Reading #5, the Time Value of Money (TVM), was a fun chapter once I learned how to let my 12C do most of the work. TVM is something everyone should know because, as a wise person once said:
– Bernstein? Bogle?
In other words, everyone has to manage their cash flow over their lifetime, regardless of whether they find investing interesting.
And knowing the very practical financial calculations of TVM gives you some great tools for computing how much you need to put away each year for your children’s college, whether to take a lump sum up front or periodic payments over time (important when you win the lottery), how much to save in order to have a certain annual cash flow in retirement, and so on.
I claim to understand this stuff pretty well now. I even scored 100%^{*} on the practice problems.
…OK, why the asterix?
Well I missed part C of the very first problem, at least according to the solution key. But in my opinion, this is an error in the study guide. There is no CFA errata for the 2008 exam yet, but I’m betting when there is, this will be on there.
The Correct Solution Key to Practice Problems #5
Speaking of TVM problems, retirement, and so forth, some of the problems in the chapter ask you to work out how much money someone needs to put away each year for the next X years in order to have an annual cash flow of Y for something like 20 years once they retire.
This always begs the question of what happens if someone lives longer than they predicted? Now you could tack on a few years to your estimated lifetime, but the fact is, you may turn out to live a a lot longer than you thought.
As was first brought to my attention by one of Bernstein’s books, and as the TVM calculations will demonstrate, in many cases it doesn’t cost much more in the periodic savings payments to create a perpetuity for yourself instead of an annuity. No worries then!
An example: You plan to retire 30 years from today at age 65. How much should you invest at the end of each year for the 30 years you have left to work, earning 8% annually, in order to have a cash flow of $100,000 per year for 20 years starting the day you retire?
And how much more would it cost you to have that $100K coming in for 40 years? 57 years? An infinite number of years?
Hopefully I’ll get this right after bragging about my TVM practice test performance…

20 Years: Your annual payment would be $9,360.26
40 Years: Your annual payment would be $11,368.48
57 years: Your annual payment would be $11,768.78
∞ Years: Your annual payment would be $11,917.04
The payment for 20 years is a bit lower, but planning on only living to 85 is probably a bit risky – at least given the age of my grandparents.
40 years seems safe, but for only an extra $550 a year, you get a perpetuity. Security for your family while you’re alive, an endowed chair in your name in the finance department after you’re gone… ðŸ™‚
I love the blog! It is very informative and helpful. Quick question though — are you using any supplement guides like Schwesher? Or are you just using the textbooks?
Thanks for the comments! No supplements so far. The study guides that you get from the CFA Institute when you register for the exam are all I’m using. They’ve been adequate so far but I’m only a couple hundred pages into Volume I.
Lumilog
I wonder if these guides are available in libraries or say on ebay for used prices? I’d like to see what they say (but 18lbs. for just the level I – if that’s correct) seems kind of excessive. Isn’t mathematics supposed to be terse and elegant!