Q1. Karl and Karen Arlt are both thirty-five years old and have two children, Noah and Jamie ages 5 and 7, respectively. Karen is a tenured professor at the local state college and Karl is an engineer working at an electrical utility company. Together the Arlts have a combined income of $150,000 per year. The Arlts are meeting with a financial consultant Katherine Ryals, CFA, for the first time who was recommended to them by Karl’s brother who is also training with Ryals to become a financial consultant himself. The four of them are meeting around the Arlt’s dining room table where Ryals is gathering information to determine an investment policy statement for the Arlts who state they want to retire when they are 60 years old. One of the questions asks the Arlts about their general feelings of risk and Karen blurts out “the recent turmoil in the financial markets due to the mortgage crisis makes me sick to my stomach!” Up to this point in their lives the Arlt’s have not amassed a significant amount of financial wealth nor have they given much thought about leaving a bequest.
It is now two weeks later and the Arlt’s are meeting with Ryals and Karl’s brother again. Ryals suggests that they purchase a million dollar variable universal life (VUL) policy whereby their premium payments will go into mutual fund type investments resulting in equity-like returns. She states “because your incomes are stable your human capital is fixed income-like thus to be able to replace your steady income your demand for life insurance is high.” She goes on to state “since your incomes are stable your assets should be invested in more equity-like investments like the ones found in the VUL thus it is the perfect investment vehicle for you.”
Ryal’s analysis reveals that to maintain their current $150,000 per year income when they retire in 25 years at age 60 assuming a 3% increase in income per year would require an income stream of about $314,000 per year. This represents a portfolio worth approximately $3.3 million at retirement, assumes they live another 20 years during retirement, achieve a 7% rate of return on their portfolio during retirement, and there is nothing left of the portfolio at the end of 20 years. Ryals goes on to further explain that to amass the equivalent of $3.3 million 25 years from now given they have no retirement savings now and assuming a 10% yearly rate of return would require them to save roughly $2,500 per month.
After careful consideration of their insurance needs the Arlts decide to purchase term insurance on both of them and invest a portion of their after tax income into a deferred variable annuity. Upon retirement the Arlts are expecting to choose the largest cash outflow possible from the annuity utilizing the “joint and survivor” payout option.

Based on the information regarding Karl and Karen’s incomes the discount rate used to determine their human capital would be:

A)   low representing lower risk due to their stable incomes.

B)   high because their incomes would have a low variability over time.

C)   indeterminate since the discount rate is based on factors other than the variability in their incomes.

答案和详解如下：

Q1. Karl and Karen Arlt are both thirty-five years old and have two children, Noah and Jamie ages 5 and 7, respectively. Karen is a tenured professor at the local state college and Karl is an engineer working at an electrical utility company. Together the Arlts have a combined income of $150,000 per year. The Arlts are meeting with a financial consultant Katherine Ryals, CFA, for the first time who was recommended to them by Karl’s brother who is also training with Ryals to become a financial consultant himself. The four of them are meeting around the Arlt’s dining room table where Ryals is gathering information to determine an investment policy statement for the Arlts who state they want to retire when they are 60 years old. One of the questions asks the Arlts about their general feelings of risk and Karen blurts out “the recent turmoil in the financial markets due to the mortgage crisis makes me sick to my stomach!” Up to this point in their lives the Arlt’s have not amassed a significant amount of financial wealth nor have they given much thought about leaving a bequest.
It is now two weeks later and the Arlt’s are meeting with Ryals and Karl’s brother again. Ryals suggests that they purchase a million dollar variable universal life (VUL) policy whereby their premium payments will go into mutual fund type investments resulting in equity-like returns. She states “because your incomes are stable your human capital is fixed income-like thus to be able to replace your steady income your demand for life insurance is high.” She goes on to state “since your incomes are stable your assets should be invested in more equity-like investments like the ones found in the VUL thus it is the perfect investment vehicle for you.”
Ryal’s analysis reveals that to maintain their current $150,000 per year income when they retire in 25 years at age 60 assuming a 3% increase in income per year would require an income stream of about $314,000 per year. This represents a portfolio worth approximately $3.3 million at retirement, assumes they live another 20 years during retirement, achieve a 7% rate of return on their portfolio during retirement, and there is nothing left of the portfolio at the end of 20 years. Ryals goes on to further explain that to amass the equivalent of $3.3 million 25 years from now given they have no retirement savings now and assuming a 10% yearly rate of return would require them to save roughly $2,500 per month.
After careful consideration of their insurance needs the Arlts decide to purchase term insurance on both of them and invest a portion of their after tax income into a deferred variable annuity. Upon retirement the Arlts are expecting to choose the largest cash outflow possible from the annuity utilizing the “joint and survivor” payout option.

Based on the information regarding Karl and Karen’s incomes the discount rate used to determine their human capital would be:

A)   low representing lower risk due to their stable incomes.

B)   high because their incomes would have a low variability over time.

C)   indeterminate since the discount rate is based on factors other than the variability in their incomes.

Correct answer is A)
The Human Capital equation is:

Since the Arlts both have stable incomes with Karen being a tenured college professor and Karl working in the utility industry, neither of which are closely tied to the economy, the risk of their incomes is low thus the risk premium would also be low resulting in a lower overall discount rate and higher human capital.

Thank you!