Question

Marc wishes to buy a $500,000 home using Loan 1 (mortgage rate: 10.60%, maturity: 30 years, origination fee: 4 points, prepayment penalty: 2%) with loan to value of 80% or using Loan 2 (mortgage rate: 9.60%, maturity: 30 years, origination fee: 3 points, prepayment penalty: 2%) with loan to value of 70%.The borrower plans to be in the home for 5 years. Alternative investments of similar risk can provide 19.00% IRR and borrowing from alternative sources (than mortgage) would cost effectively 23.00%. If the borrower has cash for down payment (and origination fee (discount points)) of the larger loan only, which mortgage loan is better for the borrower and why?

Answer 1

LOAN TO VALUE 80%(LOAN1)

Cost of Home

$500,000

Loan amount=80%*500000

$400,000

Down Payment

$100,000

Origination fee=4%*400000

$16,000

Alternative Source Loan

$16,000

X

Total Initial Loan=400000+16000

$416,000

a

Monthly interest payment for alternative loan

$306.67

(23%*16000)/12

Pv

Mortgage Loan

$400,000

Nper

Number of months =30*12

360

Rate

Monthly Interest rate for Mortgage Loan

0.8833%

(10.6/12)

PMT

Monthly Payment

$3,688.90

(Using PMT function of excel with Rate =0.8833%, Nper=360,Pv=-400000)

b=a+PMT

Total Monthly Payment

$3,995.56

Calculation of Terminal Payment

FV

Future Value of Mortgage Payment for 60 months

$290,232.52

(Using FV function of excel with Rate=0.8833%, Nper=60, Pmt=-3688.90)

FV1

Future Value of Mortgage Loan

$677,993.30

(Using FV function of excel with Rate=0.8833%, Nper=60, Pv=-400000)

c=FV1-Fv

Terminal Payment for Mortgage Principal Balance

$387,761

d

Prepayment Penalty=2%*387761=

$7,755

e

Payment of Principal of alternative Source Loan

$16,000

T=c+d+e

Total Terminal Payment at end of 5 years

$411,516

(Using RATE function of excel with Nper =60,Pmt=3995.56,Pv=-416000,Fv=411516)

RATE

Effective Interest Rate Paid

0.95%

Annualized Interest Rate

11.36%

LOAN TO VALUE 70%(LOAN2)

Cost of Home

$500,000

Loan amount=70%*500000

$350,000

Down Payment Required

$150,000

Down Payment cash available

$100,000

Alternative Source Loan

$50,000

(150000-100000)

Origination fee=3%*350000

$10,500

Total Alternative Source Loan=10500+50000

$60,500

X

Total Initial Loan=350000+60500

$410,500

a

Monthly interest payment for alternative loan

$1,159.58

(23%*60500)/12

Pv

Mortgage Loan

$350,000

Nper

Number of months =30*12

360

Rate

Monthly Interest rate for Mortgage Loan

0.8000%

(9.6/12)

PMT

Monthly Payment

$2,968.56

(Using PMT function of excel with Rate =0.8%, Nper=360,Pv=-350000)

b=a+PMT

Total Monthly Payment

$4,128.14

Calculation of Terminal Payment

FV

Future Value of Mortgage Payment for 60 months

$227,462.54

(Using FV function of excel with Rate=0.8%, Nper=60, Pmt=-2968.56)

FV1

Future Value of Mortgage Loan

$564,546.83

(Using FV function of excel with Rate=0.8%, Nper=60, Pv=-350000)

c=FV1-Fv

Terminal Payment for Mortgage Principal Balance

$337,084

d

Prepayment Penalty=2%*337084=

$6,742

e

Payment of Principal of alternative Source Loan

$60,500

T=c+d+e

Total Terminal Payment at end of 5 years

$404,326

(Using RATE function of excel with Nper =60,Pmt=404326,Pv=-410500,Fv=404326)

RATE

Effective Interest Rate Paid

0.99%

Annualized Interest Rate

11.85%

LOAN 1 is better

It has lower annualized cost