INVESTMENT PROPERTY ANALYSIS

Use the following information to answer questions 1 - 3.

You are considering the purchase of an office building for $1.5 million today. Your expectations include these: first-year gross potential income of $340,000; vacancy and collection losses equal to 15 percent of gross potential income; operating expenses equal to 45 percent of effective gross income. You expect to sell the property five years after it is purchased. You estimate that the market value of the property will increase four percent per year after it is purchased and you expect to incur selling expenses equal to 6 percent of the estimated future selling price.

1. What is the estimated net operating income (NOI) for the first year of operations?

Solution:

Item	Amount
Potential gross income	$340,000
less: V&C allowance (at 15% of PGI)	51,000
Effective gross income	289,000
less: Operating expenses	130,000
Net operating income	$158,950

2. What is the estimated overall rate of return (capitalization rate) for the first year of operations?

Solution: The overall rate = NOI / PRICE = $158,950 / $1,500,000 = 0.106 = 10.6 percent

3. What dollar amount will you net from the sale of the property at the end of year 5?

Solution:

Item	Amount
Selling price (SP)	$1,824,979
less: Selling expenses (at 6% of SP)	109,499
Net selling price	$1,715,480

4. A retail shopping center is purchased for $2.1 million for 1996. During the next four years, the property appreciates at four percent per year. At the time of purchase, the property is financed at a 75 percent loan to value ratio for 30 years at eight percent with monthly amortization. At the end of year 4, the property is sold with eight percent selling expenses. What is the before-tax equity reversion?

Solution:

Item	Amount
Loan amount = 0.75 x (2,100,000)	$1,575,000
Monthly payments	11,556.79
Remaining mtg. balance	1,515,450

Selling price [2,100,000 x (1.04)⁴]	2,456,703
less: Selling expenses (at 8% of SP)	196,536
Net selling price	2,260,167
less: Unpaid mtg. balance	1,515,450
Before-tax equity reversion	$ 744,717

5. An office building is purchased with the following projected cash flows:

-NOI is expected to be $130,000 in year 1 with five percent annual increases.

-The purchase price of the property is $720,000.

-100% equity financing is used to purchase the property

-The property is sold at the end of year 4 for $860,000 with selling costs of four percent.

-The before-tax required rate of return is 14 percent.

a. Calculate the before-tax internal rate of return (IRR).

b. Calculate the before-tax net present value (NPV).

Solution:

Year	Purchase Price	Net Operating Income	Net Selling Price	Total Cash Flow	Present Value at 14%
0	($720,000)			($720,000)	($720,000)
1		130,000		130,000	114,035
2		136,500		136,500	105,032
3		143,325		143,325	96,740
4		150,491	825,600	$976,091	$577,924

NPV = 173,732

IRR = 21.88 percent

6. With a purchase price of $350,000, a warehouse provides for an initial before-tax cash flow of $30,000, which grows by six percent per year. If the before-tax equity reversion after four years equals $90,000, and an initial equity investment of $175,000 is required, what is the IRR on the project? If the before-tax required rate of return on the project is 10 percent, should the project be undertaken?

Solution:

Year	Purchase Price	Net Operating Income	Net Selling Price	Total Cash Flow	Present Value at 14%
0	($175,000)			($175,000)	($175,000)
1		30,000		30,000	27,273
2		31,800		31,800	26,281
3		33,708		33,708	25,325
4		35,730	90,000	$125,730	$85,875

NPV = ($10,246)

IRR = 7.84 percent

7. You are considering the acquisition of an office building. The purchase price is $775,000. Seventy-five percent of the purchase price can be borrowed with a 30-year, 7.5 percent mortgage. Payments will be made annually. Up-front financing costs will total three percent of the loan amount. The expected before-tax cash flows from operations—assuming a 5-year holding period—are as follows:

Year	Expected NOI
1	$48,492
2	53,768
3	59,282
4	65,043
5	71,058

The before-tax cash flow from the sale of the property is expected to be $295,050. What is the net present value of this investment, assuming a 12 percent required rate of return? What is the before-tax internal rate of return?

