $1,079.68

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:

Interest rate Loan Term Loan Amount Monthly PaymentsAssumption 9% 20 yrs.. $100,000 $899.73Second mortgage 9% 20 yrs.. 30,000 269.92

$130,000 $1,169.65

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 6-6Loan 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..) = $50,0006-12

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 thecombined loans is as follows:

$1,765.87 (MPVIFA, ?%, 15 yrs..) = $150,000.

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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.

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%:$873.70Payments on a loan for $100,000 at 9%:839.20Savings 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 nowdiscount 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: $83,668.75Balance of $100,000 loan at 9% after 10 years:82,739.23Savings $929.52

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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.

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Problem 6-8(a)

Monthly payment reduction during the first year (50% of $726.96):$363.48Monthly 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.

(b)Based on the results from (a), the buydown loan is worth $6,005.66 in present valueterms. 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 = -$140,000I = 7/12 or 0.58N = 15x12 or 180FV = 0

Solve for the payment:PMT = $1,258.36

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

I = 8%/12N = 15x12 or 180FV = 0PMT = $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 $131,675.49Cash down payment 60,000.00Cash equivalent value of property$191,675.49

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(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%/12N = 5x12 or 60FV = $108,378PMT = $1,258.36

Solve for PV:PV = $134,804.72

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

Problem 6-10

Question: A borrower is making a choice between a mortgage with monthly payment or bi-weekly payments; the loan will be $200,000@6% interest for 20 years. A) How would you analyze these alternatives? B) What if the bi-weekly loan was available for 5.75%? How would your answerchange?

A. Calculate Monthly Payments:

PV = <$200,000> FV = 0

N = 240 (12*20)I = 6%

Solve: PMT = $1,432.86

B. Calculate Bi-Weekly Payments: $1432.86 ÷ 2 = $71643. Remember: bi-weekly payments total 26 per year

C. Calculate maturity period:

PV = <$200,000>FV = 0 I = 6%PMT = $716.43 (1432.86/2)Solve: N = 17.3 years (449 payments / 26 payments per year)

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D. Compare Total Payments :

$1,432.86*240 = $343,866.40 $716.43*449 = $321,677.07

- Bi-weekly payments would be less costly by $22,209.33 (343,886.40-321,977.07).

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E. Recalculate the above based on 5.75% interest:

PV = <$200,000>FV = - 0I = 5.75%PMT = 716.43N = ?? 16.73 years (435 payments / 26 payments per year)

$1,432.86*240 = $343,886.40 $716.43*435 = $311,647.05

Conclusion: Bi-weekly payments would be even less costly by $32,239.35 (343,886.40-311,647.05).

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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 -1000001 1074.61 833.33 241.27 99,759 250.00 824.612 1074.61 831.32 243.28 99,515 249.40 825.213 1074.61 829.30 245.31 99,270 248.79 825.824 1074.61 827.25 247.35 99,023 248.18 826.435 1074.61 825.19 249.42 98,773 247.56 827.056 1074.61 823.11 251.49 98,522 246.93 827.677 1074.61 821.02 253.59 98,268 246.30 828.308 1074.61 818.90 255.70 98,013 245.67 828.939 1074.61 816.77 257.83 97,755 245.03 829.5710 1074.61 814.62 259.98 97,495 244.39 830.2211 1074.61 812.46 262.15 97,233 243.74 830.8712 1074.61 810.27 264.33 96,968 243.08 831.5213 1074.61 808.07 266.54 96,702 242.42 832.1814 1074.61 805.85 268.76 96,433 241.75 832.8515 1074.61 803.61 271.00 96,162 241.08 833.5216 1074.61 801.35 273.26 95,889 240.40 834.2017 1074.61 799.07 275.53 95,613 239.72 834.8818 1074.61 796.78 277.83 95,335 239.03 835.5719 1074.61 794.46 280.14 95,055 238.34 836.2720 1074.61 792.13 282.48 94,773 237.64 836.9721 1074.61 789.77 284.83 94,488 236.93 837.6722 1074.61 787.40 287.21 94,201 236.22 838.3923 1074.61 785.01 289.60 93,911 235.50 839.1024 1074.61 782.59 292.01 93,619 234.78 839.8325 1074.61 780.16 294.45 93,325 234.05 840.5626 1074.61 777.71 296.90 93,028 233.31 841.2927 1074.61 775.23 299.37 92,728 232.57 842.0428 1074.61 772.74 301.87 92,427 231.82 842.7829 1074.61 770.22 304.38 92,122 231.07 843.5430 1074.61 767.68 306.92 91,815 230.31 844.3031 1074.61 765.13 309.48 91,506 229.54 845.0732 1074.61 762.55 312.06 91,194 228.76 845.8433 1074.61 759.95 314.66 90,879 227.98 846.6234 1074.61 757.33 317.28 90,562 227.20 847.4135 1074.61 754.68 319.92 90,242 226.40 848.20

