# Application chapters 10 - 15 Flashcards

## solving equations

Using the same values except that the

construction costs are fixed at $86,667 (the original expected value), find the

value of the land. Value of land if economy improves $160,000. Then with the value of land if economy falters $70,000. Then the risk-neutral probability of the economy improvement 33.33%. The riskless interest rate is zero.

Current Value = Expected Value = (UpValue x UpProb)

+ [DownValue x (1− UpProb)]

(value of land if economy improves - construction cost if economy improves) x risk-neutral probability of economy improvement + (value of land if economy falters - construction cost if economy falters) x 1 -risk-neutral probability of economy faltering

($160,000.00 - $86,667.00) x 2/3 + ($70,000 - $86,667) x 1 -2/3

= 24,441.89

riskless interest rate meaning that when the value goes below zero, it then is equal to zero.

(-$11,111.89)

Using the same values except that the

construction costs are $100,000 if the economy improves, $80,000 if the economy falters, find the

value of the land. Value of land if economy improves $160,000. Then with the value of land if economy falters $70,000. Then the risk-neutral probability of the economy improvement 33.33%. The riskless interest rate is zero.

Current value = expected value = (UpValue x UpProb) + (DownValue x (1 - UpProb))

(160,000 - 100,000)(1/3) + (70,000 - 80,000)(1 - 1/3) = $20.000

Using the same values except that the

construction costs are $75,000 if the economy improves, $37,500 if the economy falters, find the

value of the land. Value of land if economy improves $150,000. Then with the value of land if economy falters $75,000. Then the risk-neutral probability of the economy improvement 25.00%. The riskless interest rate is zero.

?

Using the same values except that the

construction costs are $125,000 if the economy improves, $62,500 if the economy falters, find the

value of the land. Value of land if economy improves $250,000. Then with the value of land if economy falters $125,000. Then the risk-neutral probability of the economy improvement 50%. The riskless interest rate is zero.

?

Using the same values except that the

construction costs are $100,000 if the economy improves, $50,000 if the economy falters, find the

value of the land. Value of land if economy improves $200,000. Then with the value of land if economy falters $100,000. Then the risk-neutral probability of the economy improvement 75%. The riskless interest rate is zero.

?

Using the same values except that the

construction costs are $50,000 if the economy improves, $25,000 if the economy falters, find the

value of the land. Value of land if economy improves $100,000. Then with the value of land if economy falters $50,000. Then the risk-neutral probability of the economy improvement 10%. The riskless interest rate is zero.

?

Using the same values except that the

construction costs are $47,500 if the economy improves, $23,750 if the economy falters, find the

value of the land. Value of land if economy improves $100,000. Then with the value of land if economy falters $47,500. Then the risk-neutral probability of the economy improvement 20%. The riskless interest rate is zero.

?

Return to the original values and find the value

of the land, assuming that economic uncertainty increases such that improved

properties either rise to $180,000 or fall to $60,000, with all other values

remaining the same. Following the same math, the risk-neutral probabilities are

the same (the up probability is 1/3). The value to developing is $80,000 in the up

state and $0 in the down state (the construction costs exceed the developed

value). Construction cost if the economy improves $100,000.

Current value = expected value = (UpValue x UpProb) + (DownValue x (1 - UpProb)

The option price rises to $26,667 ($80,000 x 1/3). This value is higher

than in the original example and demonstrates that volatility favors the option

holder. Higher volatility increases the upside profit potential without increasing

the loss potential due to the limited downside risk afforded by long option

positions

Return to the original values and find the value

of the land, assuming that economic uncertainty increases such that improved

properties either rise to $200,000 or fall to $190,000, with all other values

remaining the same. Following the same math, the risk-neutral probabilities are

the same (the up probability is 1/3). The value to developing is $80,000 in the up

state and $0 in the down state (the construction costs exceed the developed

value). Construction cost if the economy improves $100,000.

?

Return to the original values and find the value

of the land, assuming that economic uncertainty increases such that improved

properties either rise to $250,000 or fall to $100,000, with all other values

remaining the same. Following the same math, the risk-neutral probabilities are

the same (the up probability is 25%). The value to developing is $80,000 in the up

state and $0 in the down state (the construction costs exceed the developed

value). Construction cost if the economy improves $100,000.

?