Solution:

Borrow 75% of purchase price = 0.75 x 775,000 = $581,250

CF₀ = fraction of purchase price not financed using debt + up-front financing costs

= 25% of purchase price + 3% of loan amount

= (0.25 x $775,000) + (0.03 x $581,250) = $193,750 + $17,438 = $211,188 outflow

N = 30

I/YR = 7.5%

PV = 581,250

PMT = ?

FV = 0

Debt service equals $49,215 annually.

Year	Equity Investment	NOI	Debt Service	BTER	Total Cash Flow	Present Value at 14%
0	($211,188)				($211,188)	($211,188)
1		48,492	49,215		(723)	(646)
2		53,768	49,215		4,553	3,630
3		59,282	49,215		10,067	7,165
4		65,043	49,215		15,828	10,059
5		71,058	49,215	295,050	$316,893	$179,814

NPV = ($11,166)

IRR = 10.75 percent

Use the following information to answer questions 8-11.

You are considering the purchase of an apartment project for $1.4 million today. Your expectations include these: first-year gross potential income of $230,000; vacancy and collection losses equal to seven percent of gross potential income; and operating expenses equal to 30 percent of the effective gross income. You can obtain a standard fixed-rate mortgage for 80 percent of the purchase price at 10 percent (annual) interest for 30 years. Payments will be made monthly.

8. What is the total amount of debt service for the first year of operations?

Solution: Loan amount = 0.80 x (1,400,000) = 1,120,000

Monthly payment = $9,828.80

Annual payment = monthly payment x 12 = 9,828.80 x 12 = $117,945.62

9. How much mortgage interest will be paid during the first year?

Solution: Remaining mortgage balance = $1,113,774

Interest = 117,946 - (1,120,000 - 1,113,774) = 117,946 - 6,226 = $111,720

10. Calculate the expected net operating income for the first year.

Solution:

Item	Amount
Potential gross income	$230,000
less: V&C allowance (at 7% of PGI)	16,100
Effective gross income	213,900
less: Operating expenses	64,170
Net operating income	$149,730

Note: Cap Rate = NOI / VALUE = 149,730 / 1,400,000 = 10.7%

11. After servicing the mortgage debt, how much income from the property in the first year will be available to pay federal income taxes?

Solution:

Item	Amount
Net operating income	$149,730
less: Debt service	117,946
Before-tax cash flow	$ 31,784

Case Problems

1. An investment opportunity having a market price of $100,000 is available. You could obtain a $75,000, 25-year mortgage loan requiring equal monthly payments with interest at 9.5 percent. The following operating results are expected during the first year.

Effective gross income	$25,000
less: operating expenses	13,000
NOI	$12,000

For the first year only, determine the:

a. Gross income multiplier

Solution: Market price / Gross income = $100,000 / $25,000 = 4

b. Operating expense ratio

Solution: Operating expenses / Effective gross income = $13,000 / $25,000 = 52 percent

c. Debt coverage ratio

Solution: NOI / Annual debt service = $12,000 / $7,863 = 1.5

d. Overall cap rate

Solution: NOI / Market price = $12,000 / $100,000 = 12 percent

e. Equity dividend rate

Solution: Before-tax cash flow / Equity = $4,137 / $25,000 = 16.5 percent

2. You are considering the purchase of a quadruplex apartment. Effective gross income during the first year of operations is expected to be $33,600 ($700 per month per unit). First-year operating expenses are expected to be $13,440 (at 40 percent of EGI). The purchase price of the quadruplex is $200,000. The acquisition will be financed with $60,000 in equity and a $140,000 standard fixed-rate mortgage. The interest rate on the debt financing is eight percent and the loan term is 30 years. Assume, for simplicity, that payments will be made annually and that there are no up-front financing costs.

a. What is the (overall) capitalization rate?

Solution: NOI / Market price = $20,160 / $200,000 = 10.08 percent

b. What is the (effective) gross multiplier?

Solution: Market price / Effective gross income = $20,000 / $33,600 = 5.95

c. What is the equity dividend rate (i.e., the before-tax return of equity)?

