Practice Problem III

You are considering purchasing an apartment for \$1,400,000 which contains 30 one bedroom apartments and 10 two bedroom apartments with a closing on May 28th. Land is estimated to be 20% of the purchase price. The one bedroom apartments are expected to rent for \$450 per month and the two bedroom apartments are expected to rent for \$650 per month. You expect rents to increase by 4% per year. You project that your vacancy and collection losses will be about 5%. You expect that operating expenses will be 30% of the adjusted gross income. The Friendly Federal Savings Bank has agreed to lend to you at a 8.75% annual interest rate with an amortization period of 30 years paid monthly. The loan will have only a term of 10 years. The amount of the loan is going to be based upon a 1.6 Debt Service Coverage Ratio for the first year's NOI. The bank is going to charge three points. On January 1 of the forth year, you expect to refinance the project with a new loan from Friendly Federal at 7.25% with a thirty year amortization, also a ten year term, with only a 4 point loan origination fee which is to be paid out of the proceeds from refinancing. The loan amount will be based upon a 1.6 DSCR of the year four NOI. Your accountant has advised you that for this investment analysis, you should use expect a 31% marginal tax rate. You expect to sell the property at the end of the fifth year. The sales price is expected to be based upon an 11.5% capitalization rate of the year six NOI. Sales expenses are projected at 7%. Your cost of equity capital is 12%.

1. What is the loan amount and the monthly and annual debt service? (2 points)

 Loan Amount \$1,056,628.41 PDS \$8,312.50 Annual Debt Service \$ 99,750.00

2. Prepare an amortization schedule for the first three years for the original mortgage and two more years for the refinanced mortgage which shows the annual debt service, the annual interest charge, the principal paid, and the balance at the end of the year. (3 points)

 1 2 3 4 5 ADS 99750 99750 99750 112205 112205 Interest 92155.2 91463.3 90708.5 98939 97944.6 Principal 7594.8 8286.66 9041.54 13266.2 14260.6 EYR Bal. 1.04903e+06 1.04075e+06 1.03171e+06 1.35741e+06 1.34315e+06

3. How much equity cash is required? (2 points)

 Cost 1.4e+06 Less MTG 1.05663e+06 Plus PTS 31698.9 Cash Req. 375070

4. Project the expected after tax cash flows for each of the five years of the holding period. Also project the sixth year NOI. (5 points)

 1 2 3 4 5 6 GPI 240,000 249,600 259,584 269,967 280,766 291,997 Less V&C 12000 12480 12979.2 13498.368 14038.303 14599.835 Adj Gross 228,000 237,120 246,605 256,469 266,728 277,397 Less Exp. 68400 71136 73981.44 76940.6976 80018.326 83219.059 NOI 159,600 165,984 172,623 179,528 186,709 194,178 Less ADS 99750 99750 99750 112205.184 112205.18 BTCF 59,850 66,234 72,873 67,323 74,504 Less Int. 92,155 91,463 90,708 98,939 97,945 Less Dep. 25455 40,727 40,727 40,727 40,727 Less Pts. 3,170 3,170 3,170 5,483 5,483 UnexpPts 22,189 Tax Inc. 38,820 30,624 38,018 12,190 42,555 Tax 12,034 9,493 11,785 3,779 13,192 ReFin Cash 284,142 ATCF 47,816 56,741 61,088 347,686 61,312

5. What is the after tax cash flow from reversion? (4 points)

 Sale Price 1688502.64 Basis Less S/E -135080.21 Cost 1400000 A/R 1553422.43 Acc. Depr. 188,364 Less Mtg -1343150.01 A/B 1,211,636 BTCFr 210272.41 A/R 1553422.43 Less A/B -1211636.36 Tax. Gain 341786.06 UnexpPts 43861.66 Tax Inc 297924.40 Taxes 92356.57 ATCFr 117915.85

6. What is the NPV for this investment? (2 points)

 NPV= 78,998

7. What is the indicated internal rate of return? (2 points)

 IRR= 18.09%

8. What is the indicated financial manager's rate of return (FMRR)? (2 points)

 FMRR= 16.36% Initial Cost -375070.4407 Terminal Value \$800,223.33

Annual Debt Service = NOI/DSCR = 159,600/1.6 = 99,750

Periodic Debt Service (PDS) = 99,750/12 = 8,312.50

Loan Amount:  PMT = 8,312.50; n=360; i/yr = 8.75 Solve for PV = 1,056,628.41

Back to Question 1

To calculate an amortization schedule on the HP10B, first enter the original mortgage information:

PMT = 8,312.50; n=360; i/yr = 8.75 Solve for PV = 1,056,628.41

Next hit the cream key then the AMORT key (the FV key), the display shows PEr 1-12

Hit the equals sign (=).  Display flashes Int then shows the interest paid during the first 12 months = 92,155.20

Hit the equals sign (=) again.  Display flashes Prin then shows the principle paid during the first 12 months = 7,594.80

Hit the equals sign (=) again.  Display flashes bAL then shows the balance at the end of  the first 12 months = 1,049,033.61

To calculate the amortization schedule for the next 12 months, simply hit the cream key then the AMORT key (the FV key), the display shows PEr 13-24.

Then hit the equals sign (=) again.  Then you can display the interest, principle, and balance for the second 12 payments.

Keep repeating the process for the remainder of the desired amortization schedule.

Back to Question 2

Points charge = Loan amount * points = 1,056,628.41 * .03 = 31698.85
Points must be amortized over the live of the loan (10 years in this problem)
Annual Expense = 31,698.85 ÷ 10 = 3,169.89

Back to Question 3

When the loan is refinanced in year 4, only 3 years of points have been expensed.  The remaining points can be expensed in the year of refinancing.
Unexpensed points charge = Original points - points expensed = 31698.85 - 3*3169.89
= 22,189.18

Back to Question 4

 GPI 240,000 = (30*450 + 10*650)*12 Less V&C 12000 = 240,000 * .05 Adj Gross 228,000 = 240,000 - 12000 Less Exp. 68400 = 228,000 * .3 NOI 159,600 = 228,000 - 68400

Back to Question 4

Depreciation Calculation

Depreciable basis  = Purchase Price - Land = 1,400,000 - (.2*1,400,000)
= 1,120,000

Depreciation for years 2-5 = Depreciable Basis ÷ Class Life = 1,120,000 ÷ 27.5
= 40,727.27

Depreciation for year 1 =  depreciation * (12 - month placed in service + ½)÷12
= 40,727,27 * (12-5+½)÷12  = 28,848.48

Back to Question 4

Refinancing:

Annual Debt Service = NOI/DSCR = 179,528/1.6 = 112,205

Periodic Debt Service (PDS) = 112,205/12 = 9,350.42

Loan Amount:  PMT = 9,350.42; n=360; i/yr = 7.25 Solve for PV = 1,370,674.55

Back to Question 2

Cash flow from refinancing = New loan - points paid - balance on old loan
= 1370674.55 - 1370674.55*.04 -
1031705.41 = 284,142.16

Back to Question 4

Taxes = Taxable Income * Tax Rate = 297924.40 * .31 = 92356.57