Fill in the blanks and compute the yield for the following ...



Solution to Exam 1

Real Estate Finance and Investments

Professor Thibodeau

1. You are considering the purchase of an office property for $6,000,000 today. Annual first year rents are estimated to be $22 per square foot and annual non-rental income $60,000. You expect gross potential income to increase 3% per year. Vacancy and collection allowances are currently 12% of gross potential income and this rate is expected to remain constant in the future. Fixed expenses are currently $80,000 and are expected to remain constant for the next five years. Variable expenses are currently $5.50 per square foot and are expected to increase 3% per year. You can obtain a constant monthly payment mortgage for 80 percent of the purchase price at 7.25% annual interest with monthly payments for 30 years, a 2% loan origination fee, and a 3% prepayment penalty. You expect the property value to increase 3% annually over an anticipated 4-year holding period. You will pay a 4% selling commission when you sell the property. You are in the 36% tax bracket for ordinary income and capital gains are taxed at 15%. For tax purposes, assume land value is 25% of the purchase price and the depreciable basis will be depreciated over 39 years. The pro-forma on page 4 provides expected cash flows for this property.

a. What is the (before debt, before tax) yield on the property? (5 points)

Year: 0 1 2 3 4

Price 6,000,000

NOI 457,900 474,037 490,658 507,778

Sales Proceeds 6,482,931

Cash Flows - 6,000,000 457,900 474,037 490,658 6,990,709

IRR on the property is 9.75%

b. What is the expected before tax IRR on equity? (5 points)

Year: 0 1 2 3 4

Price 6,000,000

- Loan - 4,800,000

+ Fee 96,000

BTCF from Rent 64,966 81,103 97,725 114,844

BTCF from Sale 1,752,951

Cash Flows - 1,296,000 64,966 81,103 97,725 1,867,795

BTIRR on equity is 13.89%

c. Should you purchase the property if you discount expected after tax cash flows at 12%? Why or why not? (5 points)

Year: 0 1 2 3 4

Price 6,000,000

- Loan - 4,800,000

+ Fee 96,000

ATCF from Rent 67,544 76,618 85,908 95,416

ATCF from Sale 1,690,828

Cash Flows - 1,296,000 67,544 76,618 85,908 1,786,244

Expected ATNPV = $21,725. Purchase the property since the expected ATNPV > 0.

Expected ATIRR = 12.50%. Purchase the property since the expected ATIRR > 12%.

d. What is the lenders expected yield on the loan (use monthly cash flows)? (5 points)

Month(s): 0 1-48 48

- Loan - 4,800,000

+ Fee 96,000

Monthly Payment 32,744.50

Mortgage Balance 4,592,214

Prepayment Penalty 137,766

Cash Flow -4,704,000 32,744.50 4,729,980

The lenders yield is 8.47%.

e. Suppose the lender requires a 1.3 Debt Service Coverage ratio for year 1 (DSC = NOI/Debt Service).

What is the most you can borrow (assuming a 7.25% annual rate, 30 year, monthly payment loan)?

(5 points)

DSC = NOI/DS

1.3 = $457,900/DS

DS = $457,900/1.3

= $352,230.77

PMT = DS/12

= $ 29,352.56

So the maximum loan is the present value of $29,352.56 discounted monthly at an annual rate of 7.25% for 360 months. The maximum loan amount is $4,302,782.87.

f. Suppose the market value of the property at the end of year four really is $ 6,753,053 and the expected after tax cash flows for year 5 in the pro-forma on page 4 accurately reflect expected cash flows. What is your marginal after tax internal rate of return from holding the property one more year (e.g. for year 5)? (5 points)

$1,690,828 = (105,144 + 1,900,907)/(1 + d)

d = 18.64%

g. Is the before tax leverage associated with this acquisition positive, negative or neutral? Defend your answer. (5 points)

Before tax leverage is positive since 9.75% > 8.47%.

