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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.
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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.
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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
90% Loan
80% Loan
Difference
Interest rate
8.5%
8.0%
Loan term
25 yrs.
25 yrs.
Loan Amount
$90,000
80,000
$10,000
Monthly Payments
$724.70
617.45
$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
90% Loan
80% Loan
Difference
Loan Amount
$90,000
80,000
Points
$1,800
0
Net Proceeds
$88,200
80,000
$8,200
Monthly Payments
$724.70
617.45
$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
90% Loan
80% Loan
Difference
Loan Amount
$90,000
80,000
$10,000
Monthly payments
$724.70
617.45
$107.25
Loan Balance
$83,508.62
73,819.37
$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%
Combined
Loan Amount
$180,000
40,000
$220,000
Interest rate
9%
13%
Loan term
20 yrs..
20 yrs..
$2,088.14 x (MPVIFA, ?%, 20 yrs.) = $220,000
3
Monthly Payments
$1619.51
468.63
$2,088.14
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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
Combined
Loan Amount
$180,000
40,000
$220,000
Interest rate
9%
13%
Loan term
20 yrs..
20 yrs..
Monthly Payments
$1619.51
468.63
$2,088.14
Loan Balance
$159,672.44
37,038.81
$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
$180,000
40,000
$220,000
Combined
Interest rate
9%
13%
Loan term
20 yrs..
10 yrs..
Monthly Payments
$1619.51
597.24
$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.
Combined
Loan Amount
$180,000
40,000
$220,000
Interest rate
9%
13%
Loan term
20 yrs..
10 yrs..
Monthly Payments
$1619.51
597.24
$2,216.75
Loan Balance
$159,672.68
26,248.89
$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.
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(a)
Alternative
Old loan
New loan
Savings
3/9/2016
Interest rate
11%
10%
Loan term
30 yrs..
25 yrs..
Loan amount
$95,000
92,306
Monthly Payments
$904.71
838.79
$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
Cost of refinancing
Net proceeds
$92,306.00
$4,769.19
$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
Old loan
New loan
Loan Amount
$95,000
92,306
Interest rate
11%
10%
Loan term
30 yrs..
25 yrs..
Monthly payments
$904.71
838.79
65.92
Loan Balance
$87,648.82*
86,918.44
$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.
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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:
First mortgage
Interest rate
10.5%
Loan Term
20 yrs..
Loan Amount
$120,000
Monthly Payments
$1,198.06
Loan Term
20 yrs..
20 yrs..
Loan Amount
$100,000
20,000
$120,000
Monthly Payments
$899.73
234.32
$1,134.05
or
Alternative 2: Purchase of $160,000 home:
Assumption
Second mortgage
Interest rate
9%
13%
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.
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(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:
Assumption
Second mortgage
Interest rate
9%
9%
Loan Term
20 yrs..
20 yrs..
Loan Amount
$100,000
20,000
$120,000
Monthly Payments
$899.73
179.95
$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:
Assumption
Second mortgage
Interest rate
9%
9%
Loan Term
20 yrs..
20 yrs..
Loan Amount
$100,000
30,000
$130,000
Monthly Payments
$899.73
269.92
$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 6-6
Loan
Wraparound
Existing
Difference
Amount
$150,000
100,000
$50,000
Payment
$1,800.25
1,100.25
$700.25
Term
15 yrs.
15 yrs. (remaining)
$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
Second mortgage
Existing loan
Difference
Amount
$50,000
100,000
$150,000
Payment
$665.87
1,100.00
$1765.87
Term
15 yrs.
15 yrs. (remaining)
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.
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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%:
Payments on a loan for $100,000 at 9%:
Savings by getting the loan at 9%:
$873.70
839.20
$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:
Balance of $100,000 loan at 9% after 10 years:
Savings
$83,668.75
82,739.23
$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):
Monthly payment reduction during the second year (25% of 4726.96):
$363.48
$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.
