Question

NEEDS TO BE DONE IN EXCEL WITH CALCULATIONS.

An investor has $60,000 to invest in a 280,000 property. He can obtain either a $220,000 loan at 9.5 percent for 20 years or a $180,000 loan at 9 percent for 20 years and second mortgage for $40,000 at 13 percent for 20 years. All loans require monthly payments and are fully amortizing

a. Which alternative should the borrower choose, assuming he will own the property for the full loan term?

b. Would your answer change if the borrower plans to own the property only five years?

c. Would your answers to (a) and (b) change if the second mortgage had a 10 year term?

Answer 1

Sol. a.

Here, we need to calculate the monthly payments to compare both the options.

To calculate the same, we will use the Present Value of Ordinary Annuity formula as we already have the loan amount (present value) and payments need to be made at equal intervals (monthly).

Here, C will be the monthly payment.

i will be the interest rate of loan.

n will be the no. of installments.

Using the above formula in excel, we get the below results:

So, we shall choose the option 1 as the EMI is less.

Sol. b.

We shall choose option 1 only as the duration of holding the property would not affect the EMIs.

Sol. c.

(a) If we change mortgage term to 10 years, the EMI for Option 2 (B) would be 597

Total EMI for Option 2 = 1620 + 597 = 2217 for the first 10 years and 1620 for the next 10 years.

In this case, we need to calculate the Present Value of all the EMIs of both the options to decide which option is better.

Also, we would need to assume a risk free rate to calculate the same.

Calculating the Present Value of all EMIs in excel sheet we get:

If Risk Free Rate < 10% then PV 1 < PV 2

If Risk Free Rate = 10% then PV 1 = PV 2

If Risk Free Rate > 10% then PV 1 > PV 2

So depending upon the risk free rate, we shall choose which is better alternative.

(b) If property is hold for any tenure less than 10 years then we shall choose option 1 only as the EMIs for the first 10 years are less.