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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