A Time-Value Exercise for Your Students

 

I have a confession to make. I have been teaching the Introductory Corporate Finance Finance course for 18 years and have, for the first time, required students to purchase a financial calculator. (Hard to believe, eh?)

How have I taught Time Value up to this point? I simply require them to have a calculator with an exponent key, then use "Martin's Method." Martin's Method is as follows:

1. Draw a time line and indicate the cash inflows and outflows.
2. Choose a "focal point" on the line and discount or compound, as necessary, all outflows, then all inflows, to that point.
3. Equate the values at that point of the inflows and the outflows, and solve for the unknown.

The above approach is simple and intuitive, and yet, forces students to understand what is happening to "make the formulas work". Further, it allows one to solve the most complex problems in a few steps.

However, I have now added instruction on the use of a financial calculator to my TVM sessions. Why? For the same reason those in K-12 teaching have been pushing for calculator use for many years - once students understand the problem-solving process, why not reduce the tedium of repetitive calculations via the use of a mechanical aid? (As the parent of an 11-year old, I should point out that I have mixed feelings about this argument for lower-level students, but I digress.)

Anyway, here's a simple TVM exercise to introduce both techniques to your students. First, the problem.

As of January 16, the average rate on a conventional 30-year mortgage had fallen to 6.89% from 7.87% a year earlier and, as a result, refinancings currently constitute approximately 60% of all mortgage applications. (Twenty percent is typical.) If Henry had borrowed $200,000 one year ago, and is able to refinance the outstanding balance at today’s rate, by how much will his monthly payment fall?,/p>

Using Martin's Method, we draw the time line, choose the focal point as time 0, and set up the following equations:

Step 1: $200,000 = Payment x PVIFA(.0787/12, 360) ---> Payment = $1,449.44

Step 2: Outstanding balance = $1,449.44 x PVIFA(.0787/12, 348) ---> OB = $198,285.70

Step 3: $198,285.70 = Payment x PVIFA(.0689/12, 360) ---> New Payment = $1,304.58

Now, here's the same problem worked using a HP10B calculator ("gold" refers to the key on the leftmost column of the keypad, second up from the bottom):

Step 1: gold, clear all
12, gold, P/YR
30, gold, xP/YR
200,000 , PV
7.87, I/YR
PMT = -$1,449.4447

Step 2: gold, clear all
12, gold, P/YR
29, gold, xP/YR
1449.4447, PMT
7.87, I/YR
PV = $198,285.6966

Step 3: gold, clear all
12, gold, P/YR
30, gold, xP/YR
198,285.6966, PV
6.89, I/YR
PMT = -$1,304.5838

Using both approaches will take a bit longer; however, it will go a long way to ensuring that students will understand why they get the answers they get. (My own bias is that the "why" is as important as the "how".) Also, I should point out that the first two lines in each step are redundant -- at this point, however, I think students should be attempting to minimize the possibility of error, rather than maximizing speed.

Do you have some calculator tips? Some good problems? Let me know!

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