5.1 Assume you have $1 million now, and you have just retired from your job. You expect to live for 20 years, and you want to have the same level of consumption (i.e., purchasing power) for each of these 20 years, after adjusting for inflation. You also wish to leave the purchasing power equivalent of $100,000 today to your kids at the end of the 20 years as a bequest (or to pay them to take care of you).
You expect inflation to be 3% per year for the next 20 years, and nominal interest rates are expected to stay around 8% per year.
A. Calculate the actual amount of consumption, in nominal dollars, using the stated assumptions.
i. How much do you need for your kids?
ii. If you plan to consume $1.03 in year 1, how much will you need to have to keep the same real consumption in year 2? In year 10? In year 20?
iii. How much, in nominal dollars, will $1 of retirement funds earn in year 1? Year 2? Year 10? Year 20?
iv. In an Excel spreadsheet (or in a manual table), calculate the following:
a. annual investment earnings for each year
b. total savings after investment earnings for each year
c. subtract annual consumption from total savings each year
d. by trial and error, or with the Goal Seek command, determine the amount of consumption that will give you exactly $100,000, in today's purchasing power, at the end of 20 years
Hint: You will need to make your annual consumption column dependent on the inflation rate, your investment earnings will grow at the nominal rate, and the bequest of $100,000 will grow at the inflation rate.
B. Do the calculation again using real rates, and setting inflation to equal 0. If you set up your Excel spreadsheet carefully, you should be able to set the inflation rate to equal 0 and enter the real rate of return as the investment earning rate.
i. What is the amount of real consumption in year 1? In year 2? In year 10? In year 20?
ii. Show that this is consistent with your calculation using nominal rates.
iii. How much, in real dollars, does that leave for your kids?
iv. Show that your bequest is consistent with the nominal rate results above.
5.2 A. Linus is 18 years old now, and is thinking about taking a 5-year university degree. The degree will cost him $25,000 each year. After he's finished, he expects to make $50,000 per year for 10 years, $75,000 per year for another 10 years, and $100,000 per year for the final 10 years of his working career. If Linus lives to be 100, and if real interest rates stay at 5% per year throughout his life, what is the equal annual consumption he could enjoy until that date?
B. Linus is also considering another option. If he takes a job at the local grocery store, his starting wage will be $40,000 per year, and he will get a 3% raise, in real terms, each year until he retires at the age of 53. If Linus lives to be 100, what is the equal annual consumption he could enjoy until that date?
C. From strictly a financial point of view, is Linus better off choosing option A or B?
The solution discusses TVM concepts for retirement planning.