**1i.**An investor would like to purchase a new apartment property for $2 million. However, she faces the decision of whether to use 70 percent or 80 percent financing. The 70 percent loan can be obtained at 10 percent interest for 25 years. The 80 percent loan can be obtained at 11 percent interest for 25 years. NOI is expected to be $190,000 per year and increase at 3 percent annually, the same rate at which the property is expected to increase in value. The building and improvements represent 80 percent of value and will be depreciated over 27.5 years (per year). The project is expected to be sold after five years. Assume a 36 percent tax bracket for all income and capital gains taxes.

**a.**What would the BTIRR and ATIRR be at each level of financing (assume monthly mortgage amortization)?

**b.**What is the break-even interest rate (BEIR) for this project?

**c.**What is the marginal cost of the 80 percent loan? What does this mean?

**d.**Does each loan offer favorable financial leverage? Which would you recommend?

**1ii.** What is financial leverage? Why is a one-year measure of return on investment inadequate in determining whether positive or negative financial leverage exists?

**2i.** You are advising a group of investors who are considering the purchase of a shopping center complex. They would like to finance 75 percent of the purchase price. A loan has been offered to them on the following terms: The contract interest rate is 10 percent and will be amortized with monthly payments over 25 years. The loan also will have an equity participation of 40 percent of the cash flow after debt service. The loan has a “lockout” provision that prevents it from being prepaid before year 5.

The property is expected to cost $5 million. NOI is estimated to be $475,000, including overages, during the first year, and to increase at the rate of 3 percent per year for the next five years. The property is expected to be worth $6 million at the end of five years. The improvement represents 80 percent of cost, and depreciation will be over 39 years. Assume a 28 percent tax bracket for all income and capital gains and a holding period of five years.

**a.**Compute the BTIRR and ATIRR after five years, taking into account the equity participation.

**b.**What would the BEIR be on such a project? What is the projected cost of the equity participation financing?

**c.**Is there favorable leverage with the proposed loan?

**2ii.** What is the break-even mortgage interest rate (BEIR) in the context of financial leverage? Would you ever expect an investor to pay a break-even interest rate when financing a property? Why or why not?

**3i.**A developer wants to finance a project costing $1.5 million with a 70 percent, 25-year loan at an interest rate of 8 percent. The project’s NOI is expected to be $120,000 during year 1 and the NOI, as well as its value, is expected to increase at an annual rate of 3 percent thereafter. The lender will require an initial debt coverage ratio of at least 1.20.

**a.**Would the lender be likely to make the loan to the developer? Support your answer with a cash flow statement for a five-year period. What would be the developer’s before-tax yield on equity (BTIRR)?

**b.**Based on the projection in (a), what would be the maximum loan amount that the lender would make if the debt coverage ratio was 1.15 for year 1? What would be the loan-to-value ratio?

**c.**Assuming conditions in part (a), suppose that mortgage interest rates suddenly increase from 8 percent to 10 percent. NOI and value will now increase at a rate of 5 percent. If the desired DCR is 1.20, will the lender be as willing to make a conventional loan now? Support your answer with a cash flow statement.

**3ii.**What is positive and negative financial leverage? How are returns or losses magnified as the degree of leverage increases? How does leverage on a before-tax basis differ from leverage on an after-tax basis?

**4i.** Ace Development Company is trying to structure a loan with the First National Bank. Ace would like to purchase a property for $2.5 million. The property is projected to produce a first year NOI of $200,000. The lender will allow only up to an 80 percent loan on the property and requires a DCR in the first year of at least 1.25. All loan payments are to be made monthly, but will increase by 10 percent at the beginning of each year for five years. The contract rate of interest on the loan is 12 percent. The lender is willing to allow the loan to negatively amortize; however, the loan will mature at the end of the five-year period.

**a.**What will the balloon payment be at the end of the fifth year?

**b.**If the property value does not change, what will the loan-to-value ratio be at the end of the five-year period?

**4ii.**In what way does leverage increase the riskiness of a loan?

**5i.** An institutional lender is willing to make a loan for $1 million on an office building at a 10 percent interest (accrual) rate with payments calculated using an 8 percent pay rate and a 30-year loan term. (That is, payments are calculated as if the interest rate were 8 percent with monthly payments over 30 years.) After the first five years the payments are to be adjusted so that the loan can be amortized over the remaining 25-year term.

**a.**What is the initial payment?

**b.**How much interest will accrue during the first year?

**c.**What will the balance be after five years?

**d.**What will the monthly payments be starting in year 6?

**5ii.**What is meant by a participation loan? What does the lender participate in? Why would a lender want to make a participation loan? Why would an investor want to obtain a participation loan?