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(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
N
FV
PMT
Solve for PV:
PV
=
=
=
=
8%/12
15x12 or 180
0
$1,258.36
=
$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 5 th year.
I
N
FV
PMT
Solve for PV:
PV
=
=
=
=
8%/12
5x12 or 60
$108,378
$1,258.36
=
$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.
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Chapter 6 Appendix
Problem 6A-1
(a)
Loan
Monthly payment
$100,000, 10% interest, 15 yrs (monthly payments)
$1,074.61
Before-tax
Month
Balance
Payment
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
-100000
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
90993.83
Interest
Principal
833.33
831.32
829.30
827.25
825.19
823.11
821.02
818.90
816.77
814.62
812.46
810.27
808.07
805.85
803.61
801.35
799.07
796.78
794.46
792.13
789.77
787.40
785.01
782.59
780.16
777.71
775.23
772.74
770.22
767.68
765.13
762.55
759.95
757.33
754.68
752.02
241.27
243.28
245.31
247.35
249.42
251.49
253.59
255.70
257.83
259.98
262.15
264.33
266.54
268.76
271.00
273.26
275.53
277.83
280.14
282.48
284.83
287.21
289.60
292.01
294.45
296.90
299.37
301.87
304.38
306.92
309.48
312.06
314.66
317.28
319.92
322.59
After-tax
Value
of Deduction
Balance
99,759
99,515
99,270
99,023
98,773
98,522
98,268
98,013
97,755
97,495
97,233
96,968
96,702
96,433
96,162
95,889
95,613
95,335
95,055
94,773
94,488
94,201
93,911
93,619
93,325
93,028
92,728
92,427
92,122
91,815
91,506
91,194
90,879
90,562
90,242
89,919
250.00
249.40
248.79
248.18
247.56
246.93
246.30
245.67
245.03
244.39
243.74
243.08
242.42
241.75
241.08
240.40
239.72
239.03
238.34
237.64
236.93
236.22
235.50
234.78
234.05
233.31
232.57
231.82
231.07
230.31
229.54
228.76
227.98
227.20
226.40
225.60
AT Payment
-100000
824.61
825.21
825.82
826.43
827.05
827.67
828.30
828.93
829.57
830.22
830.87
831.52
832.18
832.85
833.52
834.20
834.88
835.57
836.27
836.97
837.67
838.39
839.10
839.83
840.56
841.29
842.04
842.78
843.54
844.30
845.07
845.84
846.62
847.41
848.20
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%
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(b)
Before-tax
Month
Balance
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Payment Interest
-95000
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
1074.61
90993.83
Principal
833.33
789.66
787.28
784.89
782.47
780.04
777.58
775.11
772.61
770.10
767.56
765.00
762.42
759.82
757.19
754.55
751.88
749.19
746.48
743.75
740.99
738.21
735.41
732.58
729.73
726.86
723.96
721.04
718.09
715.12
712.12
709.10
706.06
702.99
699.89
696.77
After-tax
Value
of Deduction
Balance
241.27
284.95
287.32
289.72
292.13
294.57
297.02
299.50
301.99
304.51
307.05
309.61
312.19
314.79
317.41
320.06
322.72
325.41
328.12
330.86
333.62
336.40
339.20
342.03
344.88
347.75
350.65
353.57
356.52
359.49
362.48
365.50
368.55
371.62
374.72
377.84
94,759
94,474
94,186
93,897
93,605
93,310
93,013
92,714
92,412
92,107
91,800
91,490
91,178
90,863
90,546
90,226
89,903
89,578
89,250
88,919
88,585
88,249
87,910
87,568
87,223
86,875
86,524
86,171
85,814
85,455
85,092
84,727
84,358
83,987
83,612
83,234
AT Payment
-96500
250.00
824.61
236.90
837.71
236.18
838.42
235.47
839.14
234.74
839.86
234.01
840.59
233.28
841.33
232.53
842.07
231.78
842.82
231.03
843.58
230.27
844.34
229.50
845.11
228.73
845.88
227.95
846.66
227.16
847.45
226.36
848.24
225.56
849.04
224.76
849.85
223.94
850.66
223.12
851.48
222.30
852.31
221.46
853.14
220.62
853.98
219.77
854.83
218.92
855.69
218.06
856.55
217.19
857.42
216.31
858.29
215.43
859.18
214.54
860.07
213.64
860.97
212.73
861.87
211.82
862.79
210.90
863.71
209.97
864.64
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%.
