# Real Estate Finance Study Set 1

## Quiz 12 :Financial Leverage and Financing Alternatives

Question Type
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
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Net operating income:
It reflects the profitability of real estate investment. It examines the cash flow of investment property before the factors such as taxes and finance costs. The difference between all the operating expenses and the revenue generated by particular property is estimated as the Net Operating Income.
a.
Value of property after
year:
Value of property after five years can be calculated with the help of growth rate.
Value of apartment is
, apartment is sold after
year, and growth rate is
.
Write the expression to calculate the value of property.
Here,
is the current value of property,
is the growth rate, and
is the number of year.
Substitute
for
,
for
, and
for
.
Hence, the value of property after
year is
.
Interest per annum when loan is
financing:
Interest paid per annum can be calculated with the help of interest rate and proportion of loan.
Proportion of loan is
, and interest on loan is
.
Write the expression to calculate the interest per annum.
Substitute
for value of property,
for proportion of loan, and
for interest rate.
Hence, the interest per annum is
.
Computation of before tax internal rate of return:
Before tax internal rate of return can be computed with the help of net cash flows at each year.
Expected net operating income in first year is
, and expected growth rate for net operating income is
.
Calculation of IRR is given in below excel.
The resultant figure from the excel sheet is given below.
Hence, the before tax internal rate of return (BTIRR) is
.
Computation of after-tax internal rate of return:
After tax internal rate of return can be computed with the help of net cash flows at each year.
Calculation of IRR is given in below excel.
The resultant figure from the excel sheet is given below.
Hence, the after-tax internal rate of return (ATIRR) is
.
Interest per annum when loan is
financing:
Interest paid per annum can be calculated with the help of interest rate and proportion of loan.
Proportion of loan is
, and interest on loan is
.
Write the expression to calculate the interest per annum.
Substitute
for value of property,
for proportion of loan, and
for interest rate.
Hence, the interest per annum is
.
Computation of before tax internal rate of return:
Before tax internal rate of return can be computed with the help of net cash flows at each year.
Expected net operating income in first year is
, and expected growth rate for net operating income is
.
Calculation of IRR is given in below excel.
The resultant figure from the excel sheet is given below.
Hence, the before tax internal rate of return is
.
Computation of after-tax internal rate of return:
After tax internal rate of return can be computed with the help of net cash flows at each year.
Calculation of IRR is given in below excel.
The resultant figure from the excel sheet is given below.
Hence, the after-tax internal rate of return is
.
b.
Break even interest rate:
Break-even mortgage rate refers to that rate at which financial leverage does not fetch any benefit to the investor. The rise of the mortgage rate above the break-even mortgage rate causes financial leverage to fetch negative returns.
On the other hand, if mortgage rate falls below the break-even mortgage rate, then financial leverage will fetch positive returns.
Break even interest rate is the rate is calculated by after tax IRR divided by one minus tax rate. Break even interest rate in case of 70% loan is calculated below:
Hence, the break-even interest rate is
.
Break even interest rate in case of 80% loan is calculated below:
Hence, the break-even interest rate is
.
c.
Marginal cost:
The increase or decrease in the collective cost of a production run for making one extra unit of a thing. It is registered in circumstances where the breakeven point has been achieved. The fixed expenses have just been consumed by the units already produced and the variable costs must be represented.
Marginal cost for
loan:
Marginal cost can be computed with the help of interest rate charges on both loans.
Write the expression to calculate the marginal cost.
Substitute
for interest rate on
loan, and
for interest rate on
loan.
Hence, the marginal cost for
loan is
.
d.
Financial Leverage:
The benefit that an investor receives from the use of debt is known as financial leverage. Benefit from use of financial leverage arises when rate of interest paid by the investor on the borrowed amount is lower than the rate of return received from the investment. The return on the equity of the investor is enlarged by the use of financial leverage.
Whether each loan offers favorable financial leverage:
When investor selects the
loan financing, investor will get
before tax internal rate of return and if investor selects
loan financing then the investor will get
before tax internal rate of return.
And if, investor selects the
loan financing, investor will get
after tax internal rate of return and if investor selects
loan financing then investor will get
after tax internal rate of return.
Hence, the only loan that offers favorable financial leverage is
loan.

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Why might a lender prefer a loan with a lower interest rate and a participation
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Participation loan:
It is a kind of loan in which lender participates in the net operating income. To participate in the net operating income lender lowers the interest rate. In return, borrower lets lender have some part of his income. In this, lender becomes a type of equity partner instead of debt provider.
The reason for which a lender prefer loan with a lower interest rate and participation:
The loan with participation is given significance by a lender and also lower interest rate is given importance as it evades against inflation. Net operating income and the resale value moves in same way as inflation. So, if the inflation rises, the rise in net operating income will compensate the loss of purchasing power of money. The lender also does not require participating in losses.
Hence, a lender prefers loan with lower interest rate and participation because participation loan acts as hedge against inflation.

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How do you think participations affect the riskiness of a loan
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Participation loan:
It is a kind of loan in which lender participates in the net operating income. To participate in the net operating income lender lowers the interest rate. In return, borrower lets lender have some part of his income. In this, lender becomes a type of equity partner instead of debt provider.
The way in which participation affects the riskiness of the loan:
Participation loan have lower rate of interest than rate of interest in loan without participation. Participation loan also provides some part of the cash inflow to the lender. In the time of inflation, cash inflow rises, which lead to rise in cash inflow for lender. So, it reduces the risk for lender, as participation loan guards the lender against unexpected inflation.
It also reduces the risk for investor, as investor has to pay less fixed payment. In the event of less cash inflow or no cash inflow, the investor has to make lower payment because of the low interest rate.

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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
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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 Essay Answer: Tags Choose question tag 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.) Essay Answer: Tags Choose question tag What is financial leverage Why is a one-year measure of return on investment inadequate in determining whether positive or negative financial leverage exists Essay Answer: Tags Choose question tag 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. Essay Answer: Tags Choose question tag 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 Essay Answer: Tags Choose question tag 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 Essay Answer: Tags Choose question tag 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 Essay Answer: Tags Choose question tag 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 Essay Answer: Tags Choose question tag What is the motivation for a sale-leaseback of the land Essay Answer: Tags Choose question tag What criteria should be used to choose between two financing alternatives Essay Answer: Tags Choose question tag Why might an investor prefer a loan with a lower interest rate and a participation Essay Answer: Tags Choose question tag In what way does leverage increase the riskiness of a loan Essay Answer: Tags Choose question tag 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
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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 Essay Answer: Tags Choose question tag 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
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.)