Household Saving and Investment Decisions

1. Many experts recommend that when making a savings plan, you should aim for a replacement rate equal to 75% of your income. You are currently 30 years old and plan to retire at 65. The real interest rate is 3% per annum.

a) If your real income is $40,000 a year, what is your target level of retirement income?

b) From your answer in a), how large should your retirement fund be at age 65 to be able to withdraw your target retirement income every year for the next 20 years?

c) How much do you need to save each year in order to accumulate the necessary retirement fund computed in b)?

2. You are currently 30 years old, you plan to retire at 65 and live up to 90 with your retirement fund. You plan to maintain the same consumption level C, in each of the next 60 years. The monthly real interest rate is 2% per annum. Your preretirement income is $50,000 a year.

a) How large should your retirement fund be at age 65 to be able to withdraw your target retirement income every year for the next 25 years? Leave your answer in terms of consumption level C.

b) How much do you need to save each year in order to accumulate the necessary retirement fund computed in a)? Leave your answer in terms of consumption level C.

c) From answers in a) and b), solve for the consumption level C.

3. You are now 30 years old and considering full time study for an MBA degree. Tuition and other direct cost will be $20,000 per year for two years. In addition, you have to give up a job with a salary of $35,000 per year. Assume tuition is paid and salary received at the end of this year. Assume a real interest rate of 3% and ignore taxes. With an MBA degree, you can find a job that pays a constant real amount of $42,000 and last until a retirement of 65.

a) In present value terms, what is the cost from obtaining an MBA degree? (Hint: During your full time study, you have to pay for tuition in addition to giving up your current job)

b) What is the present value from an increased in salary from an MBA degree?

c) What the net present value from an MBA degree? Based on this cost-benefit analysis, should you pursue an MBA degree?

4. Suppose you currently renting an apartment at $6000 a year and have an option to buy it for $150,000. Property taxes are $1,500 per year and are deductible for income tax purposes. Annual maintenance cost on the property are $1,200 per year and are not tax deductible. You expect property taxes and maintenance cost to increase at the rate of inflation. Your income tax rate is 20%, and you are earn a before-tax real interest rate of 5% per year and you plan to keep the apartment forever.

a) If your income on interest is taxed at the rate of 20%, what is your real after-tax interest rate?

b) What is the present value from renting the apartment forever? What is the present value from buying and owning the apartment?

c) Would you choose to buy or own an apartment? Briefly explain.