Question

You have worked hard over the last three years to save up enough money for a down payment on your first home. After meeting with your lender, you are faced with two loan options. Both loans are 30 year, fixed rate mortgages with payments of $1,800 per month. Origination fees will be 2% of the loan amount for either loan. Loan A has a contract interest rate of 3.0% with no points, while Loan B has a rate of 2.75% with 1.25 points.

1) What is your EBC if you select Loan A? Enter your answer as a whole number with 2 decimal points (no percent sign).

2) What is your EBC if you select Loan B? Enter your answer as a whole number with 2 decimal points (no percent sign).

3) If you intend to stay in the house for 30 years, which loan should you choose?

a. Loan A b. Loan B c. I would be indifferent between the two choices.

4) You decide you would like to limit your out of pocket closing costs, so you select Loan A, with no discount points. Your best friend is going to move in with you and pay $800 per month in rent. If you add the extra money to your monthly mortgage payment, how many years will it take you to pay off your mortgage?

a. 15.8 years b. 17.64 years c. 30 years d. 211.67 years

Five years later, you are offered your dream job in Turks and Caicos. You need to sell this house in order to purchase a new one where you are moving. Your roommate would like to remain in the home until they finish their PhD in 6 years. They are willing to sign a six year lease with the following terms: Rent will be $2,000/month for the first three years, and increase to $2,200/month for the remaining three years. The average investor’s holding period on residential rental properties is six years. You have estimated sale proceeds will be $530,688.37 at the end of the investor’s holding period. The appropriate discount rate is 4.2%.

5) What is the minimum price you should list the property for (i.e. the maximum an investor would be willing to pay)? Round up to the nearest whole dollar. *Remember, the value of an investment property comes from its cash flows. That is, you need to consider both the estimated proceeds at the end of the holding period AND the stream of cash flows the investor will receive from rent while they own the property. I recommend converting the monthly rents into annual cash flows for simplicity in solving this problem.

6) What will the investor’s “going-in” IRR be if they pay exactly list price? Round to two decimal places.

7) Rather than add your friend’s rent to your monthly mortgage payments, you have been saving towards your moving expenses. If you close on the home after making your last payment in year 5, how much will your loan payoff amount be (in other words, what is the outstanding balance on your loan after 5 years)? Round to two decimal places.

8) Assuming you sell the home for exactly list price, pay 6% in real estate broker commissions and $10,500 in seller closing costs, what will be your net proceeds from the sale? Round to the nearest whole dollar. *don’t forget to include your loan payoff amount from #7!

You are starting to have second thoughts about moving. After going back and forth for several weeks you decide that you will make a decision based on whether or not you will refinance the house. If you refinance you will stay, if you don’t you will move. You can refinance the home with a new interest rate of 2.75% for a 30 year term. You will refinance on the same day you would have closed on the home (so you can use the outstanding loan balance you calculated in #7 here). The cost of refinancing is 5% of the loan amount. Assume you anticipate selling the home (or refinancing again) in 7 years.

9) What is the net benefit of refinancing? Round to two decimal places. *Hint you are solving for net benefit of refinancing, not solving for NPV (so you do not need a discount rate to answer this question).

10) Will you be moving to Turks and Caicos?

a. Yes b. No

Answer 1

1) For Loan A

Monthly interest rate = 3%/12 = 0.0025

Present value of Loan amount = 1800/0.0025*(1-1/1.0025^360) = $426940.89

However, 2% of this was deducted as origination cost

So, Net amount received by borrower = 426940.89 *0.98 = $418402.07

So, effective monthly rate (r) on the loan is given by

1800/r*(1-1/(1+r)^360) = 418402.07

Solviing , r= 0.0026322

So, Effective borrowing cost EBC = 1.0026322^12-1 = 3.20% effective p.a.

2)

For Loan B

Monthly interest rate = 2.75%/12 = 0.00229167

Present value of Loan amount = 1800/0.00229167*(1-1/1.00229167^360) = $440915.83

However, 2% of this was deducted as origination cost and 1.25% as discount points

So, Net amount received by borrower = 440915.83 *0.9675 = $426586.07

So, effective monthly rate (r) on the loan is given by

1800/r*(1-1/(1+r)^360) = 426586.07

Solviing , r= 0.002505417

So, Effective borrowing cost EBC = 1.002505417^12-1 = 3.05% effective p.a.

3) If it is intended to stay for 30 years, one should Choose Loan B as its EBC is lower and hence a higher loan amount is available at the same monthly mortgage payment.

4) New Monthly mortgage payment =$1800+$800 = $2600

So, No of months required to pay off the mortgage (n) is given by

2600/0.0025*(1-1/1.0025^n)= 426940.89

=> 1-1/1.0025^n =0.41052

=> 1.0025^n = 1.69641

Taking natural log of both sides

n = ln(1.69641)/ln(1.0025) =211.67

So, no of months required = 211.67

No of years required = 211.67/12 = 17.64 years (option b is correct)