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



Real Estate Finance and Investments

Solution to Exam 1

Fall 2005

Professor Thibodeau

1. You are considering the purchase of an office property for $54,000,000 today. Annual first year rents are estimated to be $25 per square foot triple-net. You expect to lease 90% of the space for the duration of a five year holding period. In addition, this property has parking spaces for 700 cars. You expect to lease 400 spaces at $100 per month. In addition, you expect to lease 200 of the remaining 300 spaces at an average daily rent of $10.08 per work-day (assume 250 work-days per year). You expect gross rental income to increase 3% per year and parking revenue to increase 2% per year. This triple net lease requires tenants to pay all fixed and variable expenses (e.g. property taxes, insurance, utilities, etc.) but requires you pay the property management expenses. You expect to pay a property management company 4% of effective gross income to manage the property (including the parking structure). In addition, you plan to set aside $16,000 in reserves at the end of year 1. Reserves will increase 3% per year. You can obtain a constant monthly payment mortgage for 70 percent of the purchase price at 5.75% annual interest with monthly payments for 30 years, a 1% loan origination fee, and a 3% prepayment penalty. You estimate the future selling price by capitalizing NOI at 8.5%. You expect to pay a 2% selling commission when you sell the property at the end of the five year holding period. You are in the 36% tax bracket for ordinary income and capital gains are taxed at 15%. For tax purposes, assume land value is 15% of the purchase price and the building will be depreciated over 39 years. Exhibit 1 on page 3 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 5

Price 54,000,000

NOI 4,384,640 4,506,733 4,632,299 4,761,440 4,894,259

Sales Proceeds 58,002,876

Cash Flows - 54,000,000 4,384,640 4,506,733 4,632,299 4,761,440 62,897,135

IRR on the property is 9.76%

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

Year: 0 1 2 3 4 5

Price 54,000,000

- Loan - 37,800,000

+ Fee 378,000

BTCF from Rent 1,737,554 1,859,646 1,985,213 2,114,354 2,247,173

BTCF from Sale 21,886,846

Cash Flows -16,578,000 1,737,554 1,859,646 1,985,213 2,114,354 24,134,019

BTIRR on equity is 16.39%

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 5

Price 54,000,000

- Loan - 37,800,000

+ Fee 378,000

ATCF from Rent 1,365,206 1,433,010 1,502,427 1,573,485 1,646,213

ATCF from Sale 20,895,815

Cash Flows -16,578,000 1,365,206 1,433,010 1,502,427 1,573,485 22,542,028

Expected ATNPV = + $ 643,649. Purchase the property since the expected ATNPV > 0.

Expected ATIRR = 12.99%. Purchase the property since the expected ATIRR > 12%.

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

Month(s): 0 1-60 60

- Loan - 37,800,000

+ Fee 378,000

Monthly Payment 220,590.54

Mortgage Balance 35,064,106.63

Prepayment Penalty 1,051,923.20

Cash Flow -37,422,000 220,590.54 36,116,029.83

The lenders yield is 6.48%.

e. Suppose the lender requires a 1.4 Debt Service Coverage ratio for year 1 (DSC = NOI/Debt Service).

What is the most you can borrow (assuming a 5.75% annual rate, 30 year, monthly payment loan)?

(5 points)

DSC = NOI/DS

1.4 = $4,384,640/DS

DS = $4,384,640/1.4

= $3,131,885.71

PMT = DS/12

= $ 260,990.48

So the maximum loan is the present value of $260,990.48 discounted monthly at an annual rate of 5.75% for 360 months. The maximum loan amount is $44,722,861.

