Question

Five years a borrower incurred a mortgage for $80,000 at 10 percent for 30 years, monthly payments. Currently the market rate is 8 percent on 25-year mortgages. The existing mortgage has a prepayment penalty of 5 percent of the outstanding balance at prepayment for the first 10 years of the mortgage and the lender will charge 4 percent financing cost on a new loan. The borrower's opportunity investment rate is 8 percent. The borrower is considering refinancing the payoff of the loan (remaining balance + prepayment penalty).

Note: the borrower’s opportunity investment rate is the same as the new mortgage’s interest rate (8%). Use this rate when you calculate the present value of all savings

a. If the borrower plans to hold either mortgage for the next 25 years, should they refinance?

b. Assume the conditions in part (a) and the closing cost of the new loan is added into the loan amount. Should they refinance?

c. If the borrower plans to hold either mortgage for 8 more years only, should they refinance?

d. If the new loan term is 30 years and the borrower plans to hold it until maturity, should they refinance?

e. If the new loan term is 15 years and the borrower plans to hold it until maturity, should they refinance?

Answer 1

	EXISTING MORTGAGE
Pv	Mortgage amount	$80,000
Rate	Monthly interest =(10/12)%	0.83%
Nper	Number of months of mortgage	360	(30*12)
PMT	Monthly Payment	$702	(using PMT function of excel with Rate=0.83%, Nper=360,Pv=-80000)
A	Present value of 5 years(60 months) payment	$33,043	(using PV function of excel with Rate=0.83%, Nper=60,Pmt=-702)
B=Pv-A	Present Value of Loan Balance at end of 5 years	$46,957
C	Loan balance at end of 5 years(60 months)	$77,259	(using FV function of excel with Rate=0.83%, Nper=60,Pv=-46957)
D=0.05*C	Prepayment Penalty=5% of Loan balance=	$3,863
	Payoff of theloan	$81,122
	NEW MORTGAGE
Pv	Mortgage Amount	$81,122
Rate	Monthly interest =(8/12)%	0.6667%
Nper	Number of months of mortgage	300	(25*12)
PMT	Monthly Payment	$626	(using PMT function of excel with Rate=0.6667%, Nper=300,Pv=-81122)
	If Borrower plans tohold for next 25 yeares:
(a)	Financing Cost=4%*81122=	($3,245)
	Monthly Savings from NEW MORTGAGE	$76	(702-626)
	Present Value of savings of 25 years(300months)	$9,839	(using PV function of excel with Rate=0.6667%, Nper=300,Pmt=-76)
	Net Savings at present value=9839-3245)	$6,594
	The borrower SHOULD refinance
(b)	Closing Cost is   added into the Loan Amount
Pv	Mortgage Amount	$84,367	(81122+3245)
Rate	Monthly interest =(8/12)%	0.6667%
Nper	Number of months of mortgage	300	(25*12)
PMT	Monthly Payment	$651	(using PMT function of excel with Rate=0.6667%, Nper=300,Pv=-84367)
	Monthly savings from NEW mortgage	$51	(702-651)
	Yes, The borrower should Refinance
	There is a monthly saving with no cost
.(c)	If The borrower plans tohild 8 years only
	EXISTING MORTGAGE:
	Present value of 8 years(96 months)payment	$46,267	(Using excel PV function with Rate=0.83%, Nper=96, Pmt=-702)
	Present Value of Loan Balance	$30,993	(77259-46267)
	Loan Balance at the end of 8 years	$68,747.56	(Using excel FV function with Rate=0.83%, Nper=96, Pv=-30993)
	NEW MORTGAGE
	Present value of 8 years(96 months)payment	$44,290	(Using excel PV function with Rate=0.6667%, Nper=96, Pmt=-626)
	Present Value of Loan Balance	$36,832	(81122-44290)
	Loan Balance at the end of 8 years	$69,703.46	(Using excel FV function with Rate=0.6667%, Nper=96, Pv=-36832)
	Difference in terminal payment	($956)
	Present Value of terminal payment	($505)	(Using excel PV function with Rate=0.6667%, Nper=96, Fv=-956)
	Initial Payment for new loan	($3,245)
	Present Value of total Cost	($3,750)
	Present value of savings	$5,371.93	(using PV function of excel with Rate=0.6667%, Nper=96,Pmt=-76)
	There is net saving of	$1,621.92
	They SHOULD refinance