P1.6 Carolyn Bowen, who just turned 55, is employed as a administrative assistant for the Xcon Corporation where she has worked for the past 20 years. She is in good health, lives alone, and has two grown children. A few months ago, her husband died. Carolyn's husband left her with only their home and the proceeds from a $75,000 life insurance policy. After she paid medical and funeral expenses, $60,000 of the life insurance proceeds remained. In addition to the life insurance proceeds, Carolyn has $37,500 in a savings account, which she had accumulated over the past 10 years. Recognizing that she is within 10 years of retirement, Carolyn wishes to use her limited resources to develop an investment program that will allow her to live comfortably once she retires. Carolyn is quite superstitious. After consulting with a number of psychics and studying her family tree, she feels certain she will not live past 80. She plans to retire at either 62 or 65, whichever will better allow her to meet her long-run financial goals. After talking with a number of knowledgeable individuals-including, of course, the psychics-Carolyn estimates that to live comfortably, she will need $45,000 per year before taxes once she retires. This amount will be required annually for each of 18 years if she retires at 62 or for each of 15 years if she retires at 65. As part of her financial plans, Carolyn intends to sell her home at retirement and rent an apartment. She has estimated that she will net $112,500 if she sells the house at 62 and $127,500 if she sells it at 65. Carolyn has no financial dependents and is not concerned about leaving a sizable estate to her heirs. If Carolyn retires at age 62, she will receive from Social Security and an employer-sponsored pension plan a total of $1,359 per month ($16,308 annually); if she waits until age 65 to retire, her total retirement income will be $1,688 per month ($20,256 annually). For convenience, Carolyn has already decided that to convert all her assets at the time of retirement into a stream of annual income, she will at that time purchase an annuity by paying a single premium. The annuity will have a life just equal to the number of years remaining until her 80th birthday. If Carolyn retires at age 62 and buys an annuity at that time, for each $1,000 that she puts into the annuity she will receive an annual benefit equal to $79 for the subsequent 18 years. If she waits until age 65 to retire, each $1,000 invested in the annuity will produce an annual benefit of $89.94 for the next 15 years. Carolyn plans to place any funds currently available into a savings account paying 6% com- pounded annually until retirement. She does not expect to be able to save or invest any addi- tional funds between now and retirement. For every dollar that Carolyn invests today, she will have $1.50 by age 62, or if she leaves the money invested until age 65, she will have $1.79 for each dollar invested today.

Questions

a. Assume that Carolyn places currently available funds in the savings account. Determine the amount of money Carolyn will have available at retirement once she sells her house if she retires at (1) age 62 and (2) age 65.

b. Using the results from

a, determine the level of annual income that will be provided to Carolyn through purchase of an annuity at (1) age 62 and (2) age 65.

c. With the results found in the preceding questions, determine the total annual retirement income Carolyn will have if she retires at (1) age 62 and (2) age 65.

d. From your findings, do you think Carolyn will be able to achieve her long-run financial goal by retiring at (1) age 62 or (2) age 65? Explain.

e. Evaluate Carolyn's investment plan in terms of her use of a savings account and an annuity rather than some other investment vehicles. Comment on the risk and return characteristics of her plan. What recommendations might you offer Carolyn? Be specific.