Return to the original values and find the value

of the land, assuming that economic uncertainty increases such that improved

properties either rise to $150,000 or fall to $50,000, with all other values

remaining the same. Following the same math, the risk-neutral probabilities are

the same (the up probability is 50%). The value to developing is $80,000 in the up

state and $0 in the down state (the construction costs exceed the developed

value). Construction cost if the economy improves $100,000.

?

Return to the original values and find the value

of the land, assuming that economic uncertainty increases such that improved

properties either rise to $200,000 or fall to $100,000, with all other values

remaining the same. Following the same math, the risk-neutral probabilities are

the same (the up probability is 75%). The value to developing is $80,000 in the up

state and $0 in the down state (the construction costs exceed the developed

value). Construction cost if the economy improves $100,000.

?

Return to the original values and find the value

of the land, assuming that economic uncertainty increases such that improved

properties either rise to $350,000 or fall to $200,000, with all other values

remaining the same. Following the same math, the risk-neutral probabilities are

the same (the up probability is 10%). The value to developing is $80,000 in the up

state and $0 in the down state (the construction costs exceed the developed

value). Construction cost if the economy improves $100,000.

?

Return to the original values and find the value

of the land, assuming that economic uncertainty increases such that improved

properties either rise to $100,000 or fall to $50,000, with all other values

remaining the same. Following the same math, the risk-neutral probabilities are

the same (the up probability is 20%). The value to developing is $80,000 in the up

state and $0 in the down state (the construction costs exceed the developed

value). Construction cost if the economy improves $100,000.

?

Land that remains undeveloped is estimated to

generate an expected return of 5%, and land that is developed is estimated to

generate an expected single-period return of 25%. If the probability that a parcel

of land will be developed is 10% over the next period, what is its expected

return?

Current value = expected value = (UpValue x UpProb) + (DownValue (1 - UpProb)

(0.25% x 0.10%) + (0.05% (1 - 0.10)

= 0.07 (7%)

Land that remains undeveloped is estimated to

generate an expected return of 5.50%, and land that is developed is estimated to

generate an expected single-period return of 20%. If the probability that a parcel

of land will be developed is 15% over the next period, what is its expected

return?

?

Land that remains undeveloped is estimated to

generate an expected return of 10%, and land that is developed is estimated to

generate an expected single-period return of 30%. If the probability that a parcel

of land will be developed is 5% over the next period, what is its expected

return?

?

Land that remains undeveloped is estimated to

generate an expected return of 2.50%, and land that is developed is estimated to

generate an expected single-period return of 35%. If the probability that a parcel

of land will be developed is 20% over the next period, what is its expected

return?

?

Land that remains undeveloped is estimated to

generate an expected return of 4%, and land that is developed is estimated to

generate an expected single-period return of 27%. If the probability that a parcel

of land will be developed is 9% over the next period, what is its expected

return?

?

Land that remains undeveloped is estimated to

generate an expected return of 6%, and land that is developed is estimated to

generate an expected single-period return of 21%. If the probability that a parcel

of land will be developed is 7.5% over the next period, what is its expected

return?

?

Land that remains undeveloped is estimated to

generate an expected return of 8%, and land that is developed is estimated to

generate an expected single-period return of 33%. If the probability that a parcel

of land will be developed is 6% over the next period, what is its expected

return?

?

Land that remains undeveloped is estimated to

generate an expected return of 5%, and land that is developed is estimated to

generate an expected single-period return of 25%. If 20% of land in a database is

developed in a particular year, by how much will an index based on land that

remains undeveloped understate the average return on all land?

Current value = expected value = (UpValue x UpProb) + (DownValue (1 - UpProb)

(0.25% x 0.20%) + (0.05% (1 - 0.20%) = 0.09 (9%)

Land that remains undeveloped is estimated to

generate an expected return of 5.5%, and land that is developed is estimated to

generate an expected single-period return of 20%. If 15% of land in a database is

developed in a particular year, by how much will an index based on land that

remains undeveloped understate the average return on all land?

?

Land that remains undeveloped is estimated to

generate an expected return of 6.5%, and land that is developed is estimated to

generate an expected single-period return of 30%. If 25% of land in a database is

developed in a particular year, by how much will an index based on land that

remains undeveloped understate the average return on all land?

?

Land that remains undeveloped is estimated to

generate an expected return of 6%, and land that is developed is estimated to

generate an expected single-period return of 35%. If 30% of land in a database is

developed in a particular year, by how much will an index based on land that

remains undeveloped understate the average return on all land?

?