Exhibit 1

70% Loan-to-Value Ratio, 5.75% Annual Interest, 30 Years, 1% Fee, 3% Prepay Penalty

|PRO-FORMA OPERATING STATEMENTS AND REVERSION ESTIMATES | | |

| | | | | | |

|Year: |1 |2 |3 |4 |5 |

| | | | | | |

|Gross Rental Income |4000000 |4120000 |4243600 |4370908 |4502035 |

| less Vacancy/Collection |-400000 |-412000 |-424360 |-437091 |-450204 |

| plus Parking Revenue |984000 |1003680 |1023754 |1044229 |1065113 |

|Effective Gross Income |4584000 |4711680 |4842994 |4978046 |5116945 |

| less Management Fees |-183360 |-188467 |-193720 |-199122 |-204678 |

| less Reserves |-16000 |-16480 |-16974 |-17484 |-18008 |

|Net Operating Income |4384640 |4506733 |4632299 |4761440 |4894259 |

| less Debt Service |-2647086 |-2647086 |-2647086 |-2647086 |-2647086 |

|Before Tax Cash Flow |1737554 |1859646 |1985213 |2114354 |2247173 |

| | | | | | |

|Net Operating Income |4384640 |4506733 |4632299 |4761440 |4894259 |

| less Interest |-2160818 |-2132108 |-2101704 |-2069505 |-2035404 |

| Depreciation |-1176923 |-1176923 |-1176923 |-1176923 |-1176923 |

| Amortization |-12600 |-12600 |-12600 |-12600 |-12600 |

|Taxable Earnings |1034299 |1185101 |1341072 |1502413 |1669332 |

| | | | | | |

|Federal Income Tax |-372348 |-426637 |-482786 |-540869 |-600959 |

| | | | | | |

|Before Tax Cash Flow |1737554 |1859646 |1985213 |2114354 |2247173 |

| less Federal Income Tax |-372348 |-426637 |-482786 |-540869 |-600959 |

|After Tax Cash Flow |1365206 |1433010 |1502427 |1573485 |1646213 |

| | | | | | |

|Estimated Selling Price | | | | |59186608 |

| less Selling Costs | | | | |-1183732 |

|Net Sales Proceeds | | | | |58002876 |

| less Mortgage Balance | | | | |-35064107 |

| Prepayment Penalty | | | | |-1051923 |

|BTCF from Reversion | | | | |21886846 |

| | | | | | |

|Net Sales Proceeds | | | | |58002876 |

| less Original Cost | | | | |-54000000 |

| plus Accum. Depreciation | | | |5884615 |

|Total Gain | | | | |9887492 |

| less Recapture | | | | |0 |

|Capital Gain | | | | |9887492 |

|Capital Gain Tax Liability | | | | |-1483124 |

| | | | | | |

|Ordinary Income Tax Items from Sale (excluding Recapture) | | |

| Unamortized Fee | | | | |-315000 |

| Prepayment Penalty | | | | |-1051923 |

|Ordinary Income Tax | | | | |492092 |

| | | | | | |

|BTCF from Reversion | | | | |21886846 |

| less Ordinary Income Tax | | | | |492092 |

| Tax on Recapture | | | | |0 |

| Capital Gain Tax | | | | |-1483124 |

|ATCF from Reversion | | | | |20895815 |

2. Assume you have decided to purchase the property described in Problem #1 but you want to finance 85% of the purchase price instead of 70%. You are evaluating three alternatives. The first alternative is to obtain an 85% loan-to-value ratio loan at 6.5% annual interest with monthly payments for 30 years, a 2% loan fee and a 3% prepayment penalty. Exhibit 2 on page 7 provides the expected cash flows for this alternative. The second alternative is to finance 85% of the purchase price with a participation loan. The participation lender is willing to provide a 6% annual interest rate, 30 year, monthly payment loan with a 2% loan fee but no prepayment penalty in exchange for 20% of the before tax cash flows from operations and 10% of the before tax cash flows from the sale. Exhibit 3 on page 8 provides the expected cash flows for this alternative. The third alternative is to finance the acquisition of the property with the 70% loan-to-value ratio loan described in problem #1 and to obtain the additional $8.1M debt with an accrual rate loan. The accrual rate loan requires monthly payments for 25 years, has a 6% pay rate and a 9% accrual rate. This loan has a 2% loan fee but no prepayment penalty.

a. Is this acquisition still feasible with the 6.5% fixed rate first mortgage? Your required return for expected after tax cash flows is 14% with the additional debt. (5 points)

Year: 0 1 2 3 4 5

Price 54,000,000

- Loan - 45,900,000

+ Fee 918,000

ATCF from Rent 828,069 893,839 961,005 1,029,573 1,099,553

ATCF from Sale 13,002,739

Cash Flows -9,018,000 828,069 893,839 961,005 1,029,573 14,102,292

Expected ATNPV = + $ 978,686. Purchase the property since the expected ATNPV > 0.

