14 Questions to Introduce Present Value

When I talk with financial accounting teachers, the topic of present value will eventually come up. Teachers are often puzzled by how much they should cover. Some teachers tell me they skip present value entirely whereas others let me know that they believe extensive coverage is necessary. What does a sophomore in an introductory financial accounting class need to know about present value? What can they really understand? I find that if I throw terms like “discounted cash flows” and “the time value of money” at my sophomores, they quickly become lost. What seems crystal clear to me as the teacher can be puzzling to a young student.

However, if students are going to take other business courses or other accounting courses, they need to have some basic understanding of present value concepts. So, yesterday, in my classes here at the University of Richmond, we began to examine present value.

I did this by looking asking them the following series of questions:

1 – What is interest? (Interest is the charge for using money over time – students seem comfortable with that definition.)
2 – If I buy a piece of land and make a single payment of $200,000 today, how much do I pay and why am I paying that amount? (The students seem puzzled by that question because it is self-evident—you pay $200,000 and you pay it to acquire the land.)
3 – I buy a piece of land and agree to pay $200,000 in exactly two years. In the interim, I will pay an additional 10 percent (or $20,000) each year. How much do I pay and why am I paying that amount? (Students realize that $240,000 is paid--$200,000 for land and $40,000 as interest over the two years. The interest is necessary because of the introduction of time to the cash payment.)
4 – I buy a piece of land and agree to make a single payment of $200,000 in exactly two years. Nothing else is paid. If interest is the charge for using money over time, is it reasonable to believe that some part of that $200,000 will actually be paid as interest with the rest being the amount paid for the land? (This is obviously an essential question. I find that students are open to the possibility that part of the payment is for interest since there is a two-year wait for the cash.)
5 – I buy a piece of land and agree to make a single payment of $200,000 in exactly two years. GAAP requires that we view part of the $200,000 as payment for the land with the remainder as payment for interest since I am delaying my payment. What is our next problem? (Students understand that they do not know how to allocate the $200,000 between the land and the interest. They don’t mind the split but don’t know where to draw the line between the land and the interest.)
6 – Mathematically, we can determine the amount of interest. If we determine the interest and then remove it from the $200,000, what is left? (The remaining amount is what we are paying for the land. Again, that seems self-evident to most students. There are only two possibilities: land and interest.)
7 – Why do we determine the amount of interest and then remove it? (Interest is the charge for using money over time. Since no time has yet passed, there can be no interest at this time.)
8 – What do we mean by present value? (It is a future flow of cash with the interest removed because no time has yet passed.)
9 – When we are making a present value calculation, what are we doing? (Present value is the removal of the interest that we assume is included in the cash flows. The present value calculation removes interest because no time has yet passed.)
10 – If we buy land by agreeing to pay $200,000 in two years, how do we record the acquisition? (Both the land and the liability are recorded at present value. Accountants assume there is a charge for using money over time. Part of the $200,000 is assumed to be for interest. No time has yet passed. Thus, that interest is removed and the rest is the amount of the debt incurred today to buy the land.)
11 – Whether we use a formula, tables, or a spreadsheet, what is the purpose of the present value computation? (It mathematically removes the interest from future cash flows. We don’t have to guess at what part is interest and what part is for the land. The present value computation automatically removes the interest mathematically.)
12 – The land and the liability are both recorded at the present value of the cash flows. What happens at the end of Year One? (Time has now passed. The assumed interest rate is multiplied by the liability [principal] balance and that shows the interest expense to be recorded for that first period. It is not paid right then so it is compounded—the interest is added to the liability [principal] balance. The land account is not changed. Its cost was established when it was first acquired. The liability balance grows.)
13 – What happens at the end of Year Two? (More time has now passed. The assumed interest rate is multiplied by the new liability [principal] balance. That provides the interest expense for the second period. It is recognized and the liability is again increased because of compounding.)
14 – After two years, what is the reported liability balance? (The liability balance will be the $200,000 total that is now due to be paid. Present value removes the interest because no time has passed. The accountant then puts that interest back in over time. Mathematically, the amount has to come back to the total amount of the cash flows. Interest is taken out; then, the interest is put back in.)

Okay, you have to ask the questions carefully and guide your students as they work to get their answers. But I was pleased yesterday. After we had walked through these 14 questions, all of my students seemed to have a basic understanding of the concept of present value. We will practice this until they get smooth. However, that “mathematically remove the interest because time has not yet passed” line is one that they seem to grasp just fine. They are obviously not present value wizards yet but they know enough now that we can build on that knowledge and, eventually, they will be able to go into a finance class and not start out totally lost. And, to me, that is the purpose of an introductory course.