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Problem 6A -2
Initial loan amount
Monthly payment
$100,000
$839.20
Monthly loan schedule
Cumulative
Beginning
Month
Balance
Ending
Payment
Interest Principal Balance
Interest
Cumulative Cumulative Deferred
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
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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.
B.
C.
D.
13.66%
13.50%
14.34%
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.
B.
C.
D.
13.95%
13.67%
14.42%
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.
B.
C.
D.
20.25%
16.17%
11.36%
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.
B.
C.
D.
9.0%
10.85%
15.32%
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.
B.
C.
D.
10.24%
8.95%
14.32%
9.14%
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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.
B.
C.
D.
$128,271
$147,600
$139,828
$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.
B.
C.
D.
10.63%
9.39%
9.04%
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.
B.
C.
D.
$250,834.82
$229,165.18
$260,660.40
$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.
B.
C.
D.
15.47%
11.38%
12.96%
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.
B.
C.
D.
$1,957.50
$11,989.34
$11,250.25
$10,790.41
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MC 6-11
When calculating the cash equivalent value of an assumable loan, you find the present value of the payments using
the
A.
B.
C.
D.
Contract interest rate
Incremental borrowing cost
Market interest rate
Discount rate
MC 6-12
Which of the following is TRUE concerning Wraparound Loans:
A.
B.
C.
D.
The borrower makes payments on existing loan
The lender makes payments on existing loan
The lender only makes payments on the second mortgage
The borrower only makes payments on the second mortgage
MC 6-13
Which of the following is FALSE concerning Buydown Loans:
A.
B.
C.
D.
They are often used during periods of high inflation
They always lower the rate on the loan for the borrower for the entire loan term
Help borrowers qualify for a loan
They can be offered by home builders
MC 6-14
Which of the following is TRUE regarding the incremental Cost of Borrowing :
A.
B.
C.
D.
It should be less than the rate for a first mortgage
It should be compared to the cost of obtaining a second mortgage
It is used to calculate the APR for the loan
It is independent of Loan-to-Value Ratio
MC 6-15
The Market Value of a loan is:
A.
B.
C.
D.
The loan balance times one minus the market rate
The loan balance times one minus the original rate
The future value of the remaining payments
The present value of the remaining payments
The following questions are true-false.
TF 6-16
TF 6-17
TF 6-18
TF 6-19
TF 6-20
TF 6-21
TF 6-22
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%.
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.
The cash equivalent value of a house that sold with favorable financing is usually less than its sale price.
The effective cost of a wraparound loan should be comparable to the cost of a second mortgage with the same
loan-to-value ratio.
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.
Homeowners should not borrow refinancing costs because the effective rate of refinancing will be higher.
If interest rates decrease, the market value of a loan previously make will increase.
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TF 6-23
TF 6-24
TF 6-25
3/9/2016
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.
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.
Buydown loans are advantageous to borrowers because the effective cost of the loan is always less than the
market.
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SOLUTIONS TO CHAPTER 6
Multiple Choice
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
6.10
6.11
6.12
6.13
6.14
6.15
A
A
D
D
B
C
B
B
A
D
C
B
B
B
D
True/False
6.16
6.17
6.18
6.19
6.20
6.21
6.22
6.23
6.24
6.25
17
T
F
T
T
F
F
T
F
F
F