Understanding the time value of money for FAR is incredibly important. It appears in the accounting for leases, bond valuation, corporate finance (BEC), and pension accounting, just to name a few. Conceptually, it should be a very easy topic for students to master - a dollar today is worth more than a dollar tomorrow for the simple reason that with a dollar today one can consume, and without a dollar today one cannot consume. To compensate someone for delaying his or her consumption, interest is added to the principal amount (the amount of money that is being delayed). This interest represents the price of consumption today. The most common proxy used for this interest rate is the risk-free US Treasury rate. Any interest premium in addition to the US Treasury rate represents compensation for any other risk factors. This all should seem intuitive.
The AICPA does not allow the use of financial calculators on the CPA exam. Students are only allowed to use simple calculators that are provided with the testing software. This makes calculating present values and future values incredibly cumbersome and monotonous. Therefore, the AICPA relies heavily on discount factors and future value multiples to test students on these concepts. This is where the confusion ensues! Students need to be comfortable with this approach, so taking a step back and understanding the mechanics of what is going on is important. Here are some steps to take:
Step 1: Understand the difference between fixed cash flows and uneven cash flows
Cash flows that are fixed over a period of time – the same amount of cash is being paid or received every period – is known as an annuity. If the first payment occurs at the very beginning it’s called an annuity due, and if it occurs one year from the very beginning it’s called an ordinary annuity. Students should understand that mechanically these are the exact same thing. The only difference is the timing of the first payment – an annuity due occurs right away, thus the first cash flow is NOT discounted. After the first payment, it is EXACTLY the same thing as an ordinary annuity, with one exception: it will have one less payment on the back end – the annuity due is one period shorter. Working with annuities is simple. Since each year is the same cash flow, the discount factors and present value multiples can be applied to arrive at a discounted present value or future value, respectively.
Uneven cash flows are exactly that, they are uneven! This means that there is not a fixed cash flow in each period. Instead, cash flows occur in unequal amounts. The cash flow received in period T could be twice as much, three times as much, or half as much as the cash flow that is received in period T+1. Uneven cash flows are much more complicated to work with as a discount factor or future value multiple must be applied to each cash flow individually – the discount factors and future value multiples that are used for annuities CANNOT be applied to uneven cash flows.
Step 2: Understand the mechanics of discounting and future-valuing cash flows
Don’t lose sight of the theory during the application! Think intuitively about the problem at hand. Is the question asking for a future value or a present value? What cash flows are relevant to the problem? What interest rate is relevant to the problem? All these questions, and many more, should be coming to your mind when you are looking at any question involving discounting or future valuing cash flows. It can be tricky, which is why it’s important to spend the time to understand these topics, and working with a tutor can really help.
Step 3: Get the pencil and paper out and do some algebra!
As mentioned earlier, the AICPA likes to provide discount factors and future value multiples. This is where many students get confused. When I am working with students, I find it best to get back to the basics and start using some algebra. These discount factors and future value multiples are simple a summation of each year’s factor or multiple. Breaking it down into an algebraic formula is incredibly helpful as it ties everything together. This way, there is no longer confusion about the mechanics, but only about isolating the relevant information as discussed in step 2.
About to the Author: Tyler Remick has an undergraduate degree in Accounting, a M.S. in Finance, an M.A. in Economics, is a CPA, and is also a CFA (which is probably the most respected professional finance related certification you can earn). He is currently pursing a PhD in Economics at George Washington University. Tyler has many years of teaching and tutoring experience, particularly helping students pass all 4 sections of the CPA Exam.