Question

1. You bought your house 5 years ago, and your original home value when you bought it was $450,000, you paid 20% down and you financed closing costs equal to 4% of the mortgage amount. The mortgage was a 30-year fixed rate mortgage with a 6.5% annual interest rate. Rates on 30-year mortgages are now at 5% if you pay 2 points upfront. Your refinancing costs will be 2% of the new mortgage amount (excluding points). You won't finance the points and closing costs this time. A new down payment is not required.

What is your refinancing amount?

What is the monthly mortgage payment if you refinance? The monthly saving compared to the original mortgage?

Compared to the original mortgage on equal footing, is this refinancing proposal a good deal?

2. (a) What are the current 30-year and 15-year fixed mortgage rates?

(b) If you plan to buy a house of $200,000 with a 20% down payment, what is the monthly payment if you take out (i) a 15-year fixed rate mortgage? (ii) a 30-year fixed rate mortgage?

Answer 1

Property Value	$450,000.00
Down Payment	$90,000.00
Original Loan Amount	$360,000.00
Financing Cost (paid upfront)	$14,400.00
Interest	6.50%	0.54167% monthly
Old Monthly payment amount	$2,275.44	=$360000*0.54167%
		/((1-(1+0.54167)^-360)0
PV of Current Loan at the end of 5 years	$336,998.80	= $2275.44*((1-(1+0.54167)^-300)/0.54167%)
Points Value	$6,739.98	= 2% * 336998.80
Financing Cost	$6,739.98	= 2% * 336998.80
Total Financing Cost	$13,479.95	Points Value + Financing Cost
Total Refinancing Amount	$350,478.75	PV of Current Loan + Total Financing Cost
Interest	5%	0.41667% monthly
New Monthly payment amount	$1,881.45	=350478.75*0.41667%/((1-(1+0.41667%)^-360))
Monthly Savings	$393.99	Old Monthly Payment Amount – New Monthly Payment Amount

We have a monthly saving of $393.99, however new loan payments are to be made for 360 months as compared to old loan payment for 300 months.

So we have an effective saving of $393.99 for 300 months & additional outgo of $1881.45 from 301 to 360 months. If we calculate the IRR of this payment stream, it is negative. It can be concluded that refinancing is a good deal.

Same can also be concluded from the fact the is we calculate the payment amount of new loan for 300 months instead of 360 months (to compare on equal footing) we get $2048.86 which is less than the current monthly payment amount.

Similarly, if we calculate the monthly payment amount of current outstanding loan for 360 months, we get $2130.06, which is more than the new monthly payment amount of $1881.45.

Hence, it can be concluded that refinancing is a good proposal.

Answer 2)

Current 30 year mortgage rates were found to be in range of 4.625% to 4.75%

Property Value = 200000

Down Payment = 20% * 200000 = $40000

Finance Amount = 160000

Calculating the monthly payment on minimum rate of 4.625%

Monthly payment = 160000 * (4.625%/12)/((1-(1+(4.625%/12))^-360)/(4.625%/12)) = $822.62

Current 15 year mortgage rates were found to be in range of 4.125% to 4.25%

Calculating the monthly payment on minimum rate of 4.125%

Monthly payment = 160000 * (4.125%/12)/((1-(1+(4.125%/12))^-180)/(4.125%/12)) = $1193.55