In: Statistics and Probability
It is actually a simple calculation. We need to sum up the present values over the 48 years. This can be done as shown below. This table is for 3% discount rate
Public University | Private University | ||||
Index | Time | Monetary Value | Present Value | Monetary Value | Present Value |
0 | Year 1 | -3500 | -3500.00 | -29000 | -29000.00 |
1 | Year 2 | -3500 | -3398.06 | -29000 | -28155.34 |
2 | Year 3 | -3500 | -3299.09 | -29000 | -27335.28 |
3 | Year 4 | -3500 | -3203.00 | -29000 | -26539.11 |
4 | Year 5 | 39000 | 34650.99 | 56000 | 49755.27 |
5 | Year 6 | 39000 | 33641.74 | 56000 | 48306.09 |
6 | Year 7 | 39000 | 32661.89 | 56000 | 46899.12 |
7 | Year 8 | 39000 | 31710.57 | 56000 | 45533.12 |
8 | Year 9 | 39000 | 30786.96 | 56000 | 44206.92 |
9 | Year 10 | 72000 | 55182.00 | 89000 | 68211.09 |
10 | Year 11 | 72000 | 53574.76 | 89000 | 66224.36 |
11 | Year 12 | 72000 | 52014.33 | 89000 | 64295.49 |
12 | Year 13 | 72000 | 50499.35 | 89000 | 62422.81 |
13 | Year 14 | 72000 | 49028.50 | 89000 | 60604.67 |
14 | Year 15 | 72000 | 47600.48 | 89000 | 58839.48 |
15 | Year 16 | 72000 | 46214.06 | 89000 | 57125.71 |
16 | Year 17 | 72000 | 44868.02 | 89000 | 55461.86 |
17 | Year 18 | 72000 | 43561.18 | 89000 | 53846.46 |
18 | Year 19 | 72000 | 42292.41 | 89000 | 52278.12 |
19 | Year 20 | 88000 | 50185.17 | 118000 | 67293.75 |
20 | Year 21 | 88000 | 48723.47 | 118000 | 65333.74 |
21 | Year 22 | 88000 | 47304.34 | 118000 | 63430.81 |
22 | Year 23 | 88000 | 45926.54 | 118000 | 61583.32 |
23 | Year 24 | 88000 | 44588.87 | 118000 | 59789.63 |
24 | Year 25 | 88000 | 43290.17 | 118000 | 58048.18 |
25 | Year 26 | 88000 | 42029.29 | 118000 | 56357.46 |
26 | Year 27 | 88000 | 40805.14 | 118000 | 54715.98 |
27 | Year 28 | 88000 | 39616.64 | 118000 | 53122.31 |
28 | Year 29 | 88000 | 38462.75 | 118000 | 51575.06 |
29 | Year 30 | 88000 | 37342.48 | 118000 | 50072.87 |
30 | Year 31 | 88000 | 36254.83 | 118000 | 48614.44 |
31 | Year 32 | 88000 | 35198.87 | 118000 | 47198.48 |
32 | Year 33 | 88000 | 34173.66 | 118000 | 45823.77 |
33 | Year 34 | 88000 | 33178.31 | 118000 | 44489.10 |
34 | Year 35 | 88000 | 32211.95 | 118000 | 43193.30 |
35 | Year 36 | 88000 | 31273.74 | 118000 | 41935.24 |
36 | Year 37 | 74000 | 25532.40 | 90000 | 31052.92 |
37 | Year 38 | 74000 | 24788.74 | 90000 | 30148.46 |
38 | Year 39 | 74000 | 24066.74 | 90000 | 29270.35 |
39 | Year 40 | 74000 | 23365.76 | 90000 | 28417.82 |
40 | Year 41 | 74000 | 22685.21 | 90000 | 27590.12 |
41 | Year 42 | 74000 | 22024.47 | 90000 | 26786.52 |
42 | Year 43 | 74000 | 21382.98 | 90000 | 26006.33 |
43 | Year 44 | 74000 | 20760.18 | 90000 | 25248.86 |
44 | Year 45 | 74000 | 20155.51 | 90000 | 24513.46 |
45 | Year 46 | 74000 | 19568.46 | 90000 | 23799.48 |
46 | Year 47 | 74000 | 18998.50 | 90000 | 23106.29 |
47 | Year 48 | 74000 | 18445.15 | 90000 | 22433.29 |
1577227.43 | 1953932.18 |
We need just the one simple formula,
