FINANCE 6500 TIME VALUE PROBLEM SET
Please use your calculator to answer the following questions. Write your answer below each question, including the calculator keystrokes.
The Federal Open Market Committee (FOMC) of the Federal Reserve targets inflation as a means of controlling the economy. They have stated their desire to have an annual inflation rate of 2%. Suppose they are able to achieve this target rate year-in and year-out, and your current annual salary is $100,000. If you plan to retire 35 years from today, how much must your annual salary be 35 years hence to provide as much purchasing power as you have now? (Ignore taxes and other complications.)
Orange, clear all
35, N
2, I/YR
100,000 PV
FV 199,988.955
Now suppose that inflation gets away from the Fed (as it did in the 1970s). As a result, the annual inflation over the next 35 years is 4%, rather than 2%. Now how much must your salary be 35 years hence to provide the same purchasing power you have today?
Orange, clear all
35, N
4, I/YR
100,000 PV
FV 394,608.89
Gomez Addams invested $10,000 into a portfolio of one-year U.S. Treasury bills on January 1, 1926. He (and his descendants) reinvested the proceeds each year until the end of 2018. The average annually compounded rate of return on T-bills over the 93-year period was 2.9%. (Note: 2018-1926 = 92, plus the year 1926 = 93 years overall.) How much was the portfolio worth on December 31, 2018? (Ignore taxes and transactions costs.)
Orange, clear all
93, N
2.9, I/YR
10,000 PV
FV at end of 2018 142,767.66
Refer to the Gomez Addams problem above. Suppose that, instead of U.S. Treasury bills, Gomez had invested $10,000 in a portfolio of large-cap common stocks on January 1, 1926. (Note: a large-cap company has a market cap greater than $10b.) (https://www.investopedia.com/terms/l/large-cap.asp) The average annually compounded rate of return on large-cap stocks over the 93-year period was 9.8%, rather than 2.9 percent. How much larger would the December 31, 2018 value of his portfolio have been, had he invested in large-cap stocks rather than T-bills?
Orange, clear all
93, N
9.8, I/YR
10,000 PV
FV 59,705,952.43
In 2016 A Pevely man won the Missouri lottery and was given the choice of receiving $6.8 million in cash immediately, or 25 annual payments of $400,000 each (also beginning today).
1. At what interest rate would he be indifferent between the two options?
2. Suppose he believes he could earn 6% annually on his investments. Which option should he take?
Lump Sum
Orange, clear all
6,800,000 PV
25, N
6.0, I/YR
FV lump sum 29,184,720.89
Annuity
Orange, clear all
25, N
400,000 PMT
6.0, I/YR
FV annuity 23,262,553.08
He should choose the lump sum option
The second half of this Problem Set is to complete the following retirement exercises for yourself. Please do so with your hand calculator DO NOT use one of the many online retirem...
