Question

Solve various time value of money scenarios.

Scenario 1. Jeff just hit the jackpot in Las Vegas and won $65,000 ! If he invests it now at a 14% interest rate, how much will it be worth in 15 years? (Round your answer to the nearest whole dollar.)

Future Value = _______

Scenario 2. Donald would like to have $2,500,000 saved by the time he retires in 30 years. How much does he need to invest now at a 10% interest rate to fund his retirement goal? (Round your answer to the nearest whole dollar.)

Present Value = _______

Scenario 3. Assume that Tina accumulates savings of $1.5 million by the time she retires. If she invests this savings at 12 %, how much money will she be able to withdraw at the end of each year for 15 years? (Round your answer to the nearest whole dollar and enter as a positive amount.)

Future Value = ______

Scenario 4. Jessica plans to invest $6,000 at the end of each year for the next seven years. Assuming a 12 % interest rate, what will her investment be worth seven years from now? (Round your answer to the nearest whole dollar.)

Future Value = ______

Scenario 5. Assuming a 12 % interest rate, how much would Penelope have to invest now to be able to withdraw $11,000 at the end of every year for the next nine years? (Round your answer to the nearest whole dollar.)

Present Value = ______

Scenario 6. Aaron is considering a capital investment that costs $520,000 and will provide net cash inflows for three years. Using a hurdle rate of 10 %, find the NPV of the investment. (Round your answer to the nearest whole dollar. Use parentheses or a minus sign to represent a negative NPV.)

Net Present Value = ______

Scenario 7. What is the IRR of the capital investment described in Question 6?

Net Present Value (NPV) = ______

The IRR for the project is ______:

