1

Chapter 6

Residential Financial Analysis

2

Overview

Incremental Borrowing Cost Loan Refinancing Effective Cost of Multiple Loans Below Market Financing Cash Equivalency

3

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?

4

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…

5

Incremental Borrowing Cost – Continued

Alternative 1 Alternative 2House Value $100,000.00 $100,000.00Loan-to-Value Ratio 80% 90%Loan Amount $80,000.00 $90,000.00Interest Rate 12.00% 13.00%Loan Term 25 25Payment per Year 12 12Number of Payments 300 300

Monthly Payments $842.58 $1,015.05Additional BorrowingAdditional PaymentWhat is the cost of additional amount borrowed?

N I/Y P/Y PV PMT FV300 20.57% 12 -10,000 172.47 0

$10,000.00$172.47

6

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?

7

Incremental Borrowing Cost – Early RepaymentLoan Costs with Prepayment in 5 YearsLoan Balance Alternative 1:

N I/Y P/Y PV PMT FV240 12.00% 12 -76,523 842.58 0

Loan Balance Alternative 2:N I/Y P/Y PV PMT FV

240 13.00% 12 -86,640 1,015.05 0

What is the cost of additional amount borrowed?N I/Y P/Y PV PMT FV60 20.83% 12 -10,000 172.47 10,117

8

Incremental Borrowing Cost – Origination FeesLoan Costs with Origination Fees

Alternative 1 Alternative 2Points 2% 3%Loan Amount $78,400.00 $87,300.00

Additional BorrowingAdditional Payment

What is the cost of additional amount borrowed?N I/Y P/Y PV PMT FV

300 23.18% PV -8,900 172.47 0

$8,900.00$172.47

9

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%

10

Incremental Borrowing Cost – Maturity Differences

Alternative 1 Alternative 2House Value $100,000.00 $100,000.00Loan-to-Value Ratio 80% 90%Loan Amount $80,000.00 $90,000.00Interest Rate 12.00% 13.00%Loan Term 25 30Payment per Year 12 12Number of Payments 300 360

Monthly Payments $842.58 $995.58Additional BorrowingAdditional Payment (First 300 Months) $153.00Additional Payment (Last 60 Months) $995.58

What is the cost of additional amount borrowed?CF0 = -10,000.00C01 = 153.00 F01 = 300C02 = 995.58 F02 = 60

CPT IRR 1.572 %Annual 18.86 %

$10,000.00

11

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?

12

Loan Refinancing for Remaining Term of Original Loan

Original LoanFive Years

LaterLoan amount $80,000.00 -Loan rate 15.00% 14.00%Term (years) 30 25 Prepayment penalty 2% -Financing costs - $2,525.00

PMT of the old loan:N I/Y P/Y PV PMT FV

360 15.00% 12 -80,000.00 1,011.56 0

Loan balance after 5 years:N I/Y P/Y PV PMT FV

300 15.00% 12 -78,976.50 1,011.56 0

PMT of the new loan:N I/Y P/Y PV PMT FV

300 14.00% 12 -78,976.50 950.69 0

Prepayment penalty $1,579.53Financing costs $2,525.00Cost of new loan $4,104.53

N I/Y P/Y PV PMT FV300 17.57% 12 -4,104.53 60.87 0

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.

Las

t Com

puta

tion

wit

h C

F:

CF 0

=-4

,104

.53

C01

=60

.87

F01

=30

0C

PT

IR

R1.

4640

%A

nnua

l17

.57

%

13

Loan Refinancing – Early Repayment of New Loan

Alternatives:1. Keep the old loan for 10 more years2. Refinance now and keep it for 10 yearsPMT of the old loan:

N I/Y P/Y PV PMT FV360 15.00% 12 -80,000.00 1,011.56 0

Old loan balance after 15 years:N I/Y P/Y PV PMT FV

180 15.00% 12 -72,275.26 1,011.56 0

PMT of the new loan:N I/Y P/Y PV PMT FV

300 14.00% 12 -78,976.50 950.69 0

New loan balance after 10 years:N I/Y P/Y PV PMT FV

180 14.00% 12 -71,386.86 950.69 0No prepayment penalty and financing costs at that time for the new loan.

N I/Y P/Y PV PMT FV120 14.21% 12 -4,104.53 60.87 888.40

Return on funds committed to refinancing.

Las

t Com

puta

tion

wit

h C

F:C

F0

=-4

,104

.53

C01

=60

.87

F01

=11

9C

02 =

949.

27F

01 =

1C

PT

IR

R1.

1843

%A

nnua

l14

.21

%

14

Borrowing the Financing Costs

PMT of the old loan:N I/Y P/Y PV PMT FV

360 15.00% 12 -80,000.00 1,011.56 0

Old loan balance after 15 years:N I/Y P/Y PV PMT FV

300 15.00% 12 -78,976.50 1,011.56 0

PMT of the new loan rolling financing cost:N I/Y P/Y PV PMT FV

300 14.00% 12 -83,081.03 1,000.10 0

Effective cost:N I/Y P/Y PV PMT FV

300 14.81% 12 -78,976.50 1,000.10 0.00Return on funds committed to refinancing.

Las

t Com

puta

tion

wit

h C

F:C

F 0 =

-78,

976.

50

C01

=1,

000.

10F0

1 =

300

CP

T I

RR

1.23

44%

Ann

ual

14.8

1%

15

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

16

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

17

Effective Cost of Multiple Loans – ContinuedLoan 1 Payment:

N I/Y P/Y PV PMT FV360 7.00% 12 -100,000.00 665.30 0

Loan 2 Payment:N I/Y P/Y PV PMT FV

240 7.50% 12 -200,000.00 1,611.19 0Loan 3 Payment:

N I/Y P/Y PV PMT FV120 8.00% 12 -200,000.00 2,426.55 0

CF0 = -500,000.00C01 = 4,703.04 F01 = 120C02 = 2,276.49 F02 = 120C03 = 665.30 F03 = 120

CPT IRR 0.6239 %Annual 7.49 %

18

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

19

Below Market Financing – Continued

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

A BPrice $105,000 $100,000Loan Balance $70,000 $70,000Loan Characteristics Assumable New LoanDown payment $35,000 $30,000I 9% 11%Term (Years) 15 15Payments per Year 12 12Payment $709.99 $795.62

Return on investment:CF0 = -5,000.00C01 = 85.63 F01 = 180

CPT IRR 1.6172 %Annual 19.41 %

20

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 = 0.00C01 = 85.63 F01 = 180

I = 11%CPT NPV 7,534.00

21

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

22

Cash Equivalency - Smaller Loan Balance

Need for additional borrowing due to relatively low balance on the assumable loan reduces the financing premium on the property

A1 A2 Total BPrice $105,000 $100,000Loan Balance $50,000 $20,000 $70,000Loan Characteristics Assumable New Loan New LoanDown payment $30,000 $30,000I 9% 14% 11%Term (Years) 15 15 15Payments per Year 12 12 12Payment $507.13 $266.35 $773.48 $795.62

CF0 = 0.00C01 = 22.14 F01 = 180

I = 11%CPT NPV 1,947.59