Question

You have purchased a freehold house (i.e., no condo fee) for $300,000 with 20% down payment and the rest borrowed from your local bank as a 30-year mortgage loan at 6% (APR with monthly compounding). The mortgage can be paid off any time without penalty, i.e., it allows prepayment.

     (a) (1 point) What is your loan to value (LTV) ratio?

     (b) (2 points) What is your monthly payment?

     (c) (1 point) If your gross annual income is $72,000, and the property tax on the house is $6,000 per year, what is your payment to income (PTI) ratio?

     (d) (1 point) Why does your prepayment option affect the profitability of your bank when the interest rate falls?

     (e) (1 point) Why is your prepayment option equivalent to your right for refinancing?

     (f) (3 points) Assume that the mortgage rate falls to 5.4% (APR with monthly compounding) in three years. Will you refinance your loan despite that your bank charges you $2,000 refinancing fee? Why or why not? Be numerically specific.

Answer 1

a) 20% is the downpayment done and so it means we have taken 80% loan (i.e. 80% of the total value of house) Thus Loan to Value ratio is 80%

b) Now 20% of $300,000 = $60,000. So $240,000 is the loan taken from bank. To calculate the monthly payment, enter the following in the financial calculator.

PV = 240000; n=30*!2; 1/y = 6%/12; FV =0; Calculate PMT = $1,438.92

c) Net income is $72,000 - $6,000 = $66,000 i.e. 66000/12 = $5,500 monthly

Payment to Income ratio is the instalment payment made to bank divided by the Net Income = 1438.92 / 5500 = 26.16%

d) If the interest rate falls, we can prepay and then again take the loan (may be from same bank) at lower interest rate. So the profitability of the bank will reduce.