Your company hires 100 new employees, and as an incentive offers a profit-sharing program that will...

 

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Your company hires 100 new employees, and as an incentive offers a profit-sharing program that will pay in four years. As they are all new hires these employees aren't eligible for retirement within four years; if they cease working with the company during that time it will be for one of the following reasons: Resignation • • Ill-health • Death Anyone who resigns from the company forfeits their profit-sharing benefit but it will be paid to all other employees or their beneficiaries. The probabilities of employees leaving for each reason are given in the table below. Year 1 2 3 4 Probabilities of leaving the company: Resignation Ill-health 0.04 0.03 0.03 0.02 0.10 0.05 0.03 0.03 Death 0.01 0.01 0.02 0.02 i) Using the standard notation for a multiple decrement theory model (qq) and p)) write two expressions for the probability that one of these employees will resign after exactly two years of employment. ii) Using the information in the table above, calculate the probability described in Part (i) above. [3 31 iii) Create a "life table for this model, showing how many of the 100 new employees will leave because of each decrement in each of the next four years. Round values to whole numbers. C iv) Using your "life table", calculate the number of employees who will receive their profit-sharing benefits at Time 4. v) Only employees who resign will forfeit their benefits so your supervisor tells you that you don't need to use a multiple decrement model for the calculation in Part (iv) above. Using the probabilities of resignation only, calculate the number of employees expected to receive their profit-sharing benefits at time 4. vi) Comparing your answers for Parts (iv) and (v) above, say which answer you think is more accurate and briefly explain why. Your company hires 100 new employees, and as an incentive offers a profit-sharing program that will pay in four years. As they are all new hires these employees aren't eligible for retirement within four years; if they cease working with the company during that time it will be for one of the following reasons: Resignation • • Ill-health • Death Anyone who resigns from the company forfeits their profit-sharing benefit but it will be paid to all other employees or their beneficiaries. The probabilities of employees leaving for each reason are given in the table below. Year 1 2 3 4 Probabilities of leaving the company: Resignation Ill-health 0.04 0.03 0.03 0.02 0.10 0.05 0.03 0.03 Death 0.01 0.01 0.02 0.02 i) Using the standard notation for a multiple decrement theory model (qq) and p)) write two expressions for the probability that one of these employees will resign after exactly two years of employment. ii) Using the information in the table above, calculate the probability described in Part (i) above. [3 31 iii) Create a "life table for this model, showing how many of the 100 new employees will leave because of each decrement in each of the next four years. Round values to whole numbers. C iv) Using your "life table", calculate the number of employees who will receive their profit-sharing benefits at Time 4. v) Only employees who resign will forfeit their benefits so your supervisor tells you that you don't need to use a multiple decrement model for the calculation in Part (iv) above. Using the probabilities of resignation only, calculate the number of employees expected to receive their profit-sharing benefits at time 4. vi) Comparing your answers for Parts (iv) and (v) above, say which answer you think is more accurate and briefly explain why.

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i The probability that an employee will resign after exactly two years of employment can be expressed as t2q1 010 1 005 003 003 Here 010 represents th... View the full answer