The IRR for Project X is:
[CF] [2nd] [CLR WORK]
2,000 [+/-] [ENTER] [↓]
1,000 [ENTER] [↓][↓]
800 [ENTER] [↓][↓]
600 [ENTER] [↓][↓]
200 [ENTER] [↓]
[IRR] [CPT] gives the result, 14.48884.
A note on Net Present Value (NPV): For NPV calculations on the examination, we
recommend computing the present value of each individual cash flow and adding
them together. No need to memorize more calculator functions - you’ve got enough to
memorize for the exam! However, for the curious, the keystrokes to calculate NPV
are as follows:
The NPV of Project X is:
[CF] [2nd] [CLR WORK]
2,000 [+/-] [ENTER] [↓]
1,000 [ENTER] [↓][↓]
800 [ENTER] [↓][↓]
600 [ENTER] [↓][↓]
200 [ENTER] [↓]
[NPV] {10} [ENTER] [↓]
[CPT] gives the result, $157.63951.
7. The natural log function (Primarily for CFA Levels 2 and 3)
The natural log function is intimately related to ex. In Level 1, you will use this
function to calculate a continuously compounded return given a specific holding
period return. The natural log function (LN) is also used when working Black-
Scholes and Merton Model problems.
Example: The value of the stock is $45 (S) today and the exercise price of a call
option that trades on that stock is $50 (X). Calculate the natural log of (S/X).
Step 1: Compute S/X
45/50 = 0.90
Step 2: Compute ln(S/X)
{0.90}→[LN] = -0.10536
HOW TO USE YOUR TI BA II PLUS CALCULATOR
©2003 Schweser Study Program
8
As a check of the relationship between [LN] and [ex], press {-1.0536}→[2nd]→[ex].
The result is 0.90.
More precisely, eln(x) = x, and, ln(ex) = x
D. Your TI-BA II Plus Statistical Functions (use at your own risk).
Understanding the previous sections of this document is critical to your success on the
exam. What follows are some cool short cuts you can take to calculate the mean and
variance of a small data set. Please beware, that in many cases, doing these computations
by brute force is sometimes quicker. If you feel you’ll have a hard time memorizing
these keystrokes for the exam, don’t sweat it – focus on the actual formulas and basic
calculations. In other words, don’t get fancy – it could backfire!
As with the IRR and NPV calculations, to use the data functions in your TI-BA II Plus,
you must first familiarize yourself with the up and down arrows (↑↓) at the top of the
keyboard. These keys will help you navigate your way through the data entry process.
To enter a data series into your BAII Plus, press [2nd] →[DATA]. Notice that you can
enter both X and Y coordinates (you can actually perform a simple linear regression on
your calculator!). If you just have one data series (X), you will simply press the down
arrow through the prompts for Y data values. Notice that X and Y both begin at X (01)
and Y (01) respectively, and that [X (01), Y (01)] represents one X, Y coordinate pair.
Example: You have been given the following observations that measure the speed of
randomly selected vehicles as they pass a particular checkpoint.
30, 42, 32, 35, 28
Compute the mean ( X ), population variance, and sample variance for this data set.
Step 1: Enter the data: [2nd]→[DATA]
X (01) {30}→[ENTER]→[↓]→[↓]
X (02) {42}→[ENTER]→[↓]→[↓]
X (03) {32}→[ENTER]→[↓]→[↓]
X (04) {35}→[ENTER]→[↓]→[↓]
X (05) {28}→[ENTER]→
Step 2: Calculate the statistics: [2nd]→ [STAT]→ [↓]→[↓]
X = 33.4
[↓] = Sx = sample standard deviation = 5.459
[↓] = σx = population standard deviation = 4.883
HOW TO USE YOUR TI BA II PLUS CALCULATOR
©2003 Schweser Study Program
9
Notice that you’re simply entering through the Y (i) data entry fields – a “1” is placed in
the Y data value as you down-arrow through this value.
Also, remember that the population variance differs from the sample variance in that the
sum of the squared deviations from the mean are divided by n and n – 1 respectively. In
addition, the standard deviation is the square root of the variance.
Example: You have calculated the following returns for an individual stock and the
stock market over the past four months.
Ri (Y) Rm (X)
Month 1 12% 15%
Month 2 8% 4%
Month 3 9% 12%
Month 4 10% 14%
Calculate the stock’s mean return, the market’s mean return, and the correlation between
the stock’s returns and market returns.
Step 1: Enter the data: [2nd]→[DATA] – make sure to [2nd]→[CLR WORK] first!!
X (01): {15}→[ENTER]→[↓]
Y (01) {12}→[ENTER]→[↓]
X (02) {4}→[ENTER]→[↓]
Y (02) {8}→[ENTER]→[↓]
X (03) {12}→[ENTER]→[↓]
Y (03) {9}→[ENTER]→[↓]
X (04) {14}→[ENTER]→[↓]
Y (04) {10}→[ENTER]→[↓]
Step 2: Calculate the statistics: [2nd]→[STAT]→[↓]→
Mean of X [↓] = X = 11.25
Sample standard deviation X [↓] = SX = 4.992
Population standard deviation X [↓] = σx = 4.323
Mean of Y [↓] = Y = 9.75
Sample standard deviation Y [↓] =SY = 1.708
Population standard deviation Y [↓] =σY = 1.479
Intercept term [↓] = a = 6.55
Slope coefficient [↓] = b = 0.284
Correlation X, Y [↓] = r = 0.831
Given this data, we can say that our estimate of the beta of the stock is 0.28, the
correlation of stock i’s returns relative to the market is 83.1%, and the R2 of the
regression is (0.831) 2 = 0.691 or 69.1% (i.e., 69.1 percent of the variation in stock i’s
returns is explained by the variability in market returns).