Question

A few years back, Dave and Jana bought a new home. They borrowed $230,415 at an annual fixed rate of 5.49% (15-year term) with monthly payments of $1,881.46. They just made their 50th payment, and the current balance on the loan is $208,555.87. Interest rates are at an all-time low, and Dave and Jana are thinking of refinancing to a new 15-year fixed loan. Their bank has made the following offer: 15-year term, 3.0%, plus out-of-pocket costs of $2,937. The out-of-pocket costs must be paid in full at the time of refinancing. Build a spreadsheet model to evaluate this offer. The Excel function: =PMT(rate, nper, pv, fv, type) calculates the payment for a loan based on constant payments and a constant interest rate. The arguments of this function are: rate = the interest rate for the loan nper = the total number of payments pv = present value (the amount borrowed) fv = future value [the desired cash balance after the last payment (usually 0)] type = payment type (0 = end of period, 1 = beginning of the period) For example, for Dave and Jana’s original loan, there will be 180 payments (12*15 = 180), so we would use =PMT(0.0549/12, 180, 230415,0,0) = $1,881.46. Note that because payments are made monthly, the annual interest rate must be expressed as a monthly rate. Also, for payment calculations, we assume that the payment is made at the end of the month. The savings from refinancing occur over time, and therefore need to be discounted back to current dollars. The formula for converting K dollars saved t months from now to current dollars is: where r is the monthly inflation rate. Assume that r = 0.002 and that Dave and Jana make their payment at the end of each month. Use your model to calculate the savings in current dollars associated with the refinanced loan versus staying with the original loan. If required, round your answer to the nearest whole dollar amount. If your answer is negative use “minus sign”.

=$?

Answer 1

New monthly payment they need to make = PMT(0.03/12, 180, 208555.87,0,0) = $1440.25. Extra expense at the time of financing i.e. out-of-pocket cost of $2937.

So at the start of 25th month, they would have paid an extra amount of $2937.

At end of 25th month, total saving = $1881.46-$1440.25 = $441.21

At end of 26th month, total saving = $1881.46-$1440.25 = $441.21

The saving would be same until the end of 180th month.

So, At end of 180th month, total saving = $1881.46-$1440.25 = $441.21

but from the end of 181st month to end of 186th, they will be spending extra $1440.25

using formula to find present value( K/(1+r)^(t-1)) where r = 0.002

So total saving = -2937 + 441.21/ 1.002^1 + 441.21/1.002^2+..............+441.21/1.002^155 - 1440.25/1.002^156-1440.25/1.002^157-..........-144.25/1.002^180 = $30073.90

This mean, by refinancing the loan, Dave and Jana are able to save a total of $30073.90 in the present value.