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 
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 

Interest 
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  
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 
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. 
40,727 
40,727 
40,727 
40,727 

Less Pts. 
3,170 
3,170 
5,483 
5,483 

UnexpPts  
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  
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  
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
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 112
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 1324.
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.
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
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
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 
Depreciable basis = Purchase Price  Land = 1,400,000  (.2*1,400,000)
= 1,120,000
Depreciation for years 25 = 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 * (125+½)÷12 = 28,848.48
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
Cash flow from refinancing = New loan  points
paid  balance on old loan
= 1370674.55  1370674.55*.04  1031705.41 =
284,142.16
Taxes = Taxable Income * Tax Rate = 297924.40 * .31 = 92356.57