Balance 90993.83 752.02 322.59 89,919 225.60 90768.236-21

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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 computingthe 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%

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(b)

Before-tax After-tax Value

Month Payment Interest Principal Balance of Deduction

AT Payment

0 -95000 -965001 1074.61 833.33 241.27 94,759 250.00 824.612 1074.61 789.66 284.95 94,474 236.90 837.713 1074.61 787.28 287.32 94,186 236.18 838.424 1074.61 784.89 289.72 93,897 235.47 839.145 1074.61 782.47 292.13 93,605 234.74 839.866 1074.61 780.04 294.57 93,310 234.01 840.597 1074.61 777.58 297.02 93,013 233.28 841.338 1074.61 775.11 299.50 92,714 232.53 842.079 1074.61 772.61 301.99 92,412 231.78 842.8210 1074.61 770.10 304.51 92,107 231.03 843.5811 1074.61 767.56 307.05 91,800 230.27 844.3412 1074.61 765.00 309.61 91,490 229.50 845.1113 1074.61 762.42 312.19 91,178 228.73 845.8814 1074.61 759.82 314.79 90,863 227.95 846.6615 1074.61 757.19 317.41 90,546 227.16 847.4516 1074.61 754.55 320.06 90,226 226.36 848.2417 1074.61 751.88 322.72 89,903 225.56 849.0418 1074.61 749.19 325.41 89,578 224.76 849.8519 1074.61 746.48 328.12 89,250 223.94 850.6620 1074.61 743.75 330.86 88,919 223.12 851.4821 1074.61 740.99 333.62 88,585 222.30 852.3122 1074.61 738.21 336.40 88,249 221.46 853.1423 1074.61 735.41 339.20 87,910 220.62 853.9824 1074.61 732.58 342.03 87,568 219.77 854.8325 1074.61 729.73 344.88 87,223 218.92 855.6926 1074.61 726.86 347.75 86,875 218.06 856.5527 1074.61 723.96 350.65 86,524 217.19 857.4228 1074.61 721.04 353.57 86,171 216.31 858.2929 1074.61 718.09 356.52 85,814 215.43 859.1830 1074.61 715.12 359.49 85,455 214.54 860.0731 1074.61 712.12 362.48 85,092 213.64 860.9732 1074.61 709.10 365.50 84,727 212.73 861.8733 1074.61 706.06 368.55 84,358 211.82 862.7934 1074.61 702.99 371.62 83,987 210.90 863.7135 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

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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%.

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Problem 6A -2Initial loan amount $100,000Monthly payment $839.20

Monthly loan schedule

CumulativeBeginning Ending Interest Cumulative Cumulative Deferred

Month Balance Payment Interest Principal Balance Deduction Deduction Interest Interest

1 100,000 500.00 750.00 -250.00 100,250 500.00 500.00 750.00 250.002 100,250 500.00 751.88 -251.88 100,502 500.00 1000.00 1501.88 501.883 100,502 500.00 753.76 -253.76 100,756 500.00 1500.00 2255.64 755.644 100,756 500.00 755.67 -255.67 101,011 500.00 2000.00 3011.31 1011.315 101,011 500.00 757.58 -257.58 101,269 500.00 2500.00 3768.89 1268.896 101,269 500.00 759.52 -259.52 101,528 500.00 3000.00 4528.41 1528.417 101,528 500.00 761.46 -261.46 101,790 500.00 3500.00 5289.87 1789.878 101,790 500.00 763.42 -263.42 102,053 500.00 4000.00 6053.29 2053.299 102,053 500.00 765.40 -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 2586.0811 102,586 500.00 769.40 -269.40 102,855 500.00 5500.00 8355.48 2855.4812 102,855 500.00 771.42 -271.42 103,127 500.00 6000.00 9126.90 3126.9013 103,127 875.20 773.45 101.75 103,025 875.20 6875.20 9900.35 3025.1514 103,025 875.20 772.69 102.51 102,923 875.20 7750.40 10673.04 2922.6315 102,923 875.20 771.92 103.28 102,819 875.20 8625.60 11444.96 2819.3516 102,819 875.20 771.15 104.06 102,715 875.20 9500.80 12216.10 2715.3017 102,715 875.20 770.36 104.84 102,610 875.20 10376.01 12986.47 2610.4618 102,610 875.20 769.58 105.62 102,505 875.20 11251.21 13756.05 2504.8419 102,505 875.20 768.79 106.41 102,398 875.20 12126.41 14524.83 2398.4220 102,398 875.20 767.99 107.21 102,291 875.20 13001.61 15292.82 2291.2121 102,291 875.20 767.18 108.02 102,183 875.20 13876.81 16060.00 2183.1922 102,183 875.20 766.37 108.83 102,074 875.20 14752.01 16826.38 2074.3723 102,074 875.20 765.56 109.64 101,965 875.20 15627.21 17591.94 1964.7224 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 thedeferred interest at the end of year 1 is $3,127.

c) Interest deducted in year 2 is $875.20 x 12 = $10,502

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