Expected ATIRR = 16.77%. Purchase the property since the expected ATIRR > 14%.

b. What is the expected borrowing cost for the 6.5% fixed rate first? Use monthly cash flows to compute payments and mortgage balances but annual cash flows to compute expected yields.

(5 points)

Year(s): 0 1-5 5

- Loan - 45,900,000

+ Fee 918,000

Annual Debt Service 3,481,431

Mortgage Balance 42,967,439

Prepayment Penalty 1,289,023

Cash Flow -44,982,000 3,481,431 44,256,462

The expected borrowing cost is 7.46%.

c. Is marginal leverage positive, negative or neutral? Why? (5 points)

Marginal leverage is positive because the ATNPV for the 85% loan exceeds the ATNPV for the 70% loan. That is, marginal leverage is positive because $978,686 > $643,649.

d. What is the marginal cost of obtaining the additional debt with the 6.5% fixed-rate first (compared to the 70% loan-to-value ratio loan described in Problem #1)? Use monthly cash flows. (5 points)

Loan Option Net Loan Amount Monthly Payment Future Value

for 60 months

85% $ 44,982,000 $ 290,119.25 $ 44,256,462

70% $ 37,422,000 $ 220,590.54 $ 36,116,030

Difference 7,560,000 69,528.71 8,140,432

The expected yield on the marginal cash flows: 12.16%

e. What is the expected borrowing cost for the participation loan? Use annual before tax cash flows.

(5 points)

Year(s): 0 1 2 3 4 5

- Loan - 45,900,000

+ Fee 918,000

Annual Debt Service 3,302,324 3,302,324 3,302,324 3,302,324 3,302,324

Participation in BTCFO 216,463 240,882 265,995 291,823 318,387

Mortgage Balance 42,711,950

Participation in BTCFR 1,529,093

Cash Flow -44,982,000 3,518,787 3,543,206 3,568,319 3,594,147 47,861,754

The expected yield to the lender (or borrowing cost for the borrower) on the participation loan is 7.64%.

f. What is the marginal cost of obtaining the additional debt with the participation loan (compared to the 70% loan-to-value ratio loan described in Problem #1)? Use annual before tax cash flows.

(5 points)

Year

Loan Option Net Loan 1 2 3 4 5

Participation 44,982,000 3,518,787 3,543,206 3,568,319 3,594,147 47,861,754

70% L/V 37,422,000 2,647,086 2,647,086 2,647,086 2,647,086 38,763,116

Difference 7,560,000 871,701 896,120 921,233 947,061 9,098,638

The expected marginal cost of borrowing is 13.26%

g. What is the expected borrowing cost for the entire loan if you finance the acquisition with the 70% first mortgage described in Problem #1 and the $8.1M accrual rate second mortgage? Use monthly cash flows to compute mortgage payments and outstanding balances but annual cash flows to compute yields. (5 points)

Years

Loan Option Net Loan Amount 1-5 5

70% First 37,422,000 - 2,647,086 - 36,116,030

Accrual 7,938,000 - 626,216 - 8,745,750

Total 45,360,000 - 3,273,347 - 44,861,780

The total borrowing cost for the 70% first plus the accrual second is 7.03%.

h. What is the marginal borrowing cost for the accrual rate second mortgage? Use monthly before tax cash flows. (5 points)

The marginal borrowing cost for the accrual loan is simply the expected yield on the debt.

Loan Option Net Loan Amount Monthly Payment Mortgage Balance

for 60 months

Accrual $ 7,938,000 $ 52,188.41 $ 8,745,750

The expected yield on the accrual loan is 9.48%.

i. Would you select any of the three 85% loan-to-value ratio loan alternatives? Which one? Why?

(Ignore risk differences for the three 85% loan-to-value ratio alternatives)? (10 points)

Alternative Expected Borrowing Cost

85% L/V; Fixed 6.5% Rate 7.46%

Participation 7.64%

70% L/V; Fixed 5.75% Rate First + 9% Accrual Second 7.03%

Take the accrual—it’s the cheapest of the three alternatives.

