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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8.33. A real estate investor feels that the cash flow from a property will enable her to pay a lender $15,000 per year, at the end of every year, for 10 years. How much should the lender be willing to loan her if he requires a 9% annual interest rate (annually compounded, assuming the first of the 10 equal payments arrives one year from the date the loan is disbursed)? PMT = 15,000 per year N = 10 years R = 9% =.09 FV = 0 PV= ? [f][CLX] 15000 [CHS] [PMT] 10 [n] 9 [i] [PV] PV = $96,264.87 8.37. In Question 8.33, suppose that not only will the interest be compounded monthly , but the payments will also arrive monthly in the amount of $1,250 per month (the first payment to arrive in one month)? M=12 T = 10 N = 120 FV = 0 R = 9% /12 = i PMT = 1,250 END of month PV = ? [f][CLX] 9 [ENTER] 12 [/] [i] 1250 [PMT] [g] [END] 120 [n] [PV] PV = $98,677.12 8.39. In Question 8.37 (with 120 equal monthly payments of $1,250) suppose the borrower also offers to pay the lender $50,000 at the end of the 10-year period (coinciding with, and in addition to, the last regular monthly payment). How much should the lender be willing to lend? PMT = 1,250 FV = 50,000 M=12 T = 10 N = 120 R = 9% /12 = i PV = ? [f][CLX] 9 [ENTER] 12 [/] [i] 1250 [PMT] [g] [END] 120 [n] 50000 [FV] [PV] PV= $119,073.98

8.41. You are borrowing $80,000 for 25 years at 10% nominal annual interest compounded monthly. How much must your monthly payments be if you will completely retire the loan over the 25-year period (i.e., what is the level payment annuity with a present value of $80,000)? PV = 80,000 T = 25 I = 10% M = 12 R=I/M = 10%/12 = i N = M x T = 12 x 25 = 300 PMT = ? [f][CLX] 80000 [PV] 10[ENTER] 12[/] [i] 12[ENTER] 25[x] [n] [PMT] PMT= $726.96 8.43. At a nominal annual interest rate of 10% compounded monthly, how long (how many months) will it take to retire a $50,000 loan using equal monthly payments of $500 (with the payments made at the end of each month)? I = 10% M = 12 R = 10%/12 = i PV = 50,000 PMT = 500 N = ? [f][CLX] 50000 [CHS] [PV] 500 [PMT] 10 [ENTER] 12 [/] [i] [n] N= 216 8.45. A tenant offers to sign a lease paying a rent of $1,000 per month, in advance (i.e., the rent will be paid at the beginning of each month), for five years. At 10% nominal annual interest compounded monthly, what is the present value of this lease? PMT = 1,000 T = 5 years M = 12 N = 12x5 = 60 I = 10% annually R = 0.10/12 = 0.83% monthly PV =? [f][CLX] [g] [BEG] 1000 [PMT] 60 [n] 10 [ENTER] 12 [/] [i] [PV] PV = $47,457.58

8.47. A building is expected to require $1 million in capital improvement expenditures in five years. The building’s net operating cash flow prior to that time is expected to be at least $20,000 at the end of every month. How much of that monthly cash flow must the owners set aside each month in order to have the money available for the capital improvements, assuming the equal monthly contributions placed in this ‘‘sinking fund’’ will earn interest at a nominal annual rate of 6%, compounded monthly? T = 5 years CFj = 20,000 I=6% M=12 R=0.06/12 FV = 1,000,000 N= 5 x 12 = 60 months [f][CLX] [g] [END] 20000 [g] [CFj] 6 [ENTER] 12 [/] [i] 1000000 [FV] 60 [n] [PMT] PMT = $14,332.80 8.53. Suppose a certain property is expected to produce net operating cash flows annually as follows, at the end of each of the next five years: $15,000, $16,000, $20,000, $22,000, and $17,000. In addition, at the end of the fifth year we will assume the property will be (or could be) sold for $200,000. CF1= 15,000 CF2= 16,000 CF3 = 20,000 CF4 = 22,000 CF5 = 17,000 + 200,000 = 217,000 T = 5 a. What is the NPV of a deal in which you would pay $180,000 for the property today assuming the required expected return or discount rate is 11% per year? IRR = 11% CF0 = 180,000 NPV=? [f][CLX] 170,000[CHS][g][CF0] 15,000[g][CFj] 16,000[g][CFj] 20,000[g][CFj] 22,000[g][CFj] 217,000[CFj] 11 [i] [f] [NPV] NPV= $14,394.32 b. If you could get the property for only $170,000, what would be the expected IRR of your investment? CF0 = 170,000 [f][CLX] 170,000[CHS][g][CF0] 15,000[g][CFj] 16,000[g][CFj] 20,000[g][CFj] 22,000[g][CFj] 217,000[CFj] [f] [IRR] IRR= 13.14712 = 13.15%

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