Consider the following cash flow diagram which lasts for 60 years. What is the F

Question

Consider the following cash flow diagram which lasts for 60 years. What is the Future Worth of the diagram if the interest rate is 12 % per year for all 60 years? What is the Present Worth if the interest rate is 6 % per year for all 60 years? What is the Present Worth if the interest rate is 12% for the first, 30 years and the last 30 years is 6%. Note if the exact year is not in the table clearly state what year you are using and make any reasonable approximation. Full credit will not be given for simply a series of 60 single event series. Full credit will be given only if Uniform and possibly Gradient Series are an important part of the calculation.

Explanation / Answer

Here, we have uneven cash flows, had the cash flows be even, we could have used the formula of annuity. Hence we shall use excel to figure this out. The basic formula for Present Value is, PV = FV/(1+r)n

And for Future Value is, FV = PV(1+r)n

Here, r = rate of interest and n = time period

a) Using r = 0.12 and n = 1 to 60 we can arrive at the future value of cash flows after the end of 60 years as 715,487,000. Pls see the table below:

b.) Similarly, the present worth, if the interest rate is 6% is 1,253,871.43

C.) As the interest changes after 30 years, we need to break the cash flows into 2.

First, we will compute the present value of cash flows at the end of first 30 years; ie., the value of last 30 cash flows as on the 30th year end at 6% interest. This comes to 545,882.77

Now, we can calculate the present value @ 12% of 1st 30 cash flows + present value of this 5,45,882.77 received at the end of 30th year. This comes to 8,03,853.1

Rate 1.1200 Year No. of Years to end Cash Flow Compounding Factor Compounding Factor Future Value 0 60 2,00,000 (1.12)^60 897.5969 17,95,19,387 1 59 80,000 (1.12)^59 801.4258 6,41,14,067 2 58 79,000 (1.12)^58 715.5588 5,65,29,144 3 57 78,000 (1.12)^57 638.8918 4,98,33,558 4 56 77,000 (1.12)^56 570.4391 4,39,23,809 5 55 76,000 (1.12)^55 509.3206 3,87,08,366 6 54 75,000 (1.12)^54 454.7505 3,41,06,291 7 53 74,000 (1.12)^53 406.0273 3,00,46,018 8 52 73,000 (1.12)^52 362.5243 2,64,64,277 9 51 72,000 (1.12)^51 323.6825 2,33,05,137 10 50 71,000 (1.12)^50 289.0022 2,05,19,155 11 49 70,000 (1.12)^49 258.0377 1,80,62,637 12 48 69,000 (1.12)^48 230.3908 1,58,96,964 13 47 68,000 (1.12)^47 205.7061 1,39,88,011 14 46 67,000 (1.12)^46 183.6661 1,23,05,630 15 45 66,000 (1.12)^45 163.9876 1,08,23,182 16 44 65,000 (1.12)^44 146.4175 95,17,138 17 43 64,000 (1.12)^43 130.7299 83,66,714 18 42 63,000 (1.12)^42 116.7231 73,53,558 19 41 62,000 (1.12)^41 104.2171 64,61,459 20 40 61,000 (1.12)^40 93.0510 56,76,109 21 39 60,000 (1.12)^39 83.0812 49,84,873 22 38 59,000 (1.12)^38 74.1797 43,76,600 23 37 58,000 (1.12)^37 66.2318 38,41,447 24 36 57,000 (1.12)^36 59.1356 33,70,728 25 35 56,000 (1.12)^35 52.7996 29,56,779 26 34 55,000 (1.12)^34 47.1425 25,92,838 27 33 54,000 (1.12)^33 42.0915 22,72,943 28 32 53,000 (1.12)^32 37.5817 19,91,831 29 31 52,000 (1.12)^31 33.5551 17,44,866 30 30 51,000 (1.12)^30 29.9599 15,27,956 31 29 50,000 (1.12)^29 26.7499 13,37,497 32 28 49,000 (1.12)^28 23.8839 11,70,309 33 27 48,000 (1.12)^27 21.3249 10,23,594 34 26 47,000 (1.12)^26 19.0401 8,94,883 35 25 46,000 (1.12)^25 17.0001 7,82,003 36 24 45,000 (1.12)^24 15.1786 6,83,038 37 23 44,000 (1.12)^23 13.5523 5,96,303 38 22 43,000 (1.12)^22 12.1003 5,20,313 39 21 42,000 (1.12)^21 10.8038 4,53,762 40 20 41,000 (1.12)^20 9.6463 3,95,498 41 19 40,000 (1.12)^19 8.6128 3,44,510 42 18 39,000 (1.12)^18 7.6900 2,99,909 43 17 38,000 (1.12)^17 6.8660 2,60,910 44 16 37,000 (1.12)^16 6.1304 2,26,825 45 15 36,000 (1.12)^15 5.4736 1,97,048 46 14 35,000 (1.12)^14 4.8871 1,71,049 47 13 34,000 (1.12)^13 4.3635 1,48,359 48 12 33,000 (1.12)^12 3.8960 1,28,567 49 11 32,000 (1.12)^11 3.4785 1,11,314 50 10 31,000 (1.12)^10 3.1058 96,281 51 9 30,000 (1.12)^9 2.7731 83,192 52 8 29,000 (1.12)^8 2.4760 71,803 53 7 28,000 (1.12)^7 2.2107 61,899 54 6 27,000 (1.12)^6 1.9738 53,293 55 5 26,000 (1.12)^5 1.7623 45,821 56 4 25,000 (1.12)^4 1.5735 39,338 57 3 24,000 (1.12)^3 1.4049 33,718 58 2 23,000 (1.12)^2 1.2544 28,851 59 1 22,000 (1.12)^1 1.1200 24,640 60 0 21,000 (1.12)^0 1.0000 21,000 71,54,87,000

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