Exhibit 2

85% Loan-to-Value Ratio, 6.50% Annual Interest, 30 Years, 2% Fee, 3% Prepay Penalty

|PRO-FORMA OPERATING STATEMENTS AND REVERSION ESTIMATES | | |

| | | | | | |

|Year: |1 |2 |3 |4 |5 |

| | | | | | |

|Gross Rental Income |4000000 |4120000 |4243600 |4370908 |4502035 |

| less Vacancy/Collection |-400000 |-412000 |-424360 |-437091 |-450204 |

| plus Parking Revenue |984000 |1003680 |1023754 |1044229 |1065113 |

|Effective Gross Income |4584000 |4711680 |4842994 |4978046 |5116945 |

| less Management Fees |-183360 |-188467 |-193720 |-199122 |-204678 |

| less Reserves |-16000 |-16480 |-16974 |-17484 |-18008 |

|Net Operating Income |4384640 |4506733 |4632299 |4761440 |4894259 |

| less Debt Service |-3481431 |-3481431 |-3481431 |-3481431 |-3481431 |

|Before Tax Cash Flow |903209 |1025302 |1150869 |1280010 |1412828 |

| | | | | | |

|Net Operating Income |4384640 |4506733 |4632299 |4761440 |4894259 |

| less Interest |-2968395 |-2934036 |-2897376 |-2858260 |-2816526 |

| Depreciation |-1176923 |-1176923 |-1176923 |-1176923 |-1176923 |

| Amortization |-30600 |-30600 |-30600 |-30600 |-30600 |

|Taxable Earnings |208722 |365174 |527401 |695657 |870210 |

| | | | | | |

|Federal Income Tax |-75140 |-131463 |-189864 |-250436 |-313276 |

| | | | | | |

|Before Tax Cash Flow |903209 |1025302 |1150869 |1280010 |1412828 |

| less Federal Income Tax |-75140 |-131463 |-189864 |-250436 |-313276 |

|After Tax Cash Flow |828069 |893839 |961005 |1029573 |1099553 |

| | | | | | |

|Estimated Selling Price | | | | |59186608 |

| less Selling Costs | | | | |-1183732 |

|Net Sales Proceeds | | | | |58002876 |

| less Mortgage Balance | | | | |-42967439 |

| Prepayment Penalty | | | | |-1289023 |

|BTCF from Reversion | | | | |13746414 |

| | | | | | |

|Net Sales Proceeds | | | | |58002876 |

| less Original Cost | | | | |-54000000 |

| plus Accum. Depreciation | | | | |5884615 |

|Total Gain | | | | |9887492 |

| less Recapture | | | | |0 |

|Capital Gain | | | | |9887492 |

|Capital Gain Tax Liability | | | | |-1483124 |

| | | | | | |

|Ordinary Income Tax Items from Sale | | |

| Unamortized Fee | | | | |-765000 |

| Prepayment Penalty | | | | |-1289023 |

|Ordinary Income Tax | | | | |739448 |

| | | | | | |

|BTCF from Reversion | | | | |13746414 |

| less Ordinary Income Tax | | | | |739448 |

| Tax on Recapture | | | | |0 |

| Capital Gain Tax | | | | |-1483124 |

|ATCF from Reversion | | | | |13002739 |

Exhibit 3

85% Loan-to-Value Ratio, 6.00% Annual Interest Participation, 30 Years, 2% Fee, No Prepay Penalty

