Question

1. A lender wants an EY of 4.00% and expects an average loan payoff in 7 years. However, a particular borrower wants to borrow $400,000 for 30 years at 3.20%, compounded monthly. First, without charging a prepayment penalty, how many discount points must the lender charge to have an EY of 4%. Assume no other fees to close the loan other than discount points. Second, without charging discount points, how much of a prepayment penalty (in terms of dollars) will the lender need to charge to have an EY of 4%.

Answer 1

The EMI that has be calculated as per formula

EMI= P*R*(1+R)^N/(1+R)^N-1

Principle= $400000, N= No of months for Compunding= 7*12= 84, R= monthly compounding= 4/100

Initial EMI = 400000* 0.04 * (1+ 0.04)^ 84/ ( 1+ 0.04)^ 84 -1

= $16616.21

The above amount will be required by the Lender as per his requirement.

Now as per Borrower,

Principle= $400000, N= No of months for Compunding= 30*12= 360, R= monthly compounding= 3.2/100

EMI= 400000 * 0.032 * (1+ 0.032)^360/(1+ 0.032)^360-1

= $12800.15

Now from the lender side,

Principle= $400000, N= No of months for Compunding= 30*12= 360, R= monthly compounding= 4/100

EMI= 400000 * 0.04* (1+ 0.04)^360/(1+ 0.04)^360-1

= $16000.

As per Borrower wish, if the payment period is 30 years , the total difference in amount to be paid

$ ( 16000 *360- 12800.15 *360) = $ 1151950.25 .

Therefore similar value discount points to be provided to the borrower.

For prepayment penalty to be charged,

the EMI of the Borrower amount to be multiplied by 360 months, while the initial EMI expected by lender minimum of 84 months is to be multiplied by 84

Prepayment penalty amount

= $ ( EMI borrower wish to give*360 - Initial EMI * 84)

= $ (12800.15 * 360 - 16616.21 *84)

= $ 3212292.36 - This amount to be charged for prepayment penalty.