Question

When you bought your current house, you obtained a loan in the amount of $185,000, with a 30-year term and an interest rate of 6.35%. That was 6 years ago, and you notice that mortgage rates have fallen significantly. Your banker has given you two refinancing alternatives.

Alternative 1 is a 25 year loan with a fixed rate of 4.75%. This option requires a 2-point rate buy-down fee and closing costs of $1,700.

Alternative 2 is a 25 year loan with a fixed rate of 5.375%. This option requires no buy-down fee and has closing costs of $1,925.
What is your current loan balance?

Evaluate each of the refinancing alternatives being offered by your banker, and show both results. Does it make sense to refinance, and if so which loan makes the most sense?

Answer 1

1.Current loan balance can be calculated by using the formula,

Remaining loan balance=FV of the original principal at end 6 yrs.-FV of annuity pmts .upto end 6th year

ie.FV(rem. Bal.)= (P*(1+r)^n)-(pmt.*((1+r)^n-1)/r)

where,

FV= Future value of the remaining balance

P= Original loan mt.= $ 185000

r= rate /pmt. ,ie. 6.35% p.a. ie. 0.5292% or 0.005292

n= no.of payments, ie. 6 yrs*12 mths= 72 mths

pmt.= monthly pmt. On the on-going mortgage, ie.185000/((1-1.005292^-360)/0.005292)= $ 1151.18

Now, plugging all the values, in the formula

ie.FV(rem. Bal.)=(185000*(1+0.005292)^72)-(1151.18*((1+0.005292)^72-1)/0.005292)

169960

Alternative 1

Now the principal balance (from above) = $ 169960

so, the mthly pmt. At he new rate of 4.75% p.a., ie.0.3958% for the balance 25 yrs. *12=300 months =

169960/((1-1.003958^-300)/0.003958)=

968.93

So, the savings in monthly pmts.=1151.18-968.93=

182.25

PV of this savings for the bal.yrs.

182.25*(1-1.003958^-300)/0.003958=

31968.39

Less : Buy-down costs (169960*2%)= 3399

Less:closing costs   1700

31968.39-3399-1700=

26869

NPV of net savings in costs under this re-financing

Alternative -2

Now the principal balance (from above) = $ 169960

so, the mthly pmt. At the new rate of 5.375% p.a., ie.0.4479% for the balance 25 yrs. *12=300 months =

169960/((1-1.004479^-300)/0.004479)=

1031.03

So, the savings in monthly pmts.=1151.18-1031.03=

120.15

PV of this savings for the bal.yrs.

120.15*(1-1.004479^-300)/0.004479=

19806.04

Less:closing costs   1925

19806.04-1925

17881

NPV of net savings in costs under this re-financing

From the analysis of both alternatives , it can be concluded that

it does makes sense to refinance

as it saves in costs & the NPV of savings less costs (buy-down/closing costs) is POSITIVE ---in both alternatives.

As the net savings is more in Alternative 1,

it makes the MOST sense.