Question

You bought a house a year ago for $250,000, borrowing $200,000 at 10% on a 30-year term- loan (with monthly payments Interest rates have since come down to 9%. You can refinance your mortgage at this rate, with a closing cost that will be 3% of the loan. Your opportunity cost is 8%. Ignore tax effects. 17. ow much are your monthly payments on your current loan (at 10%)? How would your monthly payments be if you could refinance your mortgage at 9% (with a 30-year term loan)? a. H b. c. You plan to stay in this house for the next 5 years d. How much would interest rates have to go down before it would make sense to refinance . Given the refinancing cost (3%ofthe loan), would you refinance this loan? this loan (assuming that you are going to stay in the house for five years)? Page 3 TVM problems-Spring2019

Answer 1

a. Monthly loan payment at 10% interest =PMT(rate,nper,pv) in excel where rate =0.10/12, nper =30*12 = 360, pv = 200,000

Monthly loan payment =PMT(0.10/12,360,200000) = 1,755.14

b. Monthly loan payment of a 9% loan =PMT(0.09/12,360,200000) = 1,609.25

c. Difference in monthly loan payment per month = 1755.14-1609.25 = 145.90

Savings = Difference in monthly payments for 5 years (60 months) which would be savings = 145.90*60 = 8,753.87

Refinancing cost = 3% *200,000 = 6,000

Opportunity cost = 8% *200,000 = 16,000

Net refinancing cost = 16,000 - 6,000 = 10,000

Since the savings of 8,753.87 is lower than the net refinancing cost (10,000), you should not refinance the loan

d. You should refinance your loan when the net savings goes above 10,000. So, you should refinance if the interest rates reduce by another 50 basis points, that is another 0.5% to 8.5%. If the new interest rate is 8.5%, it makes sense to refinance the house