Question

A. An investor obtained a fully amortizing mortgage five years ago for $95,000 at 11% for 30 years. Mortgage rates have dropped so that a fully amortizing 25-year loan can be obtained at 10%. There is no prepayment penalty on the mortgage balance of the original loan, but three points will be charged on the new loan and other closing costs will be $2,000. All payments are monthly. (annualize rates) What rate of return must the investor be able to obtain on alternative investments to persuade him to invest elsewhere rather than refinancing. (basically, what rate of return would he "earn" by refinancing) Assume that the investor borrows only an amount equal to the outstanding balance on the loan?

B. Continuing from question 10, what rate of return would he "earn" by refinancing if he planned to own the property for only five more years?

Answer 1

Where, Principal P0 = $95,000; monthly interest rate r=11/100/12; the number of monthly payments is N=30*12 =360

Fixed Monthly payment C = r*P0/{1-(1+r)^(-N)}

C = (0.11/12)*95000/{1-(1+0.11/12)^(-360)} by solving this number we get C = $904.71

At present outstanding amount will be:-

P60 = 95000(1+0.11/12)^60 - 904.71[(1+0.11/12)^60 - 1]/(0.11/12)

= $92,306.41

The investor borrows only an amount equal to the outstanding balance on the loan is $92,306.41

Fixed repayment for next 25 years as follows:-

Where, Principal P60 = $92,306.41; monthly interest rate r=10/100/12; the number of monthly payments is N=25*12 =300

Fixed Monthly payment C = r*P0/{1-(1+r)^(-N)}

C = (0.10/12)*92306.41/{1-(1+0.10/12)^(-300)} by solving this number we get C = $838.79

Charges for refinancing = 3% on $92,306.41 plus @2,000 = $4,769.19

Savings from refinancing = ($904.71 - $838.79)*300 = $19,776

Net return from refinancing = $19,776 - $4,769.19 = $15,006.81

Rate of return = $15,006.81/($92,306.41*25) = 0.65% per annum