2. Suppose you purchased the property described in Problem #1 and you have owned and operated the property for two years. You expect to hold the property for three more years. Your property manager informs you that $200,000 in capital improvements will allow you to increase potential gross income (rents plus non-rental income) next year (e.g. in year 3) by 6% instead of 3%. After next year, rents will increase by 3% per year. Furthermore, the market value at the end of year 5 is expected to increase to $7,200,000 with the improvements. A lender is willing to let you finance 80% of the improvement expenditure with a 15-year, 8.5% fixed annual interest rate mortgage. There is a one percent loan fee but no prepayment penalty. The loan fee will not be financed. The pro-forma on page 6 provides expected cash flows for the renovated property. Should you make the investment if you discount expected after tax renovation cash flows at 14%? (15 points)

Year: 0 1 2 3

Improvements 200,000

- Loan - 160,000

+ Fee 1,600

ATCF from Rent

With Renovation 94,957 104,722 114,706

Without Renovation 85,908 95,416 105,144

Difference 9,049 9,306 9,562

ATCF from Sale

With Renovation 1,956,517

Without Renovation 1,900,907

Difference 55,610

Cash Flows - 41,600 9,049 9,306 65,172

The expected ATIRR on the renovation cash flows is 30.65% > 14.00%, so do the renovations.

Alternatively, the expected ATNPV on the renovation cash flows is + $17,488 > 0, so do the renovations.

3. Six years ago you financed the acquisition of a $1,800,000 office property with an 80%, 30 year, 7.5% annual fixed interest rate, monthly payment loan. The loan has a 2% prepayment penalty. The current market annual interest rate for 25-year fixed rate commercial loans has dropped to 6.75% with a 2% loan origination fee and a 2% prepayment penalty. If you refinance, you also have to pay $15,000 in additional closing costs. Your lender will let you refinance the outstanding mortgage balance on the existing mortgage (including the prepayment penalty), the $15,000 in closing costs, but requires that you pay the 2% loan origination fee out of pocket. Compute the before tax net present value of refinancing if you discount future expected before tax cash flows at 7% and you expect to sell the property five years from today. Should you refinance? Why or why not? (25 points)

Six Years Ago

Price = $ 1,800,000

Loan @ 80% = $ 1,440,000

Term = 30 years, monthly payments

Annual Rate = 7.5%

Monthly Payment = $ 10,068.69

MB72 = $ 1,343,199.35

PP72 = $ 26,863.99

FV72 = $ 1,370,063.34

MB132 = $ 1,221,811.17

PP132 = $ 24,436.22

FV72 = $ 1,246,247.39

Today

Loan Balance = $ 1,343,199.35

PP = $ 26,863.99

Closing Costs = $ 15,000.00

New Loan Amount $ 1,385,063.34

Fee @ 2% $ 27,701.27

Term = 25-year, monthly payments

Annual Rate = 6.75%

Monthly Payment = $ 9,569.56

MB60 = $ 1,258,550.29

PP60 = $ 25,171.01

FV60 = $ 1,283,721.30

Cash Flows: -27,701.27 today

10,068.69 - 9,569.56 = 499.13 for 60 months

1,246,247.39 - 1,283,721.30 = - 37,473.91 in 60 months

BTNPV @ 7% = - $ 28, 928.49 Forget it.

4. You are evaluating the acquisition of a $4M apartment property. The land is valued at $1.25M. The first year's expected net operating income is $360,000 and NOI is expected to increase 3% annually. You intend to hold the property for seven years and estimate future selling price by capitalizing the subsequent year's NOI at 9.0%. You have to pay a 2% selling commission when you sell the property. You have already determined that the acquisition is feasible and are trying to decide how to finance the acquisition. You are evaluating three alternative 75% loan-to-value ratio loans. Each loan has a 2% loan fee. The first alternative is a 25-year, monthly payment, 7.5% annual fixed interest rate mortgage. This loan has a 3% prepayment penalty. The second alternative is a 30-year, monthly payment, accrual loan with a 6.5% annual pay rate and an 8.0% annual accrual rate but no prepayment penalty. The third alternative is 7.75% annual rate interest only loan with monthly payments and a balloon payment of $3,050,000 at the end of seven years. Which loan would you select? Why? Make your decision using before tax cash flows. (25 points)

Loan Amount = $3,000,000

Fee @ 2% = 60,000

Net Loan Amount = $ 2,940,000

Loan Option a b c

Amount $3,000,000 $3,000,000 $3,000,000

Rates

Fixed 7.5%

Pay 6.5%

Accrual 8.0%

Interest Only 7.75%

Term 25 years 30 years IO

Monthly monthly monthly

Prepayment Penalty 3% 0% 0%

Monthly Payment $ 22,169.74 $ 18,962.04 $ 19,375.00

Mortgage Balance/ $ 2,623,719.61 $ 3,116,369.13

Balloon $ 3,050,000

Prepayment Penalty $ 78,711.59 0 0

Total FV $ 2,702,431.20 $ 3,116,369.13 $ 3,050,000.00

Yield 8.19% 8.37% 8.30%

Take a, it is the cheapest (before tax).

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