Land that remains undeveloped is estimated to

generate an expected return of 7%, and land that is developed is estimated to

generate an expected single-period return of 40%. If 35% of land in a database is

developed in a particular year, by how much will an index based on land that

remains undeveloped understate the average return on all land?

?

Land that remains undeveloped is estimated to

generate an expected return of 4.5%, and land that is developed is estimated to

generate an expected single-period return of 45%. If 5% of land in a database is

developed in a particular year, by how much will an index based on land that

remains undeveloped understate the average return on all land?

?

Land that remains undeveloped is estimated to

generate an expected return of 4%, and land that is developed is estimated to

generate an expected single-period return of 27%. If 10% of land in a database is

developed in a particular year, by how much will an index based on land that

remains undeveloped understate the average return on all land?

?

If the annual revenue in Exhibit 10.4 is

expected to rise to $40,000 and the market cap rate rises to 8%, then with all

other values remaining constant, the farmland’s price would rise to $400,000

[($40,000 – $6,000 – $2,000)/0.08]. With a price of $360,000 and an annual

operating income of $40,000, what would the cap rate be?

exhibit 10.4: Purchase price $300,000 Financing $150,000 Equity investment $150,000 Annual revenues $30,000 Less real estate taxes $6,000 Less insurance $2,000 Operating income $22,000 Less interest $12,000 Net income $10,000 ROE = $10,000/$150,000 = 6.67%

Value of Real Estate = Annual Operating Income / Cap Rate

$360,000 = $40,000 / cap rate

Cap rate = 40,000/360,000 = 11.11%

If the annual revenue in Exhibit 10.4 is

expected to rise to $45,000 and the market cap rate rises to 8%, then with all

other values remaining constant, the farmland’s price would rise to $400,000

[($45,000 – $6,000 – $2,000)/0.08]. With a price of $365,000 and an annual

operating income of $45,000, what would the cap rate be?

value of real estate = annual operating income / cap rate

365,000 = 45,000 / cap rate

cap rate = 45,000/365,000 = 0.123287671233 (12.33%)

If the annual revenue in Exhibit 10.4 is

expected to rise to $55,000 and the market cap rate rises to 8%, then with all

other values remaining constant, the farmland’s price would rise to $400,000

[($55,000 – $6,000 – $2,000)/0.08]. With a price of $375,000 and an annual

operating income of $55,000, what would the cap rate be?

?

If the annual revenue in Exhibit 10.4 is

expected to rise to $60,000 and the market cap rate rises to 8%, then with all

other values remaining constant, the farmland’s price would rise to $400,000

[($60,000 – $6,000 – $2,000)/0.08]. With a price of $380,000 and an annual

operating income of $60,000, what would the cap rate be?

?

If the annual revenue in Exhibit 10.4 is

expected to rise to $65,000 and the market cap rate rises to 8%, then with all

other values remaining constant, the farmland’s price would rise to $400,000

[($65,000 – $6,000 – $2,000)/0.08]. With a price of $385,000 and an annual

operating income of $65,000, what would the cap rate be?

?

If the annual revenue in Exhibit 10.4 is

expected to rise to $35,000 and the market cap rate rises to 8%, then with all

other values remaining constant, the farmland’s price would rise to $400,000

[($35,000 – $6,000 – $2,000)/0.08]. With a price of $400,000 and an annual

operating income of $35,000, what would the cap rate be?

?

Futures contracts on crude oil are often

denominated in 1,000-barrel sizes. In other words, each contract calls for the

holder of a short position at the delivery date of the futures contract to deliver to

the long side 1,000 barrels of the specified grade of oil using stated delivery

methods. Assume that a trader establishes a long position of five contracts in

crude oil futures at the then-current futures market price of $100 per barrel. Both

the trader on the long side of the contract and the trader on the short side of the

contract post collateral (margin) of, say, $10 per barrel. At the end of the day, the

market price of the futures contract falls to $99. How much money will each side

of the contract have (assuming that the required collateral was the only cash and

that there were no other positions)?

Market price - Future market price

$100 - $99 = $1

Each contract 1,000 barrels x number of contracts

1000 x 5 = 5,000

The long position lost 5,000 multiplied by $1 = $5,000

The short position is exactly the opposite so it gained $5,000.

The futures margin is $10 per barrel. So, both long and short, posted $10 x 5000 = $50,000 margin.

