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Mortgage Practice Problems

Question 1

You are in the process of purchasing a new home. You intend to live there for 5-10 years. You have an accepted offer of \$364,000, which is just under the asking price of \$364,900. The appraisal your lender obtains values the home at \$358,000.

Your lender has quoted you loans with the following terms:

 Loan 1 Loan 2 Loan 3 6.75% interest rate 30-year amortization Monthly compounding 75% loan-to-value (LTV) ratio 6.20% interest rate 15-year amortization Monthly compounding 80% loan-to-value (LTV) ratio 7.85% interest rate 30-year amortization Monthly compounding 92.5% loan-to-value (LTV) ratio

Determine the following:

1a. The principal for each loan (maximum amount you can borrow).

1b. The down payment for each loan.

1c. The monthly payment for each loan.

1d. What the balance will be in 5 years for each loan.

1e. How much interest you will have paid at the end of 5 years for each loan.

1f. What the balance will be in 5 years for each loan.

1g. How much interest you will have paid at the end of 5 years for each loan.

 Loan 1 Loan 2 Loan 3 Principal Down Payment Monthly Payment Balance at end of 5 years Interest Paid at end of 5 years Balance at end of 10 years Interest Paid at end of 10 years

Question 2

You are in the process of building a new home. The home will cost \$547,000 to construct, and the appraisal your lender obtained indicates a prospective value upon completion of \$565,000.

Your lender has presented you with the following three loan options:

 Loan A Loan B Loan C 7.25% interest rate 25-year amortization Monthly compounding 70% LTV ratio 1% loan origination fee 7.05% interest rate 15-year amortization Monthly compounding 80% LTV ratio 2 points 7.00% interest rate 30-year amortization Monthly compounding 75% LTV ratio 1.5% loan origination fee and 2 points

Determine the following:

2a. The principal amount for each loan.

2b. The monthly payment for each loan.

2c. The amount of the loan fees for each loan.

2d. The net disbursement for each loan.

2e. The effective borrowing cost for each loan. (Don’t forget to annualize the rate.)

 Loan A Loan B Loan C Principal Monthly Payment Points/Loan Fees Net Disbursement Effective Borrowing Cost

Question 3

You have recently purchased a 64-unit apartment building with year 1 NOI of \$11,250 per unit per year. You purchased the property based on a 9% cap rate. The appraisal your lender obtained indicated a value of \$7,650,000.

Your lender has quoted you the following terms:

6.85% interest rate

30-year amortization

Monthly compounding

65% LTV ratio

Determine the following:

3a. The purchase price you are paying based on the year 1 NOI and cap rate given.

3b. The principal amount for the loan (max loan amount).

3c. The equity contribution/down payment for the purchase.

3d. The annual debt service for the loan

3e. The debt coverage ratio based on the year 1 NOI.

3f. The debt yield based on the year 1 NOI.

3g. The before-tax cash flow for year 1.

3h. The equity dividend rate for year 1.

Question 4

You own an 18,000 SF office building with current NOI of \$31.20 per SF per year. You are refinancing the property, and the current market indicates a 10.25% cap rate. The appraisal your lender obtained indicated a value based on this NOI and cap rate.

Your lender has quoted you the following terms:

8.95% interest rate

20-year amortization

Monthly compounding

55% LTV ratio

1.55x debt coverage ratio

Prepayment penalty equal to 2% of loan balance at time of prepayment

Determine the following:

4a. The value indicated in the lender’s appraisal.

4b. The maximum amount for the loan based on the LTV ratio.

4c. The maximum amount for the loan based on maximum ADS indicated by the debt coverage ratio.

4d. The annual debt service for the lower of the loan amounts from 4b and 4c.

4e. The loan balance in year 4.

4f. The prepayment penalty if the loan is prepaid in year 4.

Bonus question

You purchased a 614,000 SF warehouse building 8 years ago for \$35,110,000. You are considering refinancing.

Currently, rental rates average \$5.75/SF. Market vacancies are 3.50%. The subject OER is stable around 12%. Market cap rates are now 7.5%.

Your lender has proposed refinancing based on a current valuation. Below are the original loan terms from 8 years ago and the new proposed loan terms.

 ORIGINAL LOAN (OLD) NEW LOAN 8.50% interest rate 30-year amortization Monthly compounding 70% LTV ratio Minimum 1.35 DCR 2% prepayment penalty (2% of loan balance at time of prepayment) 6.50% interest rate 25-year amortization Monthly compounding 75% LTV ratio Minimum 1.25 DCR

Determine the following:

B1. The current NOI based on the current market terms.

B2. The current market value based on the current NOI and current market cap rate.

B3. The maximum amount you can borrow with the new loan.

B4. The new annual debt service (ADS) based on the new loan terms.

B5. The balance of the original loan at the end of year 10.

B6. The prepayment penalty for the original loan.

B7. The net disbursement for the new loan considering the prepayment penalty for the old loan.

B8. The effective borrowing cost for the new loan.

B9. The DCR for the new loan based on the current NOI.

B10. Does the property qualify for this new loan based on its current income? Why or why not?