**6i.** A property is expected to have NOI of $100,000 the first year. The NOI is expected to increase by 3 percent per year thereafter. The appraised value of the property is currently $1 million and the lender is willing to make a $900,000 participation loan with a contract interest rate of 8 percent. The loan will be amortized with monthly payments over a 20-year term. In addition to the regular mortgage payments, the lender will receive 50 percent of the NOI in excess of $100,000 each year until the loan is repaid. The lender also will receive 50 percent of any increase in the value of the property. The loan includes a substantial prepayment penalty for repayment before year 5, and the balance of the loan is due in year 10. (If the property has not been sold, the participation will be based on the appraised value of the property.) Assume that the appraiser would estimate the value in year 10 by dividing the NOI for year 11 by a 10 percent capitalization rate.

Calculate the effective cost (to the borrower) of the participation loan assuming the loan is held for 10 years. (Note that this is also the expected return to the lender.)

**6ii.** What is meant by a sale-leaseback? Why would a building investor want to do a sale-leaseback of the land? What is the benefit to the party that purchases the land under a sale-leaseback?

**7i.** Refer to problem 6. Assume that another alternative is a convertible mortgage (instead of a participation loan) that gives the lender the option to convert the mortgage balance into a 60 percent equity position at the end of year 10. That is, instead of receiving the payoff on the mortgage, the lender would own 60 percent of the property. The loan would be for $900,000 with a contract rate of 9 percent, and it would be amortized over 20 years. Assume that the borrower will default if the property value is less than the loan balance in year 10.

**a.**What is the lender’s IRR if the property sells for the same price in year 10 as the previous example?

**b.**What is the lender’s IRR if the property sells for only $1 million after 10 years?

**c.**What is the lender’s IRR if the property sells for only $500,000 after 10 years?

(Reference Problem 6)

A property is expected to have NOI of $100,000 the first year. The NOI is expected to increase by 3 percent per year thereafter. The appraised value of the property is currently $1 million and the lender is willing to make a $900,000 participation loan with a contract interest rate of 8 percent. The loan will be amortized with monthly payments over a 20-year term. In addition to the regular mortgage payments, the lender will receive 50 percent of the NOI in excess of $100,000 each year until the loan is repaid. The lender also will receive 50 percent of any increase in the value of the property. The loan includes a substantial prepayment penalty for repayment before year 5, and the balance of the loan is due in year 10. (If the property has not been sold, the participation will be based on the appraised value of the property.) Assume that the appraiser would estimate the value in year 10 by dividing the NOI for year 11 by a 10 percent capitalization rate.

Calculate the effective cost (to the borrower) of the participation loan assuming the loan is held for 10 years. (Note that this is also the expected return to the lender.)

**7ii.** Why might an investor prefer a loan with a lower interest rate and a participation?

**8i.** A borrower and lender negotiate a $20,000,000 interest-only loan at a 9 percent interest rate for a term of 15 years. There is a lockout period of 10 years. Should the borrower choose to prepay this loan at any time after the end of the 10th year, a yield maintenance fee (YMF) will be charged. The YMF will be calculated as follows: A treasury security with a maturity equal to the number of months remaining on the loan will be selected, to which a spread of 150 basis points (1.50 percent) will be added to determine the lender’s reinvestment rate. The penalty will be determined as the present value of the difference between the original loan rate and the lender’s reinvestment rate.

**a.**How much will the YMF be if the loan is repaid at the end of year 13 if 2-year treasury rates are 6 percent? What if two-year treasury rates are 8 percent?

**8ii.** Why might a lender prefer a loan with a lower interest rate and a participation?

**9i. Excel.** Refer to the participation loan example in the chapter. Suppose the participation was reduced to 25 percent of the NOI in excess of $100,000 but increased to 75 percent of the gain in value.

**a.**What is the investor’s before- and after-tax IRR?

**b.**What is the lender’s IRR?

**9ii.** How do you think participations affect the riskiness of a loan?

**10i.** ARGUS. Refer to the Monument Office Building example. What is the leveraged IRR if the loan-to-value ratio is increased to 80 percent?

(Reference ARGUS, the Monument Office Building example)

**10ii.** What is the motivation for a sale-leaseback of the land?

**11.**What criteria should be used to choose between two financing alternatives?

**12.**What is the traditional cash equivalency approach to determine how below-market rate loans affect value?

**13.**How can the effect of below-market-rate loans on value be determined using investor criteria?

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