Question

#2 MULTIPLE CHOICE (no need to show work but please get right)

1. A property recently sold for $444,000 (cash equivalent) and had $65,700 in potential gross income (PGI) for the following year. The expenses were 33% of the effective gross income (EGI). The vacancy and collection losses were estimated at 5%. What is the overall capitalization rate (RO)?

a) 9.42%

b) 9.91%

c) 14.06%

d) 14.93%

2. The subject is located in a market where lenders are making commercial loans on properties like the subject at 8.5% per year with monthly payments and a 20-year amortization with a 75% loan-to- value ratio. The equity dividend rate (RE) in this market is 10%. What is the overall capitalization rate?

a) 8.50%

b) 8.88%

c) 10.00%

d) 10.31%

3. If the overall capitalization rate is 9.5%, the mortgage constant is 7.755%, and the loan-to-value ratio is 80%, what is the equity dividend rate (RE)?

a) 7.76%

b) 8.10%

c) 9.50%

d) 16.48%

4. If the loan-to-value ratio is 75%, the mortgage capitalization rate (RM) is 10.55%, and the debt coverage ratio (DCR) is 1.25, what is the implied capitalization rate based on the debt coverage formula (underwriter’s method)?

a) 7.91%

b) 8.44%

c) 9.90%

d) 10.55%

5. A property sold for $2,345,000. The net operating income (NOI) is $255,000, and the expenses are 35% of the effective gross income (EGI). What is the effective gross income multiplier (EGIM)?

a) 4.60

b) 5.98

c) 9.20

d) 17.07

6. The subject property is expected to generate net operating income (NOI) over the next five years as shown in the following table. The resale of the property is estimated at $5 million at the end of the fifth year. The closing costs are estimated at 5% of the sale price. The discount rate is 9.5%. Cash flows are at the end of each year. What is the value of this investment? Round your answer to the nearest $1,000.

Year	Net Income
1	$ 250,000
2	$ 300,000
3	$ 350,000
4	$ 400,000
5	$ 450,000
Resale	$4,750,000
Disc. Rate	9.50%

a) $3,904,000

b) $4,065,000

c) $4,327,000

d) $4,500,000

7. An investment was purchased for $734,500 nine years ago. It had net lease payments of $56,000 per year for nine years and a resale of $850,000 (net of all costs). The discount rate is 10.5%. What is the net present value (NPV)?

a) $0

b) -$72,240

c) $72,240

d) $115,500

8. If an investment has an overall capitalization rate of 10% and the mortgage terms were 20 years at 6% interest with monthly payments, what is the equity capitalization rate? The mortgage is fully amortized, and the loan-to-value ratio is 75%.

a) 0.0355

b) 0.0645

c) 0.0860

d) 0.1421

9. A property was purchased for $1,250,000. The NOI is $100,000. Both the NOI and value are expected to increase at a compound rate of 1% per year. What yield will be achieved if the property is held for 10 years?

a) 9%

b) 10%

c) 11%

d) 12%

10. What is the mortgage constant for a loan with a 6.75% interest rate and a 20-year amortization period with monthly payments?

a) 6.22%

b) 7.60%

c) 9.12%

d) 10.00%

Answer 1

1). PGI = 65,700

EGI = PGI*(1-vacancy& collection loss %age) = 65,700*(1-5%) = 62,415

NOI = EGI*(1-expense %age) = 62,415*(1-33%) = 41,818.05

Capitalization rate = NOI/Market price = 41,818.05/444,000 = 9.42% (option a)

2). Overall capitalization rate = (LTV debt ratio*mortgage constant) + (LTV equity ratio* equity constant)

LTV debt ratio = 75%; LTV equity ratio = 25%

equity constant =equity dividend rate = 10% or 0.10

mortgage constant = Annual debt service/Principal amount

Assume that the total value is 1 million and a loan of 750,000 is taken.

PV = 750,000; N = 20*12 = 240; rate = 8.5%/12 = 0.71%, solve for PMT. PMT = 6,508.67

Annual debt service amount = 6,508.67*12 = 78,104.91

Mortgage constant = 78,104.91/750,000 = 0.1041

Overall cap. rate = (0.75*0.1041) + (0.25*0.10) = 10.31% (option d)

3). Using the equation for overall cap. rate in ans.2, we have

9.5% = (0.8*7.755%) + (0.2*r)

9.5% - 6.20% = 0.2r

r = 3.30%/0.2 = 16.48% (option d)

4). Implied capitalization rate = LTV ratio* mortgage constant * DSCR

= 75%*10.55%*1.25 = 9.89% (option c)

5) option b - 5.98

Gross income multiplier = (255,000/(1-35%))/2,345,000 = 5.98

6). Option c - 4,327,000

Year (n)	1	2	3	4	5	5
Cash flow	250,000	300,000	350,000	400,000	450,000	4,750,000
Discount factor	0.9132	0.8340	0.7617	0.6956	0.6352	0.6352
PV of cash flow	228,311	250,203	266,579	278,230	285,852	3,017,331
Total value	4,326,506

Rounding 4,326,506 to the nearest 1,000, we get 4,327,000