Assignment: Complete the following 4-part assignment using the information below. Please show your work and calculator inputs. Be sure that you pay attention to the Period Length (i.e. annual, quarterly). One copy is due for each individual on BB by the end of Friday, June 12th. Case Study: Brian Lewerke was recently employed by the human resources department of a moderate-sized engineering firm. Management is considering the adoption of a defined-benefit pension plan in which the firm will pay 75% of an individual's last annual salary if the employee has worked for the firm for 25 years. The amount of the pension is to be reduced by 3% for every year less than 25 years employed, meaning an individual who has been employed for 15 years will receive a pension of 45% of the last year's salary [75% - (10 * 3%)]. Pension payments will start at age 65, provided the individual has retired. One of the first tasks given to Lewerke is to estimate the amount that the firm must set aside today to fund the pension plan. While management plans to hire actuaries to make the final determination, the managers believe the exercise may highlight some problems that they will want to be able to discuss with the actuaries. Lewerke must select two representative employees and estimate their annual pensions and the annual contributions necessary to fund the pensions. Lewerke decided to select Marcus Rashford and Stephen Curry. Rashford is 58 years old, has been with the firm for 27 years, and is earning $34,000 annually. Curry is 47, has been with the firm for 3 years, and earns $42,000 annually. Lewerke believes that Rashford will be with the firm until he retires; he is a competent worker whose salary will increase by 4 percent annually, and it is anticipated he will retire at age 65. Curry is a more valuable employee, and Lewerke expects Curry's salary to rise at least 7 percent annually in order to retain him until retirement at age 65. To determine the amount that must be invested annually to fund each pension, Lewerke needs in addition to an estimate of the amount of the pension) an estimate of how long the pension will be distributed (i.e. life expectancy) and how much the invested funds will earn. Since the firm must pay an interest rate of 8 percent to borrow money, he decides that the invested funds should be able to earn at least that amount. Lewerke has come to you for assistance, pleases address the following questions: 1. If each individual retires at 65, how much will their estimated individual pensions be? Estimated ending salaries: Marcus: S44,741.68 _(65-58 N, 4% I/Y, 34,000 PV, Solve FV) Stephen: $141,957.16_(65-47 N, 7% I/Y, 42,000 PV, Solve FV) Estimated pensions: Stephen: 141,957.16 (75%-12%) = $89,433.01 2. Life expectancy for both employees is 15 years after age 65. If the firm buys an annuity from an insurance company to fund each pension and the insurance company asserts it is able to earn 9% on the funds invested in the annuity, what is the cost (or the $ amount required) to purchase the annuity contracts today? (Solve for PV) Marcus: $270,486.56 (15N, 91/4, -33,556.26 PMT, FV 0.) Stephen: $720,891.63 (15N, 91/Y, -89,433.01 PMT, FV 0) 3. If the firm can earn 8% on the money it must invest annually to fund the pension plans (assuming they have not started saving yet), how much will the firm have to invest annually to have the funds necessary to purchase the annuities at the time each employee retires? Marcus: $30,314.10 (7 N, 8 1/Y, O PV, 270,486.56 FV) Stephen: $19,249.32 (18 N, 8 1/Y, O PV, FV 720,891.63) I 4. If the firm continues to estimate 8% annually on the money it must invest to fund the pension plans, yet makes annuity contributions on a quarterly basis instead of just annually, what will be the amount of each payment? How much more or less (S) will they pay each year compared to your results in Q3? Pro Assignment: Complete the following 4-part assignment using the information below. Please show your work and calculator inputs. Be sure that you pay attention to the Period Length (i.e. annual, quarterly). One copy is due for each individual on BB by the end of Friday, June 12th. Case Study: Brian Lewerke was recently employed by the human resources department of a moderate-sized engineering firm. Management is considering the adoption of a defined-benefit pension plan in which the firm will pay 75% of an individual's last annual salary if the employee has worked for the firm for 25 years. The amount of the pension is to be reduced by 3% for every year less than 25 years employed, meaning an individual who has been employed for 15 years will receive a pension of 45% of the last year's salary [75% - (10 * 3%)]. Pension payments will start at age 65, provided the individual has retired. One of the first tasks given to Lewerke is to estimate the amount that the firm must set aside today to fund the pension plan. While management plans to hire actuaries to make the final determination, the managers believe the exercise may highlight some problems that they will want to be able to discuss with the actuaries. Lewerke must select two representative employees and estimate their annual pensions and the annual contributions necessary to fund the pensions. Lewerke decided to select Marcus Rashford and Stephen Curry. Rashford is 58 years old, has been with the firm for 27 years, and is earning $34,000 annually. Curry is 47, has been with the firm for 3 years, and earns $42,000 annually. Lewerke believes that Rashford will be with the firm until he retires; he is a competent worker whose salary will increase by 4 percent annually, and it is anticipated he will retire at age 65. Curry is a more valuable employee, and Lewerke expects Curry's salary to rise at least 7 percent annually in order to retain him until retirement at age 65. To determine the amount that must be invested annually to fund each pension, Lewerke needs in addition to an estimate of the amount of the pension) an estimate of how long the pension will be distributed (i.e. life expectancy) and how much the invested funds will earn. Since the firm must pay an interest rate of 8 percent to borrow money, he decides that the invested funds should be able to earn at least that amount. Lewerke has come to you for assistance, pleases address the following questions: 1. If each individual retires at 65, how much will their estimated individual pensions be? Estimated ending salaries: Marcus: S44,741.68 _(65-58 N, 4% I/Y, 34,000 PV, Solve FV) Stephen: $141,957.16_(65-47 N, 7% I/Y, 42,000 PV, Solve FV) Estimated pensions: Stephen: 141,957.16 (75%-12%) = $89,433.01 2. Life expectancy for both employees is 15 years after age 65. If the firm buys an annuity from an insurance company to fund each pension and the insurance company asserts it is able to earn 9% on the funds invested in the annuity, what is the cost (or the $ amount required) to purchase the annuity contracts today? (Solve for PV) Marcus: $270,486.56 (15N, 91/4, -33,556.26 PMT, FV 0.) Stephen: $720,891.63 (15N, 91/Y, -89,433.01 PMT, FV 0) 3. If the firm can earn 8% on the money it must invest annually to fund the pension plans (assuming they have not started saving yet), how much will the firm have to invest annually to have the funds necessary to purchase the annuities at the time each employee retires? Marcus: $30,314.10 (7 N, 8 1/Y, O PV, 270,486.56 FV) Stephen: $19,249.32 (18 N, 8 1/Y, O PV, FV 720,891.63) I 4. If the firm continues to estimate 8% annually on the money it must invest to fund the pension plans, yet makes annuity contributions on a quarterly basis instead of just annually, what will be the amount of each payment? How much more or less (S) will they pay each year compared to your results in Q3? Pro