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

99750.00

99750.00

112205.18

112205.18

Interest

92155.1967

91463.34

90708.46

98939.00

97944.59

Principal

7594.80

8286.66

9041.54

13266.19

14260.60

EYR Bal.

1049033.61

1040746.95

1031705.41

1357410.61

1343150.01

 

 

 

 

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

Cost

1400000

Less MTG

1056628.41

Plus PTS

31698.8523

Cash Req.

375070.441

 

 

 

 

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 + )12
                                    = 40,727,27 * (12-5+)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