Solution: Debt service = $12,435

Before-tax cash flow = NOI - Debt service = $20,160 - $12,435 = $7,725

Equity dividend rate = Before-tax cash flow / equity invested = $7,725 / $60,000 = 12.88 percent

d. What is the debt coverage ratio?

Solution: NOI / debt service = $20,160 / $12,435 = 1.62

e. Assume the lender requires a minimum debt coverage ratio of 1.2. What is the largest loan that you could obtain if you decided that you wanted to borrow more than $140,000?

Solution: Minimum debt coverage ratio

= NOI / debt service = 1.2 = $20,160 / (loan amount x mortgage constant)

Loan amount = $20,160 / (1.2 x mortgage constant) = $20,160 / (1.2 x 0.0888)

Loan amount = $20,160 / (0.1066) = $189,130

3. You are considering the purchase of an apartment complex. The following assumptions are made:

-The purchase price is $1,000,000.

-Potential gross income (PGI) for the first year of operations is projected to be $171,000.

-PGI is expected to increase at 4 percent per year.

-No vacancies are expected.

-Operating expenses are estimated at 35 percent of the effective gross income.

-The market value of the investment is expected to increase 4 percent per year.

-Selling expenses will be 4 percent.

-The holding period is 4 years.

-The appropriate rate of return to discount projected NOIs and the projected NSP is 12 percent.

-The after-debt required rate of return is 14 percent.

-70 percent of the purchase price can be borrowed with a 30-year, monthly payment mortgage.

-The annual interest rate on the mortgage will be 11.5 percent.

-Financing costs will equal 2 percent of the loan amount.

-There are no prepayment penalties.

a. Calculate the net operating income (NOI) for each of the four years.

Solution:

Item	1	2	3	4
PGI	$171,000	$177,840	$184,954	$192,352
less: V&C	0	0	0	0
EGI	171,000	177,840	184,954	192,352
less: OE	59,850	62,244	64,734	64,323
NOI	$111,150	$115,596	$120,220	$125,029

b. Calculate the net selling price from the sale of the property.

Solution:

Item	Amount
Selling price [1,000,000 x (1.04)⁴]	$1,169,859
less: Selling expenses (at 4% of SP)	46,794
Net Selling price	$1,123,065

c. Calculate the net present value of this investment (assuming no mortgage debt). Should you purchase? Why?

Item	Cash Flow	Present Value at 12%
NOI Yr.1	$111,150	$99,241
NOI Yr.2	115,596	92,152
NOI Yr.3	120,220	85,570
NOI Yr.4	125,029	79,458
Reversion Yr. 4	1,123,065	713,727
Total		$1,070,150

d. Calculate the internal rate of return of this investment (assuming no mortgage debt). Should you purchase? Why?

Solution: IRR = 14.2 percent. Purchase, because before-debt required rate of return is 12 percent

e. Calculate the monthly mortgage payment. What is the total per year?

Solution: Monthly payment = $6,932 Annual payment = monthly payment x 12 = $83,184

f. Calculate the loan balance at the end of years 1, 2, 3, and 4. (Note: the unpaid mortgage balance at any time is equal to the present value of the remaining payments, discounted at the contract (face) rate of interest.)

Solution:

Unpaid mortgage balance in year 1 = $6,932 x (PVAF _{11.5%, 29}) = $697,169

Unpaid mortgage balance in year 2 = $6,932 x (PVAF _{11.5%, 28}) = $693,996

Unpaid mortgage balance in year 3 = $6,932 x (PVAF _{11.5%, 27}) = $690,437

Unpaid mortgage balance in year 4 = $6,932 x (PVAF _{11.5%, 26}) = $686,447

g. Calculate the amount of principal reduction achieved during each of four years.

Solution:

Principal reduction in year 1 = $700,000 - $697,169 = $2,831

Principal reduction in year 2 = $697,169 - $693,996 = $3,173

Principal reduction in year 3 = $693,996 - $690,437 = $3,559

Principal reduction in year 4 = $690,437 - $686,447 = $3,990

h. Calculate the total interest paid during each of the four years. (Note: Remember that debt service equals principal plus interest.)

