Question

A real estate investor wants to buy a property for $300,000 using an 80% LTV first-lien mortgage loan. A lender offers a 30-year fully amortizing CPM loan at 6% with monthly repayments. The loan requires the borrower to pay an origination fee of $5,000 upfront.

1. How much would the lender actually disburse (net loan proceeds)?

2. What is the effective interest rate on the loan if the mortgage is paid off as originally scheduled?

3. If the investor prepays the loan at the end of year 5, what will be the effective interest rate? What explains the rate difference between questions 2 and 3?

4. Assuming the lender charges a 2% prepayment penalty on the outstanding loan balance, what will be the effective interest rate if the investor prepays the loan at the end of year 10?

Answer 1

1. LTV of loan to value of property. Since its 80%, lender will make loan only for 80%of $300,000.

Also there is upfront fee payment of $5000.

Thus, actual loan proceed disbursement would be = 80%*$300,000 - $5000 = $235,000

2. Since the loan amount has to be made in monthly installments there is a monthly compounding effect that takes into place. Thus 6% loan with monthly payments actual rate for the year comes out to be

r=(1+i/n)^n-1

=> r = (1+6%/12)^12 - 1

=> r = 6.167%

But the effective rate involves rate on actual disbursement made which is only $235000 rather than @240000 but monthly payments would be made on $240000. Thus effective rate would be even higher.

Monthly EMI for 30 year loan for $240000 comes out at $1439

Since $1439 is paid for $235000 for 30years. Effective rate comes out at 6.374%

3. If the loan gets closed in year 5, first we need to calculate the principal ammount that would be remaining at the end of 60th month with proper repayments.

This comes out to be @223325 the payment for which needs to be made along with the EMI for the loan closure.

Again since this payment is made against @235000, now the effective rate comes out to be 6.7%

The difference in rates is because of the upfront payment of origination fee of $5000 while payment of EMI is on full loan.

4. If there is pre-payment penalty on outstanding.

At the end of 10th year, outstanding would be $200833.

2% penalty would be charged on this = $4017

Thus, at end of 10th year total payment needs to be made is $204850 plus the EMI.

The effective rate thus comes out to be 6.621%.