Chapter 6:
Residential Financial Analysis

Incremental Borrowing Cost
– Two loans, one for a greater sum than the
other. How should borrower compare the
alternatives? Calculate marginal or
incremental cost of borrowing.
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
Loan 1: $80,000, 12%, 25 years = $ 842.58/mo.
Loan 2: $90,000, 13%, 25 years= $ 1,015.05/mo.
$10,000
$ 172.47
 IRR?
-10000=PV
172.47=PMT
300 = n
IRR = 20.57% = incremental cost of
extra
$10,000
What if loan is repaid early (say after 5
years)?
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Loan 1: OLB after 5 years = 76,523
Loan 2: OLB
= 86,640
10,117
IRR?
-10,000=PV
172.47=pmt
10,117=FV =OLB Differential
60 =n
IRR = 20.83%
If there were origination fees?
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

Loan 1: 1,600 Fees
Loan 2: 2,700 Fees
IRR? 8,900=PV= {(90,000-80,000)-(2,700-1,600)}
172.47=pmt
300=n
IRR = 23.18%
LOAN REFINANCING
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

If interest rates fall, should loan be refinanced?
Compare costs of refinancing to benefits or
savings. Calculate IRR or NPV.
Five year old loan ($80,000 orig., 30 years, 15%)
vs. new loan of $78,976.50 (OLB of old loan) 25
years, 14%.
Loan Refinancing (con’t)

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
Costs = $4,105
Benefits = pmtold - pmtnew
(1011.56 - 950.69= 60.87)
IRR? : 4,105=PV
60.87=pmt
300=n
IRR = 17.57%
NPV = ? depends on borrower’s req’d rate of
return.
What happens if loan is repaid early?

Assume loans were prepaid after 15 years
(old loan) or 10 years after refinancing.
IRR? :
4,105 = PV
60.87 = pmt
889 = FV (OLBold-OLBnew)=(72,27571,387)
120 =n
IRR =
14.21%
What if refinancing costs can be
financed?
1
2
Simply compare new payments (based on
OLB & refinancing costs) to old payment. If
new payment is lower, refinance.
Alternatively, calculate the effective cost of
refinancing.
IRR?: 78,976.50 = PV (loan disbursment)
1,000.10= pmt (OLB &Financed
refinance cost)=(78,976.50+4105)
300 = n
IRR = 14.81%
What if the borrower wanted to
refinance for a lower interest rate,
but wishes to continue making their
current monthly payment? The
impact of this approach would be to
shorten the payback period. Let’s
revisit the first refi example. The
interest rate drops from 15% to
14%, and a refi fee of $4105 is
charged. The original loan had 25
more years (300 months) until
maturity. How long would it take to
amortize the outstanding loan
balance at the 14% rate?
PV= OLB= $78,976.50
PMT= $1011.56
I= 14%
N=?= 208.43months vs. the 300 months
remaining on the original loan
What would the lender’s yield be on the
refi loan?
PV= $74,871.50 = (78976.50 OLB – 4105
refi fee)
PMT= $1101.56
N= 208.43 months
I= ? = 14.99%
Early Loan Repayment: Lender
Inducements
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

If interest rates rise, lenders would like to
retire old loans. Lender might offer to
discount loan if prepaid.
Old loan $75,000; 8%; 15 years. 10 years
later OLB is $35,348. If current rates are
12% and lender offers to accept
repayment of only $33,348.
What is the return to the borrower?
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
IRR?: 33,348 = PV (OLB - 2000 discount)
716.74 = pmt (orig. loan pmt)
60 = n
IRR = 10.50% = return on “investment” to
buy back the loan.
Market Value of a Loan


Simple - compute the present value of the
remaining payments at the market
interest rate.
Old Loan of $80,000; 10%; 20 years. Five
years later, the OLB is $71,842. If market
rates were 15% today, what is the loan
value?
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PV = ?:
772.02 = pmt
180 = n
15% = i
PV = $55,161 is the “discounted” value of
the loan.
Makes sense if the borrower has the $$ to
pay off loan and the IRR represents on
attractive yield to alternative investments
Effective Cost of Two or more loans:


Situations exist when borrower takes a
second mortgage or perhaps assumes a
loan and needs additional funds.
You wish to buy a property priced at
$115,000. An existing mortgage can be
assumed (OLB=$75,331), payments are
$726.96 and the loan will mature in 20
years. A second mortgage for $16,669
($115,000 x .80 - $75,331) can be obtained at
14% for 20 years. Alternatively, the
purchase can be made with an 80% LTV
loan ($115,000 x .80) at 12% for 20 years.


Is the assumption attractive? IRR of
combined assumption plus second
mortgage?
IRR?:
726.96 + 207.28 = 934.24 = pmt
240 = n
92,000 = PV
IRR = 10.75%, which is lower than cost of
First mortgage financing
(12%)

Usually second mortgages have short
maturities. If the above situation called for
a 5 year second mortgage, would the
assumption make sense?
IRR?:
726.96 + 387.86* =1,114.82 = pmt
*pmt. On 2nd mtg.,i=14% ,N=5YRS
1-5 for 1,114.82 = n
6-20 for 726.96 = n
92,000 = PV
IRR = 10.29%
Wraparound Loans

Used to keep an old (low interest rate) loan
in place. Wrap lender makes loan for an
amount equal to existing loan balance plus
the additional financing required. Wrap
lender pays off old note and borrower pays
off wraparound loan. Can be used in lieu of
assumption and second mortgage in an
acquisition or as a means to borrow
against equity in a property.
$90,000 = OLB old loan (8%, 15 years remaining)
$860.09 = old pmt.
$150,000 = property value
$30,000 = desired new financing
Options:
1. New first mortgage $120,000 at 11.5% for 15
years.
2. Second mortgage of $30,000 at 15.5% for
15 years.
3. Wrap loan of $120,000 at 10% for 15 years.


Obviously the wrap rate of 10% is favorable
compared to a new first mortgage at 11.5%.
Is the wrap better than adding a second
mortgage? Calculate the incremental cost
on the additional $30,000 acquired via
wrap financing. Compare this rate to the
second.
IRR?:
30,000 = PV
429.44 = pmt
(1289.53 wrap loan
180 = n
pmt-860 old loan pmt)
IRR = 15.46% which is slightly lower than
rate on the second.
*
Original mortgagee gets screwed.
That is why the original mortgage
probably disallows further
encumbrances or includes a due-onsale clause.
BUYDOWNS

Seller (often builder) helps buyer
(borrower) qualify for mortgage
financing by “buying down” early
mortgage payments. Used most
often when interest rates are very
high. Often buydowns are executed
with graduated payments for 3-5
years.

Assume buyer seeks a $75,000 mortgage
and current rates are 15%. If loan maturity
were 30 years, payments would equal
$948.33. Borrower can’t qualify at this
payment, but if rate were 13% ($829.65
pmt) they could qualify. Builder/Seller
offers to “buy down” the interest rate from
15% to 13% for the first five years of the
loan.

How much would builder pay lender to
buydown the loan? Calculate present
value of payment short fall $118.68 (948.33
- 829.65) at 15% over 5 years.
PV = ?
PV = $4,988.67
118.68 = pmt
15% = i
60 = n