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?
?