|Year: |1 |2 |3 |4 |5 |

| | | | | | |

|Net Operating Income |4384640 |4506733 |4632299 |4761440 |4894259 |

| less Debt Service |-3302324 |-3302324 |-3302324 |-3302324 |-3302324 |

|BTCF Before Participation |1082316 |1204409 |1329975 |1459116 |1591935 |

| less Participation |-216463 |-240882 |-265995 |-291823 |-318387 |

|BTCF After Participation |865853 |963527 |1063980 |1167293 |1273548 |

| | | | | | |

|Net Operating Income |4384640 |4506733 |4632299 |4761440 |4894259 |

| less Interest |-2738667 |-2703902 |-2666992 |-2627806 |-2586204 |

| Participation |-216463 |-240882 |-265995 |-291823 |-318387 |

| Depreciation |-1176923 |-1176923 |-1176923 |-1176923 |-1176923 |

| Amortization |-30600 |-30600 |-30600 |-30600 |-30600 |

|Taxable Earnings |221987 |354426 |491789 |634288 |782145 |

|Federal Income Tax |-79915 |-127593 |-177044 |-228344 |-281572 |

| | | | | | |

|Before Tax Cash Flow |865853 |963527 |1063980 |1167293 |1273548 |

| less Federal Income Tax |-79915 |-127593 |-177044 |-228344 |-281572 |

|After Tax Cash Flow |785937 |835934 |886936 |938949 |991975 |

| | | | | | |

|Estimated Selling Price | | | | |59186608 |

| less Selling Costs | | | | |-1183732 |

|Net Sales Proceeds | | | | |58002876 |

| less Mortgage Balance | | | | |-42711950 |

| Prepayment Pen. | | | | |0 |

|BTCF from Reversion | | | | | |

|Before Particiption | | | | |15290926 |

| less Participation | | | | |-1529093 |

|BTCF from Reversion | | | | | |

|After Participation | | | | |13761834 |

| | | | | | |

|Net Sales Proceeds | | | | |58002876 |

| less Original Cost | | | | |-54000000 |

| plus Accum. Depr. | | | | |5884615 |

|Total Gain | | | | |9887492 |

| | | | | | |

|Ordinary Income Tax Items from Sale | | |

| Unamortized Fee | | | | |-765000 |

| Prepayment Penalty | | | | |0 |

| Participation | | | | |-1529093 |

|Ordinary Income Tax | | | | |825873 |

| | | | | | |

|Total Gain | | | | |9887492 |

| less Recapture | | | | |0 |

|Capital Gain | | | | |9887492 |

|Capital Gain Tax | | | | |-1483124 |

| | | | | | |

|BTCF from Reversion | | | | |13761834 |

| less Ordinary Income Tax | | | | |825873 |

| Capital Gain Tax | | | | |-1483124 |

|ATCF from Reversion | | | | |13104583 |

3. Three years ago you financed the acquisition of a $50,000,000 office property with a 75%, 30 year, 7.75% annual fixed interest rate, interest-only, monthly payment loan. The loan has yield maintenance fee that requires you to pay the difference between the contract rate and the yield on US Treasuries plus 150 basis points if you repay the loan within ten years. The current market annual interest rate for 30-year fixed rate interest only commercial loans has dropped to 6.00% with a 1% loan origination fee and a ten-year lock out provision. The lock-out prohibits you from prepaying the loan for ten years. There is no prepayment penalty if you prepay the new loan after the ten year lock-out period. If you refinance, you also have to pay $150,000 in additional closing costs. Your lender will let you refinance the outstanding mortgage balance on the existing mortgage (including the yield maintenance fee), the $150,000 in closing costs, but requires that you pay the 1% 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 ten years from today. The current yield on ten-year US Treasuries is 4.75%. The expected yield on US Treasuries ten years from now is 6%. Should you refinance? Why or why not?

Three Years Ago

Loan Amount $ 37,500,000

Loan Term 30 years

IO Rate 7.75%

Monthly Payment $ 242,187.50

Today

Mortgage Balance $ 37,500,000

Yield on US Treasuries 4.75%

+ Margin 1.50%

New IO Rate 6.25%

Spread 1.50%

Monthly Payment for YMF: (((0.0775 – 0.0625)/12) x $ 37,500.000) $ 46,875

YMF: PV of $46,875/month for 7 years discounted at 7.75% $ 3,031,635

New Loan Amount: ($ 37,500,000 + $ 3,031,635 + $150,000) $ 40,681,635

Monthly Payment on New Loan @ 6.25% $ 203,408.18

Monthly Savings: $ 38,779.32

Balance on New Loan: $ 40,681,635

Balance on Existing Loan: $ 37,500,000

Additional Lump Sum Payment in Ten Years $ 3,181,635

Cash flows:

Loan Fee Monthly Savings Lump Sum Payment

for 120 months in 120 Months

- $ 406,816.35 $ 38,779.32 - $ 3,181,635

(BT)NPV of cash flows discounted at 7%: + $ 1,349,936. DO IT!

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