Long position = $50,000 - $5,000 = $45,000

Short position = $50,000 + $5,000 = $55,000

Futures contracts on crude oil are often

denominated in 1,000-barrel sizes. In other words, each contract calls for the

holder of a short position at the delivery date of the futures contract to deliver to

the long side 1,000 barrels of the specified grade of oil using stated delivery

methods. Assume that a trader establishes a long position of five contracts in

crude oil futures at the then-current futures market price of $100 per barrel. Both

the trader on the long side of the contract and the trader on the short side of the

contract post collateral (margin) of, say, $10 per barrel. At the end of the day, the

market price of the futures contract falls to $100. How much money will each side

of the contract have (assuming that the required collateral was the only cash and

that there were no other positions)?

contracts x barrel size

5 x 1000 = 5,000

x margin

5,000 x 10 = 50,000

both long and short are $50,000 as there are not gains or losses in the next day market price.

Futures contracts on crude oil are often

denominated in 1,000-barrel sizes. In other words, each contract calls for the

holder of a short position at the delivery date of the futures contract to deliver to

the long side 1,000 barrels of the specified grade of oil using stated delivery

methods. Assume that a trader establishes a long position of ten contracts in

crude oil futures at the then-current futures market price of $100 per barrel. Both

the trader on the long side of the contract and the trader on the short side of the

contract post collateral (margin) of, say, $10 per barrel. At the end of the day, the

market price of the futures contract falls to $100. How much money will each side

of the contract have (assuming that the required collateral was the only cash and

that there were no other positions)?

?

Futures contracts on crude oil are often

denominated in 1,000-barrel sizes. In other words, each contract calls for the

holder of a short position at the delivery date of the futures contract to deliver to

the long side 1,000 barrels of the specified grade of oil using stated delivery

methods. Assume that a trader establishes a long position of five contracts in

crude oil futures at the then-current futures market price of $100 per barrel. Both

the trader on the long side of the contract and the trader on the short side of the

contract post collateral (margin) of, say, $10 per barrel. At the end of the day, the

market price of the futures contract falls to $99. How much money will each side

of the contract have (assuming that the required collateral was the only cash and

that there were no other positions)?

?

Futures contracts on crude oil are often

denominated in 1,000-barrel sizes. In other words, each contract calls for the

holder of a short position at the delivery date of the futures contract to deliver to

the long side 1,000 barrels of the specified grade of oil using stated delivery

methods. Assume that a trader establishes a long position of ten contracts in

crude oil futures at the then-current futures market price of $100 per barrel. Both

the trader on the long side of the contract and the trader on the short side of the

contract post collateral (margin) of, say, $10 per barrel. At the end of the day, the

market price of the futures contract falls to $102. How much money will each side

of the contract have (assuming that the required collateral was the only cash and

that there were no other positions)?

?

Futures contracts on crude oil are often

denominated in 1,000-barrel sizes. In other words, each contract calls for the

holder of a short position at the delivery date of the futures contract to deliver to

the long side 1,000 barrels of the specified grade of oil using stated delivery

methods. Assume that a trader establishes a long position of five contracts in

crude oil futures at the then-current futures market price of $100 per barrel. Both

the trader on the long side of the contract and the trader on the short side of the

contract post collateral (margin) of, say, $10 per barrel. At the end of the day, the

market price of the futures contract falls to $95. How much money will each side

of the contract have (assuming that the required collateral was the only cash and

that there were no other positions)?

?

Futures contracts on crude oil are often

denominated in 1,000-barrel sizes. In other words, each contract calls for the

holder of a short position at the delivery date of the futures contract to deliver to

the long side 1,000 barrels of the specified grade of oil using stated delivery

methods. Assume that a trader establishes a long position of ten contracts in

crude oil futures at the then-current futures market price of $100 per barrel. Both

the trader on the long side of the contract and the trader on the short side of the

contract post collateral (margin) of, say, $10 per barrel. At the end of the day, the

market price of the futures contract falls to $106. How much money will each side

of the contract have (assuming that the required collateral was the only cash and

that there were no other positions)?

?

To lock in sales prices for its anticipated

production, HiHo Silver Mining Company wishes to take short positions in five

silver futures contracts, settling in each quarter for the next four quarters (20

contracts total). If the initial margin requirement is $11,000 per contract, what is

the firm’s total initial margin requirement?

number of contracts x the initial margin per contract = total margin (available collateral to establish position)

11000 x 20 = $220,000