For ex, in this table the formula you need to put on excel for Present Value is Monetary Value, divided by 1.03 power the index. Below is how I did this on excel, you can see formula at top
So at 3% discount rate, we should go with private university. Let us repeat the calculation by changing 3% to 9.5%
Public University | Private University | ||||
Index | Time | Monetary Value | Present Value | Monetary Value | Present Value |
0 | Year 1 | -3500 | -3500.00 | -29000 | -29000.00 |
1 | Year 2 | -3500 | -3196.35 | -29000 | -26484.02 |
2 | Year 3 | -3500 | -2919.04 | -29000 | -24186.32 |
3 | Year 4 | -3500 | -2665.79 | -29000 | -22087.96 |
4 | Year 5 | 39000 | 27127.40 | 56000 | 38952.16 |
5 | Year 6 | 39000 | 24773.88 | 56000 | 35572.75 |
6 | Year 7 | 39000 | 22624.55 | 56000 | 32486.53 |
7 | Year 8 | 39000 | 20661.69 | 56000 | 29668.06 |
8 | Year 9 | 39000 | 18869.12 | 56000 | 27094.12 |
9 | Year 10 | 72000 | 31813.06 | 89000 | 39324.48 |
10 | Year 11 | 72000 | 29053.02 | 89000 | 35912.76 |
11 | Year 12 | 72000 | 26532.44 | 89000 | 32797.04 |
12 | Year 13 | 72000 | 24230.54 | 89000 | 29951.64 |
13 | Year 14 | 72000 | 22128.35 | 89000 | 27353.09 |
14 | Year 15 | 72000 | 20208.53 | 89000 | 24979.99 |
15 | Year 16 | 72000 | 18455.28 | 89000 | 22812.78 |
16 | Year 17 | 72000 | 16854.14 | 89000 | 20833.59 |
17 | Year 18 | 72000 | 15391.91 | 89000 | 19026.11 |
18 | Year 19 | 72000 | 14056.54 | 89000 | 17375.44 |
19 | Year 20 | 88000 | 15689.69 | 118000 | 21038.45 |
20 | Year 21 | 88000 | 14328.49 | 118000 | 19213.20 |
21 | Year 22 | 88000 | 13085.37 | 118000 | 17546.30 |
22 | Year 23 | 88000 | 11950.11 | 118000 | 16024.02 |
23 | Year 24 | 88000 | 10913.35 | 118000 | 14633.81 |
24 | Year 25 | 88000 | 9966.53 | 118000 | 13364.21 |
25 | Year 26 | 88000 | 9101.85 | 118000 | 12204.75 |
26 | Year 27 | 88000 | 8312.19 | 118000 | 11145.89 |
27 | Year 28 | 88000 | 7591.04 | 118000 | 10178.90 |
28 | Year 29 | 88000 | 6932.46 | 118000 | 9295.80 |
29 | Year 30 | 88000 | 6331.01 | 118000 | 8489.31 |
30 | Year 31 | 88000 | 5781.75 | 118000 | 7752.80 |
31 | Year 32 | 88000 | 5280.13 | 118000 | 7080.18 |
32 | Year 33 | 88000 | 4822.04 | 118000 | 6465.92 |
33 | Year 34 | 88000 | 4403.69 | 118000 | 5904.95 |
34 | Year 35 | 88000 | 4021.63 | 118000 | 5392.65 |
35 | Year 36 | 88000 | 3672.73 | 118000 | 4924.79 |
36 | Year 37 | 74000 | 2820.48 | 90000 | 3430.32 |
37 | Year 38 | 74000 | 2575.78 | 90000 | 3132.71 |
38 | Year 39 | 74000 | 2352.31 | 90000 | 2860.92 |
39 | Year 40 | 74000 | 2148.23 | 90000 | 2612.71 |
40 | Year 41 | 74000 | 1961.86 | 90000 | 2386.04 |
41 | Year 42 | 74000 | 1791.65 | 90000 | 2179.03 |
42 | Year 43 | 74000 | 1636.21 | 90000 | 1989.98 |
43 | Year 44 | 74000 | 1494.25 | 90000 | 1817.34 |
44 | Year 45 | 74000 | 1364.62 | 90000 | 1659.67 |
45 | Year 46 | 74000 | 1246.22 | 90000 | 1515.68 |
46 | Year 47 | 74000 | 1138.10 | 90000 | 1384.18 |
47 | Year 48 | 74000 | 1039.37 | 90000 | 1264.09 |
484252.42 | 549270.84 |
The choice is still private university, as its net present value is greater