Flashcards in BUSI 300 Lesson 10 Deck (13)

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1

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Consider a property that will earn a rent of $10,000 per year in perpetuity. Suppose that the cap rate for real estate is 5%.

(a) Show that the current value of this property is $200,000.

(b) Suppose now that the rent that the property earns is expected to grow at 2% per year. Show that the current value of this property is now $333,333.

(c) Suppose now that the rent that the property earns is expected to grow at 2% per year, and that the property is subject to an annual property tax equal to 1% of value. Show that the current value of this property is now approximately $277,778. (Hint: Using Equation 11.7, property value under these conditions satisfies

P = R/(r - g) - T/r, where T is the annual property tax payment and the other variables are as defined in the text.)

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(a) By equation 11.5, P = 10,000/0.05 = 200,000.

(b) By equation 11.7, P = 10,000/(0.05 - 0.02) = 333,333.33

(c) This is a bit harder. Letting t be the property tax rate, we have T = tP. Substituting this into the expression given in the hint and solving for P yields P = R / (r-g)(1 + t/r), so, using the numbers given, P = 10,000/0.036 = 277,777.78.

Algebra for formula above:

1. Original in question: P = [R/(r-g)] - (T/r)

2. Substitute in tP for T , we get P = [R/(r-g)] - (tP/r)

3. Move tP/r to left hand side, we get P + tP/r = R/(r-g)

4. Pull P out, we get P(1+t/r) = R/(r-g)

5. Divide both sides by (1+t/r), we get P = R/[(r-g)(1+t/r)]

2

## Compare and contrast the market for real estate with the market for automobiles. What characteristics do these markets have in common, and what characteristics are unique to each market? Do these differences affect the ways that the markets operate, and if so how?

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Students should offer a wide range of answers for this question. Below are some suggested answers.

Some marks are awarded for effort and creativity. Common characteristics include: (a) Both are

durable goods, and therefore have both rental and ownership markets, (b) both also large items relative

to consumers' incomes, and are therefore financed through borrowing, (c) both represent bundles of

characteristics, making the comparison of the prices of different items difficult (in fact, the first

application of hedonic pricing was to the automobile market), (d) in both cases, prices are generally

determined through bargaining between buyer and seller, both of whom have some market power, (e)

both goods are traded through brokers, though this is more common in the case of real estate. Unique

characteristics include: (a) cars are mobile (!), while real estate is fixed in space, (b) real estate is more

heterogeneous, and consequently search costs are higher for real estate, and (c) cars depreciate much

more quickly. The consequences of these differences include: (a) there is generally not an excess

supply of automobiles in a long run equilibrium (no vacancies), (b) since real estate is fixed in space,

it's price varies with location, and (c) the stock of cars adjusts much more quickly to changing

circumstances than the stock of real estate does.

3

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Using the four quadrant model of the real estate industry, illustrate and briefly explain the impacts of the following events on rents, prices, new construction, and the stock of space:

(a) An increase in the perceived risk of real estate investment.

(b) An increase in the rate at which the stock of real estate space depreciates.

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(a) This increases the capitalization rate in the asset market, pivoting the R = rP line clockwise,

leading to an increase in R, and decreases in P, C and S.

(b) This increases the level of new construction needed to maintain the existing stock, pivoting the

C = dS line clockwise, leading to increases in R, P and C, and a decrease in S.

4

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There are benefits to having some vacancy in the market. What are two positive important functions of real estate vacancies?

A. Vacancies facilitate the search and match process between buyers and sellers.

B. Vacancies provide a leeway allowing builders to accommodate new demands.

C. Vacancies increase absorption rates in the area.

D. Vacancies only provide sellers with more market power.

(1) Only Statements A and C are correct.

(2) Only Statements B and D are correct.

(3) Only Statements A and B are correct.

(4) Only Statements C and D are correct.

### Answer: (3) Real estate vacancies serve two important functions. First, vacancies facilitate the search and match process through which buyers and sellers meet. Every real estate transaction involves a match between a buyer and a seller. Because the preferences of buyers and the characteristics of properties are all different, finding a suitable match can require an extensive search of the available stock. This can be very time consuming and therefore very costly. In order for this search and match process to function effectively, there needs to be an inventory of available space, much of which may be unoccupied, in any real estate market at every point in time. Vacancies provide an inventory of space to help sellers respond to unexpected changes in demand. It is very costly, and in some cases, impossible to build new real estate space on short notice. This is especially true for office space in or near the CBD. These inventories serve as a sort of buffer, allowing builders to accommodate new demands for space without incurring the very high cost of adding a small amount of new space each period.

5

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Recently, the demand for residential properties in the small town of Kyler has grown dramatically. The vacancy rates in Kyler are high. The Thompsons own six residential properties in Kyler of which four are occupied and two are vacant but on the market. The Thompsons always raise the rents of their properties when demand grows. What will happen if the Thompsons increase the rents of their properties? (Assume that the Thompsons have the right to change the rent of any of the properties whenever they see fit.)

(1) If the Thompsons choose to raise rents, it will keep vacancies from falling below their desired levels.

(2) If the Thompsons choose to raise rents, it will increase the amount of money they earn.

(3)If the Thompsons choose to raise rents, it will cause the vacant lots to be vacant for longer and it will increase the amount of money earned by the Thompsons.

