Level 1 CFA® Exam:
TVM - Practical Problems
In this lesson, we're going to revise what we learned in our three previous lessons and solve some practical problems.
In the beginning, let us consider what kind of problems regarding the time value of money you may expect to encounter in your level 1 CFA exam.
The very basic type of exam questions involves calculating the present or the future value of a single payment. You may be also asked to compute the present or the future value of an annuity or an annuity payment. Also, you may have to determine the present value of a perpetual annuity.
Sometimes you will be asked to compute a stated annual interest rate or effective annual interest rate.
Additionally, to answer a given exam question correctly, you often need to interpret the results, for example, you may need to determine which of the two investments has a higher future value.
You can occasionally come across some questions where you will have to determine the period of time which has to pass to get a particular sum.
Before we move on to some examples, first let's take a look at the algorithm for solving problems that concern time value of money. After reading the question:
- determine what must be calculated,
- establish whether you are dealing with a single payment or an annuity,
- check if it is an ordinary annuity or annuity due,
- put the cash flows on a timeline,
- apply the formulas and – using a calculator – solve the problem,
- interpret the results when necessary.
What’s the present value of a series of 20 payments of USD 2,000 each paid at the end of each year starting at the end of the first year AND a single payment of USD 30,000 which is to be paid 10 years from now if we assume that the discount rate does not change over time and is equal to 4%.
Assume that you're planning to buy a new car for USD 90,000 in four years. In another three years, you'd like to spend USD 20,000 to redecorate your house. How much money should you invest today if you wish to make your plans come true? For the first 4 years, assume a 5% rate of return on the investment and for the next three years assume a rate of return of 3%.
How much is a promise of receiving perpetually a sum of USD 1,000 each month worth now if the stated annual interest rate is 6%?
How much is a promise of receiving perpetually a sum of USD 1,000 each year starting from the end of Year 5 worth now on the assumption that the discount rate is 10%?
You have USD 1,000. Calculate the stated annual interest rate on an assumption that in 3 years from now you want to get USD 1,500. Assume quarterly compounding.
- When you solve TVM-related questions in your level 1 CFA exam, try to remember all relevant aspects, such as:
- whether there is only one payment or a series of payments,
- whether the payments are at the beginning or at the end of the period,
- whether you are asked to calculate the present or the future value, and so on.
- What seems quite interesting about the time value of money is that we can approach these kinds of problems from many different angles. However, in your exam, you should always choose the quickest method of finding the solution because time management is of great importance then.