A. Between 8% and 10%

B. Between 10% and 12%

C. Between 12% and 14%

D. Between 14% and 16%

Reference Present Value of $1 Periods 1% | 2% | 3% | 4% | 5% | 6% | 8% | 10% | 12% | 14% | 16% | 18% | 20% 10.990 0.9800.971 0.962 0.9520.9430.926 0.9090.8930.877 0.862 0.8470.833 20.9800.961 0.943 0.925 0.907 0.890 0.857 0.826 0.797 0.7690.743 0.718 0.694 30.9710.9420.9150.889 0.8640.840 0.7940.751 0.712 0.675 0.6410.6090.579 40.9610.9240.888 0.855 0.823 0.7920.7350.6830.6360.5920.5520.516 0.482 50.9510.906 0.863 0.822 0.784 0.747 0.6810.6210.5670.5190.4760.4370.402 6 0.9420.888 0.8370.7900.746 0.7050.6300.5640.5070.4560.4100.3700.335 7 0.9330.871 0.813 0.760 0.711 0.665 0.5830.513 0.4520.4000.3540.3140.279 80.923 0.8530.789 0.7310.677 0.627 0.5400.467 0.4040.3510.3050.2660.233 90.914 0.837 0.7660.7030.645 0.592 0.5000.424 0.361 0.308 0.263 0.225 0.194 10 0.905 0.820 0.7440.676 0.614 0.5580.463 0.386 0.322 0.270 0.2270.191 0.162 110.896 0.8040.722 0.6500.5850.527 0.4290.350 0.287 0.237 0.195 0.1620.135 12 0.887 0.7880.701 0.625 0.557 0.497 0.3970.319 0.257 0.2080.168 0.137 0.112 13 0.879 0.773 0.6810.6010.5300.4690.3680.2900.2290.1820.145 0.116 0.093 14 0.870 0.7580.6610.577 0.505 0.4420.3400.2630.2050.160 0.1250.0990.078 15 0.8610.743 0.642 0.555 0.4810.4170.315 0.2390.1830.140 0.108 0.0840.065 20 0.820 0.6730.5540.4560.3770.3120.2150.1490.1040.073 0.05 0.037 0.026 25 0.780 0.610 0.4780.375 0.295 0.233 0.146 0.092 0.059 0.0380.0240.0160.010 30 0.742 0.552 0.412 0.308 0.231 0.174 0.099 0.057 0.033 0.020 0.012 0.007 0.004 400.672 0.453 0.307 0.2080.142 0.097 0.046 0.022 0.011 0.005 0.0030.001 0.001 Reference Present Value of Annuity of $1 | 4% | 5% Periods 1% | 2% | 3% | 6% | 10.990 0.9800.971 0.9620.952 0.943 0.926 0.9090.8930.877 0.862 0.847 0.833 2 1.9701.9421.913 1.886 1.8591.833 1.7831.736 1.690 1.647 1.605 1.566 1.528 3 2.9412.8842.829 2.775 2.723 2.673 2.577 2.4872.402 2.3222.2462174 2.106 43.902 3.808 3.717 3.630 3.546 |3.4653.3123.170 3.0372.9142.7982.690 2.589 8% | 10% | 12% | 14% | 16% | 18% | 20% 54.853 4.7134.5804.452 4.329 4.212 3.9933.7913.605 3.433 3.2743.127 2.991 6 5.7955.601 5.417 5.242 5.0764.917 4.623 4.355 4.1113.8893.6853.498 3.326 7 6.728 6.472 6.230 6.0025.7865.5825.2064.8684.5644.2884.039 3.8123.605 87.652 7.3257.0206.7336.4636.2105.7475.3354.9684.6394.3444.0783.837 98.566 8.162 7.7867.4357.108 6.802 6.2475.7595.3284.9464.6074.303 4.031 10 9.4718.9838.530 8.111 7.7227.360 6.7106.1455.650 5.2164.8334.4944.192 11 10.3689.7879.2538.7608.3067.887 7.1396.4955.9385.4535.0294.6564.327 12 11.255 10.575 9.9549.3858.863 |8.384 7.536 6.814 6.1945.6605.1974.793|4.439 13 12.134 11.348 10.635 9.986 9.3948.8537.9047.103 6.4245.842 5.3424.910 4.533 14 13.004 12.106 11.296 10.563 9.8999.2958.2447.3676.628 6.002 5.4685.0084.611 15 13.865 12.849 11.938 11.118 10.3809.7128.5597.606 6.811 6.142 5.5755.092 4.675 20 18.046 16.351 14.877 13.590 12.462 11.470 9.8188.514 7.4696.6235.9295.3534.870 25 22.023 19.523 17.413 15.622 14.094 12.783 10.675 9.0777.843 6.873 6.097 5.467 4.948 30 25.808 22.39619.600 17.292 15.37213.765 11.2589.4278.055 7.003 6.1775.517| 4.979 40 32.83527.35523.115 19.79317.15915.046 11.925 9.7798.2447.105 6.2335.5484.997 00848 63002 06997 86 76 77 7 2 8 3 025 85 111 39 23 45 11122 23456 78 74 39 '1 8 479 193 2398 689 92 71742 125 11-12 23345 678 0-72 11 2617 683-7 8 0611 1-1 1 1 12 22334 55679 948 37 2 00295 52327 68218 346 749 360 125 001 542 4163 076 717 74 6 87 12457 92471 48384 223 33445 9 599 01 10-12 075 114 3334 6 rsi-%-08 16 26 36 46 741 999 59 352 93 17 001 84 125 01 4. 612 4 tu %-629 7 801 3866 07 051 609 36 5 02507 56930 91521 1631 3 5 2 0012 69259 38 24791 4 96 6118 00011 22345 67891 0289 12346 0-2345 1 2 3 4 5 6789 Reference Future Value of Annuity of $1 Periods eriods000 2003.091246 5.526 43753242100100 14% 5.86746413.3742140 20% 1.000 10% 12% 16% 1.000 1000100 3374492168 1.000 0002120 340 5.066 1.154 1.000 0002030 3.12243105637 002.06032466353 1.000 1.000 1.000 2.010 2.080 2.200 3.060 3.506 3.572 060.1845416 4.060 4.506 7.442 5.204 5.309 610547793440 2160 9.930 6.308 6.633 6.802 6.975 7.336 7.716 8.115 8.536 9.442 0.5839.5498394 10.15910.583 11.027 11.491 8.142 7.214 7.898 412.1422.916 711.436 12.300 13.233 14.24015.32716.499 12.488 13.57914.776 16.085 17.519 19.08620.799 10.46210.95011.464 12.006 12.57813.1814.487 15.93717.5499.33721.321 23.521 25.959 7.434 7.662 8.923 9.487 10.08910.730 11.41 8.286 8.892 9.897 9.755 11.567 12.16912.808 13.486 14.20714.97216.645 18.531 20.65523.04525.73328.755 32.150 12.683 13.41214.192 15.026 15.91716.870 18.977 21.384 24.13327.271 30.85034.931 39.581 13.80914.680 15.618 16.627 17.71318.882 21.49524.523 28.029 32.089 36.786 42.219 48.497 14.94715.97417.086 18.29219.59921.015 24.215 27.97532.393 37.581 43.67250.81859.196 16.09717.293 18.59920.02421.57923.276 27.152 31.77237.280 43.842 51.660 60.96572.035 12 13 15 20 22.01924.297 26.870 29.778 33.06636.786 45.762 57.27572.052 91.025 115.380 146.628186.688 25 28.243 32.030 36.459 41.64647.727 54.865 73.10698.347 133334181.871249.214 342.603471.981 34.78540.56847.575 56.085 66.43979.058113.283 164.494241.333356.787 530.312 790.9481,181.882 48.88660.40275.401 95.026120.800154.762259.057 442.593767.091 1,342.0252,360.757 4,163.213 7,343.858 30 40

Answer 1

Solution:

Scenario 1:

Future value after 15 years = $65,000 * Future value of $1 at 14% for 15 periods

= $65,000 * 7.138 = $463,970

Scenario 2:

Let amount to be invested today = X

Interest rate = 10%

Period = 30 years

Future value = $2,500,000

X * Future value of $1 at 10% for 30 periods = $2,500,000

X * 17.449 = $2,500,000

X = $143,275

Scenario 3:

Let amount to be withdrawn each year = X

Present value of withdrawl = $1,500,000

X * Cumulative PV factor at 12% for 15 periods = $1,500,000

X * 6.811 = $1,500,000

X = $220,232

Hence annual withdrawl amount = $220,232

Scenario 4:

Future value after 7 years = $6,000 * cumulative FV factor at 12% for 7 periods

= $6,000 * 10.089 = $60,534

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