(4)If the Thompsons choose to raise rents, it will cause the vacant lots to be vacant for a longer period of time. It will also cause the tenants of the occupied properties to consider moving.

### Answer: (4) If the vacancy rate in a market is high, then it may not be in the owner's interest to raise rents in response to a demand shock. Doing so would just cause vacant units to be unoccupied for a longer time. Conversely, when vacancy rates are low, and time on the market is short, an increase in demand should be followed by significant rent increases to keep vacancies from falling below their desired level.

6

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If the demand for the export good of Smallville increases, what will happen to the demand curve and the rent in the space market?

(1)The demand curve will shift up and rent will decrease. (2)The demand curve will shift down and rent will decrease.

(3) The demand curve will shift up and rent will increase. (4) The demand curve will shift down and rent will increase.

### Answer: (3) A favourable event in the market for the basic or export goods that a region produces will cause production there to rise and cause the prices of these inputs to rise. It will also increase the demand for employment, thereby pushing up the demand curve in the space market and making the equilibrium rent higher.

7

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Complete the following sentence which describes one of the most important links between the space and asset markets. The _________ of/on real estate space comprises the income stream that determines the ________ of/on real estate assets.

(1) rent, value

(2) value, demand

(3) improvements, supply

(4) growth, value

### Answer: (1) The rent on real estate space comprises the income stream that determines the value of real estate assets.

8

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Lindsay is considering buying a four bedroom residential property as an investment. She thinks that rents over the next four years will be exceptionally high at $26,000, $28,000, $31,000, and $27,000 per annum for the corresponding property she is looking at. She plans to sell the property after 4 years for $675,000. The rate of return on comparable investments is 9.6% per annum.

Approximately how much is Lindsay willing to spend today to purchase this property? (Round up to the next higher hundred dollars).

1) $383,500

2) $477,700

3) $557,100

4) $731,900

### Answer: (3) Using the formula Pt = Rt + 1/(1 + r) + Rt + 2/(1 + r) ^2) + Rt + 3/(1 + r) ^3) + ....... therefore we have Pt = $26,000/(1 + .096) + $28,000/(1 + 0.096)^2) + $31,000/(1 + 0.096) ^3) + $27,000/(1 + 0.096) ^4) + $675,000/(1 + 0.096) ^4) = $23,722.63 + $23,309.71 + $23,546.70 + $18,712.06 + $467,801.44 = $557,092.54. Rounded up to the next highest hundred dollars is $557,100

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Lindsay is considering buying a four bedroom residential property as an investment. She thinks that rents over the next four years will be exceptionally high at $26,000, $28,000, $31,000, and $27,000 per annum for the corresponding property she is looking at. She plans to sell the property after 4 years for $675,000. The rate of return on comparable investments is 9.6% per annum

Now assume that Lindsay is planning to buy this property and never sell it. Also, assume that she expects to always earn a rent of $29,000 per annum from the tenants of the residential property. If this is the case, how much would Lindsay be willing to spend to purchase this property? (Rounded to the nearest hundred dollars.)

1) $302,100

2) $437,600

3) $566,000

4) $599,300

### Answer: (1) Using the formula to find the value of an investment that pays a fixed amount each period in perpetuity is P = R/r = $2,900/0.096 = $302,083.33. Rounded up to the next highest hundred dollars is $302,100.

10

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Lindsay is considering buying a four bedroom residential property as an investment. She thinks that rents over the next four years will be exceptionally high at $26,000, $28,000, $31,000, and $27,000 per annum for the corresponding property she is looking at. She plans to sell the property after 4 years for $675,000. The rate of return on comparable investments is 9.6% per annum.

Now assume that Lindsay thinks that she will earn a rent of $29,000 in the first year, and the rent that she earns will grow at a rate 2.6% per annum every year after. She will never sell the property. How much would Lindsay be willing to spend to purchase this property? (Rounded to the nearest hundred dollars.)

1) $389,300

2) $414,300

3) $524,800

4) $583,300

### Answer: (2) Using the formula P = R/(r ! g), $29,000/(0.096 ! 0.026) = $29,000/0.07 = $414,285.71. Rounded up to the next highest hundred dollars is $414,300

11

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What should capitalization rates be based on?

1) The risk associated with a particular property class or location.

2) The overall level of interest rates in the economy.

3) The rates earned on other comparable properties.

4) All of the above are true.

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Answer: (4)

There are three basic determinants or components to the capitalization rate for real estate. First,

capitalization rates should depend on the overall level of interest rates in the economy. If interest rates

rise, then, other things being equal, we expect the yield on real estate investments to rise as well. By

the same token, the capitalization rate should also depend on the yields of other, comparable

investments. Second, capitalization rates should depend on the risk associated with a particular property

class or location. Third, capitalization rates should depend on the rate at which rents are expected to

grow in the future.

12

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In Holtsville over the last ten years there has been an increase in the number of telecommuters. This has led to a decrease in the demand for space. What will happen to rent, price, construction, and stock in Holtsville?

1) Rent and stock will decrease and price and construction will increase.

2) Rent and construction will increase and price and stock will decrease.

3) Rent, price, construction, and stock will decrease.

4) Rent, price, construction, and stock will increase.

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Answer: (3)

A decrease in the demand for space, shifts the demand curve down in the northeast quadrant, leading

to decreases in rent, price, construction, and stock.

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