Solution:

Interest paid in year 1 = $83,184 - $2,831 = $80,354

Interest paid in year 2 = $83,184 - $3,173 = $80,011

Interest paid in year 3 = $83,184 - $3,559 = $79,626

Interest paid in year 4 = $83,184 - $3,990 = $79,194

i. Calculate the (after-debt) required initial equity investment.

Solution: Loan amount (0.70 x $1,000,000) = $700,000

Up-front financing costs (0.02 x $700,000) = $14,000

Equity investment = $1,000,000 - $700,000 + $14,000 = $314,000

j. Calculate the before-tax cash flows (BTCF) for each of the four years.

Solution:

Item	1	2	3	4
NOI	$111,150	$115,596	$120,220	$125,029
less: Debt Service	83,184	83,184	83,184	83,184
BTCF	$27,966	$32,412	$37,036	$41,845

k. Calculate the before-tax equity reversion (BTER) from the sale of the property.

Solution:

Item	Amount
Net selling price	$1,123,064
less: Unpaid mortgage balance in year 4	686,447
Before-tax equity reversion	$436,618

l. Calculate the (after-debt) net present value of this investment. Should you purchase? Why?

Solution:

Item	Cash Flow	Present Value at 12%
NOI Yr.1	$27,966	$24,532
NOI Yr.2	32,412	24,940
NOI Yr.3	37,035	24,998
NOI Yr.4	41,844	24,775
Reversion Yr. 4	436,618	258,513
Total		$357,758

NPV = Present value of the cash flows less the equity investment = $357,758 - $314,000 = $43,758

Decision: Purchase the property because the NPV > 0; wealth will increase by $43,758.

m. Calculate the (after-debt) internal rate of return of this investment (assuming no debt and no taxes). Should you purchase? Why?

Solution: IRR = 18.2 percent

Decision: Purchase the property because IRR > 13 percent, the required return.

n. Calculate, for the first year of operations, the: (1) overall capitalization rate, (2) (after-debt) return on equity, (3) gross multiplier, (4) debt coverage ratio.

Solution:

Overall capitalization rate = NOI / Market price = $111,150 / $1,000,000 = 11.12 percent

Return on equity = BTCF / equity = $27,966 / $314,000 = 8.9 percent

Gross rent multiplier = Market price / EGI = $1,000,000 / $171,000 = 5.84

Debt service coverage ratio = NOI / Debt service = $111,150 / $83,184 = 1.34

4. Shown is the actual three-year operating statement of a two-story store and apartment building.

	3 Years	2 Years	Last year
Income (actual)
Store rentals	$21,600	$22,400	$24,000
Apartment rentals	16,500	17,900	17,700
Effective Gross Income	$38,000	$40,300	$41,700

Expenses
Taxes, real estate	5,200	5,200	5,400
Insurance	1,300	50	150
Utilities	2,500	2,900	2,800
Custodian	1,800	2,000	2,100
Supplies	116	190	125
Repairs	616	8,000	3,100
Miscellaneous	1,000	1,100	900
Total Expenses	$12,532	$19,440	$14,575

Net Operating Income	$25,568	$20,860	$27,125

In addition, you have the following information: (1) Insurance premiums on the various policies are paid for a three-year period and come due at various times; (2) utilities are expected to be the average of the last three years, plus 5 percent; (3) many major repairs were made two years ago, and expensive repairs should not be needed for another 10 years.

Prepare a reconstructed operating statement for this year using the information given and your common sense as a guide. Be sure to explain your choices. Use percentages in your analysis where appropriate.

Solution:

	This year
Income
Store rentals (based on 5.4% increase over past 2 years)	$25,292
Apartment rentals (based on 3.7% increase over past 2 years)	18,355
Effective Gross Income	$43,651

Expenses
Taxes, real estate (same as last year)	5,400
Insurance (same as 3 years ago)	1,500
Utilities (average of last 3 years + 5%)	2,870
Custodian (increase $150 over last year)	2,250
Supplies (average of last 3 years)	144
Repairs (average of last year and 3 years ago)	1,858
Miscellaneous (average of last 3 years)	1,000
Total Expenses	$15,022

Net Operating Income	$28,629