Chapter 6
Residential Financial Analysis
1
Overview





Incremental Borrowing Cost
Loan Refinancing
Effective Cost of Multiple Loans
Below Market Financing
Cash Equivalency
2
Incremental Borrowing Cost

Compare financing alternatives



What is the real cost of borrowing more money
at a higher interest rate?
Alternatively, what is the required return to
justify a lower down payment?
Basic principle when comparing choices: What
are the cash flow differences?
3
Incremental Borrowing Cost –
Continued

Example:


Home Value = $150,000
Two Financing Alternatives:



#1: 90% Loan-to-Value, 8.5% Interest Rate, 30
Years
#2: 80% Loan-to-Value, 8.0% Interest Rate, 30
Years
It appears there is only a 50bp interest rate
difference, but…
4
Incremental Borrowing Cost –
Continued
House Value
Loan-to-Value Ratio
Loan Amount
Interest Rate
Loan Term
Payment per Year
Number of Payments
Alternative 1 Alternative 2
$100,000.00 $100,000.00
80%
90%
$80,000.00
$90,000.00
12.00%
13.00%
25
25
12
12
300
300
Monthly Payments
$842.58
$1,015.05
Additional Borrowing
$10,000.00
Additional Payment
$172.47
What is the cost of additional amount borrowed?
N
I/Y
P/Y
PV
PMT
300
12
-10,000
172.47
20.57%
FV
0
5
Incremental Borrowing Cost –
Continued



20.57% represents the real cost of
borrowing the extra $10,000
Can you earn an equivalent risk adjusted
return on the $10,000 that is not invested
in the home?
Alternatively, can you borrow the additional
$10,000 elsewhere at a lower cost?
6
Incremental Borrowing Cost –
Early Repayment
Loan Costs with Prepayment in 5 Years
Loan Balance Alternative 1:
N
I/Y
P/Y
PV
240
12.00%
12
-76,523
Loan Balance Alternative 2:
N
I/Y
P/Y
240
13.00%
12
PV
-86,640
What is the cost of additional amount borrowed?
N
I/Y
P/Y
PV
60
12
-10,000
20.83%
PMT
842.58
FV
0
PMT
1,015.05
FV
0
PMT
172.47
FV
10,117
7
Incremental Borrowing Cost –
Origination Fees
Loan Costs with Origination Fees
Points
Loan Amount
Additional Borrowing
Additional Payment
Alternative 1 Alternative 2
2%
3%
$78,400.00
$87,300.00
$8,900.00
$172.47
What is the cost of additional amount borrowed?
N
I/Y
P/Y
PV
300
PV
-8,900
23.18%
PMT
172.47
FV
0
8
Incremental Borrowing Cost –
Second Mortgage





In the first case we compared 80 and 90% LTV loans
By borrowing $90,000, cost of additional $10,000 was
20.57%
What if we borrow $80,000 (80% LTV) and shop for loan
for $10,000 with 25 year term
If we can borrow that $10,000 at a cost less than 20.57%
then we would have loan with a lower cost than 90% LTV
loan.
Suppose a lender can loan us that $10,000 at 18%

Composite cost of borrowing would be



($80,000 / $90,000) × 12% + ($10,000 / $90,000) × 18%
This is 12.66%
It is clear that break-even rate for second mortgage is 20.57%
9
Incremental Borrowing Cost –
Maturity Differences
House Value
Loan-to-Value Ratio
Loan Amount
Interest Rate
Loan Term
Payment per Year
Number of Payments
Alternative 1 Alternative 2
$100,000.00 $100,000.00
80%
90%
$80,000.00
$90,000.00
12.00%
13.00%
25
30
12
12
300
360
Monthly Payments
Additional Borrowing
Additional Payment (First 300 Months)
Additional Payment (Last 60 Months)
$842.58
$995.58
$10,000.00
$153.00
$995.58
What is the cost of additional amount borrowed?
CF0 =
-10,000.00
C01 =
153.00 F01 =
300
C02 =
995.58 F02 =
60
CPT IRR
1.572 %
Annual
18.86 %
10
Loan Refinancing

Borrower consideration




Lower interest rates in the market than on the
current loan
The borrower can secure lower monthly
payments
There is a cost to refinance
Application of basic capital budgeting
investment decision:

