Numerical Example. Sum of Contract and Rider (if applicable) Contributions = $50,000 Annuity Account Value = $40,000 Withdrawal amount - $4,000 Adjustment = $36,000 ($40,000 - $4,000)/$40,000 = 0.90 Guaranteed Minimum Death Benefit = $45,000 ($50,000 x 0.90) The following terms apply:
Numerical Example. The Stackelberg models produce the following optimal values for our decision variables based on equation (18) and (25): α = 3, Pw1 = 21170, Pa = 1550, qM1 = 23248.59, qÆ2 = 266, U1(C) = 0 Pw1 = 21170, C3r = 700, C3p = 800, qM1 = 23248.59, qÆ3 = 102, U2(C) = 17963 Pw2 = 21080, C1r = 7550, C1p = 850, qM2 = 23560.80, qÆ1 = 1126, U3(C) = 18148 The result shows that the OEM, as the leader of the agent would choose option M2. The agent as the follower of the manufacturer and the leader of the customer, would choose option A1. And the customer has to choose option C3, which makes sense. In other words, the obtain sub-perfect-equilibrium (SPE), (M2, A1, C3) is tangible.
Numerical Example. Excess Withdrawals during the Accumulation Phase are illustrated as follows: Covered Fund Value before the Excess Withdrawal adjustment = $50,000 Benefit Base = $100,000 Excess Withdrawal amount: $10,000 Covered Fund Value after adjustment= $50,000 - $10,000 = $40,000 Covered Fund Value adjustment = $40,000/$50,000 = 0.80 Adjusted Benefit Base = $100,000 x 0.80 = $80,000
Numerical Example. Assume that the Participant was granted an Award of [ ] Stock Units and the Corporation’s TSR Percentile Rank for the Performance Period was [ ]. In that case, the number of Stock Units subject to the Award that would vest would be [ ]. The remaining [ ] Stock Units subject to the Award that did not vest would terminate as of the end of the Performance Period.
Numerical Example. Consider a supermarket that purchases 200 kg of apples from its supplier at the wholesale price of 1.5 euros per kg. The shelf life of the fruit is four weeks and the supermarket divides it into four quality periods with the length of one week (there are four quality levels). It is predicted it can sell 100 kg during the first week at the price of 4 euros per kg, 60 kg during the second week at the price of 3.5 euros per kg, and 40 kg during the third week at the price of 2.5 euros per kg. The supermarket anticipates selling all of them during the first three weeks and the revenue that it predicts equals 410 euros. It usually does not sell apples with the quality level 4 and if something remains at the end of the third week, it will be left at the corner of the supermarket so people who need can use it as a donation otherwise it would be wasted. Based on the previous data, about 60% of their surplus inventories usually will be wasted. This does not seem an efficient way and a large portion of the surplus inventories are going to be wasted when they cannot sell their goods at the level that they have predicted before. 1𝑖𝑖 Consider the supermarket sells 80, 70, and 15 kg of the apples during the first, second, and the third period respectively. So, it sells 20 kg lower than the amount that is predicted for the first period. In the second period, it sells 10 kg more than what was anticipated and for the third period, it cannot sell more than 15 kg which is 25 kg less than the predicted quantity. Considering the indicator of apples in the supermarket 1 (i=1) and 𝐼𝑠𝑢𝑟 = 5 kg (j=2,3,4), there is 20 kg surplus inventory at the beginning of the second quality period and 35 kg surplus inventory at the beginning of the last quality period. As mentioned before, the supermarket does not sell the apples with quality level 4 and they will be left at a corner of the supermarket to be picked up by people who need them. Finally based on the previous data, 60% of them will be wasted which equals 21 kg. Although the supermarket is predicted to gain 410 euros in revenue by selling the apples during different periods, the real revenue equals 302.5 euros and 21 kg of the apples will be wasted. The owner of the supermarket decides to use smart contracts with a blockchain platform to cooperate with other parties to avoid food waste and find a quick way to decide about the surplus inventories when they have better quality. This may help her to minimize food waste, maximize i...
Numerical Example. Covered Fund Value before XXX = $55,000 Benefit Base = $100,000 XXX % = 5% XXX Amount = $100,000 x 5% = $5,000 Total annual withdrawal: $10,000 Excess Withdrawal = $10,000 – $5,000 = $5,000 Covered Fund Value after XXX = $55,000 – $5,000 = $50,000 Covered Fund Value after Excess Withdrawal = $50,000 – $5,000 = $45,000 Covered Fund Value Adjustment due to Excess Withdrawal = $45,000/$50,000 = 0.90 Adjusted Benefit Base = $100,000 x 0.90 = $90,000 Adjusted XXX Amount = $90,000 x 5% = $4,500 (Assuming no XXX increase on succeeding Ratchet Date)
