**1i.**A $100,000 loan can be obtained at a 10 percent rate with monthly payments over a 15-year term.

**a.**What is the after-tax effective interest rate on the loan, assuming the borrower is in a 30 percent tax bracket and the loan is held only three years? Assume that the benefit of interest deductions for tax purposes occurs at the same time payments are made.

**b.**Calculate the after-tax effective cost for the above loan, assuming 5 points are charged and that the points are tax-deductible at the time they are paid.

**c.**How does the after-tax cost in part (b) compare with the pretax effective cost of the loan?

**1ii. **A borrower can obtain an 80 percent loan with an 8 percent interest rate and monthly payments. The loan is to be fully amortized over 25 years. Alternatively, he could obtain a 90 percent loan at an 8.5 percent rate with the same loan term. The borrower plans to own the property for the entire loan term.

**a.**What is the incremental cost of borrowing the additional funds? (Hint: The dollar amount of the loan doesn’t affect the answer.)

**b.**How would your answer change if two points were charged on the 90 percent loan?

**c.**Would your answer to part (b) change if the borrower planned to own the property for only five years?

**1iii.**What are the primary considerations that should be made when refinancing?

**2i.** A mortgage for $100,000 is made with initial payments of $500 per month for the first year. The interest rate is 9 percent. After the first year, payments will increase to an amount that makes the loan fully amortizable over the remaining 24 years with constant monthly payments.

**a.**Calculate the interest deductions for the loan for the first year.

**b.**How much, if any, interest must be deferred until the second year?

**c.**How much interest will be deducted in the second year?

**2ii. **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 a 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?

**2iii.** What factors must be considered when deciding whether to refinance a loan after interest rates have declined?

**3i.**An investor obtained a fully amortizing mortgage 5 years ago for $95,000 at 11 percent for 30 years. Mortgage rates have dropped, so that a fully amortizing 25-year loan can be obtained at 10 percent. There is no prepayment penalty on the mortgage balance of the original loan, but three points will be charged on the new loan and other closing costs will be $2,000. All payments are monthly.

**a.** Should the borrower refinance if he plans to own the property for the remaining loan term? Assume that the investor borrows only an amount equal to the outstanding balance of the loan.

**b.** Would your answer to part (a) change if he planned to own the property for only five more years?

**3ii.** Why might the market value of a loan differ from its outstanding balance?

**4i.** Secondary Mortgage Purchasing Company (SMPC) wants to buy your mortgage from the local savings and loan. The original balance of your mortgage was $140,000 and was obtained 5 years ago with monthly payments at 10 percent interest. The loan was to be fully amortized over 30 years.

**a.**What should SMPC pay if it wants an 11 percent return?

**b.**How would your answer to part (a) change if SMPC expected the loan to be repaid after five years?

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**4ii.** Why might a borrower be willing to pay a higher price for a home with an assumable loan?

**5i. **You have a choice between the following two identical properties: Property A is priced at $150,000 with 80 percent financing at a 10.5 percent interest rate for 20 years. Property B is priced at $160,000 with an assumable mortgage of $100,000 at 9 percent interest with 20 years remaining. Monthly payments are $899.73. A second mortgage for $20,000 can be obtained at 13 percent interest for 20 years. All loans require monthly payments and are fully amortizing.

**a.**With no preference other than financing, which property would you choose?

**b.**How would your answer change if the seller of Property B provided a second mortgage for $20,000 at the same 9 percent rate as the assumable loan?

**c.**How would your answer change if the seller of Property B provided a second mortgage for$30,000 at the same 9 percent rate as the assumable loan so that no additional down payment would be required by the buyer if the loan were assumed?

**5ii.** What is a buydown loan? What parties are usually involved in this kind of loan?

**6i.** An investor has owned a property for 15 years, the value of which is now to $200,000. The balance on the original mortgage is $100,000 and the monthly payments are $1,100 with 15 years remaining. He would like to obtain $50,000 in additional financing. A new first mortgage for $150,000 can be obtained at a 12.5 percent rate and a second mortgage for $50,000 at a 14 percent rate with a 15-year term. Alternatively, a wraparound loan for $150,000 can be obtained at a 12 percent rate and a 15-year term. All loans are fully amortizing. Which alternative should the investor choose?

**6ii.**Why might a wraparound lender provide a wraparound loan at a lower rate than a new first mortgage?

**7i.** A builder is offering $100,000 loans for his properties at 9 percent for 25 years. Monthly payments are based on current market rates of 9.5 percent and are to be fully amortized over 25 years. The property would normally sell for $110,000 without any special financing.

**a.**At what price should the builder sell the properties to earn, in effect, the market rate of interest on the loan? Assume that the buyer would have the loan for the entire term of 25 years.

**b.**How would your answer to part (a) change if the property is resold after 10 years and the loan repaid?

**7ii.** Assuming the borrower is in no danger of default, under what conditions might a lender be willing to accept a lesser amount from a borrower than the outstanding balance of a loan and still consider the loan paid in full?

**8i.** A property is available for sale that could normally be financed with a fully amortizing $80,000 loan at a 10 percent rate with monthly payments over a 25-year term. Payments would be $726.96 per month. The builder is offering buyers a mortgage that reduces the payments by 50 percent for the first year and 25 percent for the second year. After the second year, regular monthly payments of $726.96 would be made for the remainder of the loan term.

**a.**How much would you expect the builder to have to give the bank to buy down the payments as indicated?

**b.**Would you recommend the property be purchased if it was selling for $5,000 more than similar properties that do not have the buydown available?

**8ii.**Under what conditions might a home with an assumable loan sell for more than comparable homes with no assumable loans available?

**9i.** An appraiser is looking for comparable sales and finds a property that recently sold for $200,000. She finds that the buyer was able to assume the seller’s fully amortizing mortgage which had monthly payments based on a 7 percent interest rate. The balance of the loan at the time of sale was $140,000 with a remaining term of 15 years (monthly payments). The appraiser determines that if a $140,000 loan was obtained on the same property, monthly payments at the market rate for a 15-year fully amortizing loan would have been 8 percent with no points.

**a.**Assume that the buyer expected to benefit from the interest savings on the assumable loan for the entire loan term. What is the cash equivalent value of the property?

**b.**How would your answer to part (a) change if you assumed that the buyer only expected to benefit from interest savings for five years because he would probably sell or refinance after five years?

**9ii.** What is meant by the incremental cost of borrowing additional funds?

**10.i.** A borrower is making a choice between a mortgage with monthly payments or bi-weekly payments. The loan will be $200,000 at 6 percent interest for 20 years.

**a.**How would you analyze these alternatives?

**b.**What if the biweekly loan was available for 5.75 percent? How would your answer change?

**10ii.**Is the incremental cost of borrowing additional funds affected significantly by early repayment of the loan?

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