1
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 theproperty value to increase 3% annually over an anticipated 4-yearholding 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.
- What is the (before debt, before tax) yield on the property? (5 points)
Year:01234
Price6,000,000
NOI457,900474,037490,658507,778
Sales Proceeds6,482,931
Cash Flows- 6,000,000457,900474,037490,6586,990,709
IRR on the property is 9.75%
- What is the expected before tax IRR on equity? (5 points)
Year:01234
Price6,000,000
- Loan- 4,800,000
+ Fee96,000
BTCF from Rent64,96681,10397,725114,844
BTCF from Sale1,752,951
Cash Flows- 1,296,00064,96681,10397,7251,867,795
BTIRR on equity is 13.89%
- Should you purchase the property if you discount expected after tax cash flows at 12%? Why or why not? (5 points)
Year:01234
Price6,000,000
- Loan- 4,800,000
+ Fee96,000
ATCF from Rent67,54476,61885,90895,416
ATCF from Sale1,690,828
Cash Flows- 1,296,00067,54476,61885,9081,786,244
Expected ATNPV = $21,725. Purchase the property since the expected ATNPV > 0.
Expected ATIRR = 12.50%. Purchase the property since the expected ATIRR > 12%.
- What is the lendersexpected yield on the loan (use monthly cash flows)? (5 points)
Month(s):01-4848
- Loan- 4,800,000
+ Fee96,000
Monthly Payment32,744.50
Mortgage Balance4,592,214
Prepayment Penalty137,766
Cash Flow-4,704,00032,744.504,729,980
The lenders yield is 8.47%.
- 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.
- 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%
- 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:0123
Improvements200,000
- Loan- 160,000
+ Fee1,600
ATCF from Rent
With Renovation94,957104,722114,706
Without Renovation85,90895,416105,144
Difference9,0499,3069,562
ATCF from Sale
With Renovation1,956,517
Without Renovation1,900,907
Difference55,610
Cash Flows- 41,6009,0499,30665,172
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:-27,701.27today
10,068.69 - 9,569.56 =499.13for 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 Optionabc
Amount$3,000,000$3,000,000$3,000,000
Rates
Fixed7.5%
Pay6.5%
Accrual8.0%
Interest Only7.75%
Term25 years30 yearsIO
Monthlymonthlymonthly
Prepayment Penalty3%0%0%
Monthly Payment$ 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$ 78,711.5900
Total FV$ 2,702,431.20$ 3,116,369.13$ 3,050,000.00
Yield8.19%8.37%8.30%
Take a, it is the cheapest (before tax).