What is our return on an investment in a new
loan?
11
Loan Refinancing for Remaining Term of Original Loan
300
P/Y
12
PV
-80,000.00
PMT
1,011.56
FV
0
Loan balance after 5 years:
N
I/Y
300
15.00%
P/Y
12
PV
-78,976.50
PMT
1,011.56
FV
0
PMT of the new loan:
N
I/Y
300
14.00%
P/Y
12
PV
-78,976.50
PMT
950.69
FV
0
Prepayment penalty
$1,579.53
Financing costs
$2,525.00
Cost of new loan
$4,104.53
N
I/Y
P/Y
PV
PMT
FV
300
12
-4,104.53
60.87
0
17.57%
It appears that 4,104.53 committed to refinancing earns 17.57%
annual return over 25 years.
Unless you can earn more than that with similar risk you should refinance.
F01 =
PMT of the old loan:
N
I/Y
360
15.00%
Last Computation with CF:
-4,104.53
CF0 =
C01 =
60.87
1.4640 %
CPT IRR
17.57 %
Annual
Loan amount
Loan rate
Term (years)
Prepayment penalty
Financing costs
Five Years
Original Loan
Later
$80,000.00
15.00%
14.00%
30
25
2%
$2,525.00
12
PMT
1,011.56
FV
0
Old loan balance after 15 years:
N
I/Y
P/Y
180
15.00%
12
PV
-72,275.26
PMT
1,011.56
FV
0
PMT of the new loan:
N
I/Y
300
14.00%
PV
-78,976.50
PMT
950.69
FV
0
P/Y
12
New loan balance after 10 years:
N
I/Y
P/Y
PMT
FV
PV
180
14.00%
12
950.69
0
-71,386.86
No prepayment penalty and financing costs at that time for the new loan.
N
P/Y
PV
I/Y
120
12
-4,104.53
14.21%
Return on funds committed to refinancing.
PMT
60.87
FV
888.40
Last Computation with CF:
-4,104.53
CF0 =
F01 =
C01 =
60.87
F01 =
C02 =
949.27
1.1843 %
CPT IRR
14.21 %
Annual
Alternatives:
1. Keep the old loan for 10 more years
2. Refinance now and keep it for 10 years
PMT of the old loan:
N
I/Y
P/Y
PV
360
15.00%
12
-80,000.00
119
1
Loan Refinancing – Early Repayment of New Loan
13
P/Y
12
PV
-80,000.00
PMT
1,011.56
FV
0
Old loan balance after 15 years:
N
I/Y
P/Y
300
15.00%
12
PV
-78,976.50
PMT
1,011.56
FV
0
PMT of the new loan rolling financing cost:
N
I/Y
P/Y
PV
300
14.00%
12
-83,081.03
PMT
1,000.10
FV
0
PMT
1,000.10
FV
0.00
Effective cost:
N
P/Y
PV
I/Y
300
12
-78,976.50
14.81%
Return on funds committed to refinancing.
Last Computation with CF:
-78,976.50
CF0 =
F01 =
C01 =
1,000.10
1.2344 %
CPT IRR
14.81 %
Annual
PMT of the old loan:
N
I/Y
360
15.00%
300
Borrowing the Financing Costs
14
Effective Cost of Multiple
Loans

Basic Technique




Compute the payments for the loans
Combine into a cash flow stream
Compute the effective cost of the amount
borrowed, given the cash flow stream
Compare the cost to alternative financing
options
15
Effective Cost of Multiple
Loans – Continued

Example:




You need a $500,000 financing package.
$100,000 at 7.0%, 30 Years
$200,000 at 7.5%, 20 Years
$200,000 at 8.0%, 10 Years
16
Effective Cost of Multiple
Loans – Continued
Loan 1 Payment:
N
I/Y
360
7.00%
Loan 2 Payment:
N
I/Y
240
7.50%
Loan 3 Payment:
N
I/Y
120
8.00%
P/Y
12
PV
-100,000.00
PMT
665.30
FV
0
P/Y
12
PV
-200,000.00
PMT
1,611.19
FV
0
P/Y
12
PV
-200,000.00
PMT
2,426.55
FV
0
CF0 =
-500,000.00
C01 =
4,703.04
F01 =
C02 =
2,276.49
F02 =
C03 =
665.30
F03 =
CPT IRR
0.6239 %
Annual
7.49 %
120
120
120
17
Below Market Financing

A seller with a below market rate
assumable loan may increase the home
price


All else equal, a buyer is paying a higher
price for lower payments
Similar to other problems, we compute
interest rate and compare it to other
equivalent risk investments
18
Below Market Financing –
Continued
Price
Loan Balance
Loan Characteristics
Down payment
I
Term (Years)
Payments per Year
Payment
A
B
$105,000
$100,000
$70,000
$70,000
Assumable
New Loan
$35,000
$30,000
9%
11%
15
15
12
12
$709.99
$795.62



Return on investment:
CF0 =
-5,000.00
C01 =
85.63
F01 =
CPT IRR
1.6172 %
Annual
19.41 %
180
The buyer can secure
below market
financing by paying
$5,000 more for an
identical home
The below market
financing results in a
monthly payment of
$85.63 less than if
regular financing was
used
The buyer earns
19.41% on the
$5,000 investment by
reducing the monthly
payment by $85.63
19
Cash Equivalency

How much more a borrower would be most
willing to pay for a property with an
assumable loan?

This is same as PV of payment savings
discounted at the rate a new loan could be
obtained
CF0 =
C01 =
I=
CPT NPV
0.00
85.63
11%
7,534.00
F01 =
180
20
Cash Equivalency – Continued

Together with the financing premium, a buyer
could be willing to pay $107,534 for this property
to receive the benefit of below-market financing



Does this mean the house is worth more than
$100,000?
Need to separate the value of the property with and
without the effects of financing
Note that the amount of cash invested in this property
would be $100,000 if you take away the assumable
loan benefit
21
Cash Equivalency - Smaller
Loan Balance
Price
Loan Balance
Loan Characteristics
Down payment
I
Term (Years)
Payments per Year
Payment
CF0 =
C01 =
I=
CPT NPV

0.00
22.14
11%
1,947.59
A1
A2
$105,000
$50,000
$20,000
Assumable
New Loan
$30,000
9%
14%
15
15
12
12
$507.13
$266.35
F01 =
Total
$773.48
B
$100,000
$70,000
New Loan
$30,000
11%
15
12
$795.62
180
Need for additional borrowing due to relatively low balance on the
assumable loan reduces the financing premium on the property
22