Homework Answers
To calculate the DBO and develop model, the current service cost needs to be considered
Current Service Cost = Present Value of DBO apportioned across the period
The crux of the matter is that the employer would invest that much amount year on year (with the power of compounding or time value of money) so that the total amount accumulated in the fund should be total annual retirement benefit payable to employee.
Inputs are assumed as similar given in question, as given in question the fund still has capacity to earn interest over the period of retirement
| Calculation of Defined Benefit Plan | ||||||||
| Ref | Inputs | |||||||
| 1 | Years until Retirement Service | 25 | ||||||
| 2 | Total Life Expectancy | 70 | ||||||
| 3 | Final Year of Work Salary | $ 1,00,000.00 | ||||||
| 4 | % | 1% | ||||||
| 5 | Discount Rate | 4% | ||||||
| 6 | Benefit Period (Annual) | 1 | ||||||
| 7 | Annual Retirement Benefit payment | $ 25,000.00 | ||||||
| 8 | Annual Retirement Earned Yearly | $ 1,000.00 | ||||||
| Output | ||||||||
| Year | Equal Apportined Amt of DBO | DF@4% |
Current Service Cost (CSC) |
Opening Balance PBO |
Interest @4% |
Benefits |
Closing Balance PBO |
|
| Ref | A = 8 | B =1/(1+R)^Np | C= A X B | D | E = D x 4% | F | G= D + C - F | |
| 0 | $ 1,000.00 | 0.3901 | $ 390.12 | $ - | $ - | $ - | $ 390.12 | |
| 1 | $ 1,000.00 | 0.4057 | $ 405.73 | $ 390.12 | $ 15.60 | $ - | $ 811.45 | |
| 2 | $ 1,000.00 | 0.4220 | $ 421.96 | $ 811.45 | $ 32.46 | $ - | $ 1,265.87 | |
| 3 | $ 1,000.00 | 0.4388 | $ 438.83 | $ 1,265.87 | $ 50.63 | $ - | $ 1,755.33 | |
| 4 | $ 1,000.00 | 0.4564 | $ 456.39 | $ 1,755.33 | $ 70.21 | $ - | $ 2,281.93 | |
| 5 | $ 1,000.00 | 0.4746 | $ 474.64 | $ 2,281.93 | $ 91.28 | $ - | $ 2,847.85 | |
| 6 | $ 1,000.00 | 0.4936 | $ 493.63 | $ 2,847.85 | $ 113.91 | $ - | $ 3,455.40 | |
| 7 | $ 1,000.00 | 0.5134 | $ 513.37 | $ 3,455.40 | $ 138.22 | $ - | $ 4,106.99 | |
| 8 | $ 1,000.00 | 0.5339 | $ 533.91 | $ 4,106.99 | $ 164.28 | $ - | $ 4,805.17 | |
| 9 | $ 1,000.00 | 0.5553 | $ 555.26 | $ 4,805.17 | $ 192.21 | $ - | $ 5,552.65 | |
| 10 | $ 1,000.00 | 0.5775 | $ 577.48 | $ 5,552.65 | $ 222.11 | $ - | $ 6,352.23 | |
| 11 | $ 1,000.00 | 0.6006 | $ 600.57 | $ 6,352.23 | $ 254.09 | $ - | $ 7,206.89 | |
| 12 | $ 1,000.00 | 0.6246 | $ 624.60 | $ 7,206.89 | $ 288.28 | $ - | $ 8,119.76 | |
| 13 | $ 1,000.00 | 0.6496 | $ 649.58 | $ 8,119.76 | $ 324.79 | $ - | $ 9,094.13 | |
| 14 | $ 1,000.00 | 0.6756 | $ 675.56 | $ 9,094.13 | $ 363.77 | $ - | $ 10,133.46 | |
| 15 | $ 1,000.00 | 0.7026 | $ 702.59 | $ 10,133.46 | $ 405.34 | $ - | $ 11,241.39 | |
| 16 | $ 1,000.00 | 0.7307 | $ 730.69 | $ 11,241.39 | $ 449.66 | $ - | $ 12,421.73 | |
| 17 | $ 1,000.00 | 0.7599 | $ 759.92 | $ 12,421.73 | $ 496.87 | $ - | $ 13,678.52 | |
| 18 | $ 1,000.00 | 0.7903 | $ 790.31 | $ 13,678.52 | $ 547.14 | $ - | $ 15,015.98 | |
| 19 | $ 1,000.00 | 0.8219 | $ 821.93 | $ 15,015.98 | $ 600.64 | $ - | $ 16,438.54 | |
| 20 | $ 1,000.00 | 0.8548 | $ 854.80 | $ 16,438.54 | $ 657.54 | $ - | $ 17,950.89 | |
| 21 | $ 1,000.00 | 0.8890 | $ 889.00 | $ 17,950.89 | $ 718.04 | $ - | $ 19,557.92 | |
| 22 | $ 1,000.00 | 0.9246 | $ 924.56 | $ 19,557.92 | $ 782.32 | $ - | $ 21,264.79 | |
| 23 | $ 1,000.00 | 0.9615 | $ 961.54 | $ 21,264.79 | $ 850.59 | $ - | $ 23,076.92 | |
| 24 | $ 1,000.00 | 1.0000 | $ 1,000.00 | $ 23,076.92 | $ 923.08 | $ - | $ 25,000.00 | |
| 25 | $ 25,000.00 | $ 1,000.00 | $ 25,000.00 | $ 1,000.00 | ||||
| 26 | $ 1,000.00 | $ 40.00 | $ - | $ 1,040.00 | ||||
| 27 | $ 1,040.00 | $ 41.60 | $ - | $ 1,081.60 | ||||
| 28 | $ 1,081.60 | $ 43.26 | $ - | $ 1,124.86 | ||||
| 29 | $ 1,124.86 | $ 44.99 | $ - | $ 1,169.86 | ||||
| 30 | $ 1,169.86 | $ 46.79 | $ - | $ 1,216.65 | ||||
| 31 | $ 1,216.65 | $ 48.67 | $ - | $ 1,265.32 | ||||
| 32 | $ 1,265.32 | $ 50.61 | $ - | $ 1,315.93 | ||||
| 33 | $ 1,315.93 | $ 52.64 | $ - | $ 1,368.57 | ||||
| 34 | $ 1,368.57 | $ 54.74 | $ - | $ 1,423.31 | ||||
| 35 | $ 1,423.31 | $ 56.93 | $ - | $ 1,480.24 | ||||
| 36 | $ 1,480.24 | $ 59.21 | $ - | $ 1,539.45 | ||||
| 37 | $ 1,539.45 | $ 61.58 | $ - | $ 1,601.03 | ||||
| 38 | $ 1,601.03 | $ 64.04 | $ - | $ 1,665.07 | ||||
| 39 | $ 1,665.07 | $ 66.60 | $ - | $ 1,731.68 | ||||
| 40 | $ 1,731.68 | $ 69.27 | $ - | $ 1,800.94 | ||||
| 41 | $ 1,800.94 | $ 72.04 | $ - | $ 1,872.98 | ||||
| 42 | $ 1,872.98 | $ 74.92 | $ - | $ 1,947.90 | ||||
| 43 | $ 1,947.90 | $ 77.92 | $ - | $ 2,025.82 | ||||
| 44 | $ 2,025.82 | $ 81.03 | $ - | $ 2,106.85 | ||||
| 45 | $ 2,106.85 | $ 84.27 | $ - | $ 2,191.12 | ||||
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