Chapter 3 Real Estate System Study Questions
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Commercial Real Estate Analysis and Investments (Geltner)
Chapter 8: Present Value Mathematics for Real Estate
Reading: All sections EXCEPT the following: 8.2.4, 8.2.5, 8.2.6, 8.2.8, 8.2.9
Study Questions #: 1-6, 8, 11, 21, 22, 24, 27, 33, 37, 39, 41, 43, 45, 47, 53
Gabriella Riffle-Gonzalez 8.1. What is the present value of an offer of $15,000 one year from now if the opportunity cost of
capital (discount rate) is 12% per year simple interest?
PV = ?
R = 12% = 0.12
FV = $15,000
[f][CLX] 15000 [ENTER] 1.12 [/] PV = $13,392.86
8.2. What is the present value of an offer of $14,000 one year from now if the opportunity cost of
capital (discount rate) is 11% per year simple interest?
PV=? FV=14,000
R=11%=.11
[f][CLX] 14000 [ENTER] 1.11 [/]
PV= $12,612.61
8.3. What is the present value of an offer of $15,000 two years from now if the opportunity cost of
capital (discount rate) is 12% per year compounded annually?
N = 2
PV = ?
FV = 15,000
R = 12% = .12
[f][CLX] 15000 [ENTER] 1.12 [g][x
2
] [/]
PV= $11,957.91
8.4. What is the present value of an offer of $14,000 two years from now if the opportunity cost of
capital (discount rate) is 11% per year compounded annually?
N=2
PV= ?
FV = 14,000
R = 11%
[f][CLX] 14000 [ENTER] 1.11 [g][x
2
] [/]
PV= $11,362.71
8.5. What is the future value of $20,000 that grows at an annual interest rate of 12% per year for
two years?
PV = 20,000
FV= ?
R = 12%
N=2
[f][CLX] 20000 [ENTER] 1.12 [g][x
2
] [x]
FV= $25,088
8.6. What is the future value of $25,000 that grows at an annual interest rate of 11% per year for
two years?
PV = 25,000
R= 11%
N= 2
FV= ?
[f][CLX] 25000 [ENTER] 1.11 [g][x
2
] [x]
FV= $30,802.50
8.8. What is the present value of an offer of $14,000 one year from now if the opportunity cost of
capital (discount rate) is 11% per year nominal annual rate compounded monthly?
PV=?
FV= 14,000
R=11%/12 months = 0.0091666666667
m is the number of compounding periods per year (e.g., 12 in the example of monthly compounding)
T is the length of time between when the PV and FV cash flows occur measured in years
N=12 x 1 = 12
[f][CLX] 14000 [ENTER] .11 [ENTER] 12 [/] 1 [+] 12 [y
x
]
PV= $12,547.96
8.11. What is the effective annual rate (EAR) of 8% nominal annual rate compounded monthly?
M = 12
I = 8%
EAR = (1+.08/12)
12
-1
[f][CLX] .08 [ENTER] 12 [/] 1 [+] 12 [y
x
] 1 [-] EAR = .082999507 = 8.3%
8.21. If you invested $15,000 and received back $30,000 five years later, what annual interest (or
growth) rate (compounded annually) would you have obtained?
PV = 15,000
FV = 30,000
N = 5
[f][CLX] 30,000 [ENTER] 15,000 [/] 1 [ENTER] 5 [/] [y
x
] 1 [-]
R=0.148698355 = 14.87%
8.22. If you invested $40,000 and received back $100,000 seven years later, what annual interest (or
growth) rate (compounded annually) would you have obtained?
PV=40,000
FV=100,000
N=7
[f][CLX] 100,000 [ENTER] 40,000 [/] 1 [ENTER] 7 [/] [y
x
] 1 [-]
R=0.139852281 = 13.99%
8.24. In Question 8.22, what nominal annual rate compounded monthly would you have obtained?
N= 12 x 7 = 84
[f][CLX] 100,000 [ENTER] 40,000 [/] 1 [ENTER] 84 [/] [y
x
] 1 [-]
R=0.01097 = 1.1%
8.27. If you invest $15,000 and it grows at an annual rate of 10% (compounded annually), how many
years will it take to grow to $30,000?
PV = 15,000
R = 10%
FV = 30,000
N=?
[f][CLX] 30,000 [g][LN] 15,000 [g][LN] [-] 1.1 [g][LN] [/]
N=7.27254
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EXERCISES
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Liability
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