Lesson 14.4: Showing Numeric Work and Self-Grading

Introduction

In the CFA Level III examination, candidates are required to demonstrate their understanding of complex concepts through constructed responses or essay questions. The ability to present numeric work clearly and logically is crucial for achieving full credit in these essay responses. This lesson focuses on the importance of clearly presenting calculations with appropriate units, stating necessary assumptions, and practicing self-grading against a model rubric.

Learning Objectives

Present calculations and numeric answers clearly with units.
State assumptions where a prompt allows judgment.
Self-grade practice essays against a model rubric.
Present numeric work and final answers clearly.
State necessary assumptions when judgment is required.

Presenting Calculations and Numeric Answers Clearly

Importance of Clarity in Numeric Work

When grading essay responses, examiners look for clarity and precision in the presentation of calculations. Candidates should ensure that all numeric work is shown in an organized manner that includes the appropriate units. This enables the grader to follow the thought process and assess the work accurately.

Example 1: Calculating the Net Present Value (NPV)

Consider an investment that requires an initial outlay of $100,000 and is expected to generate cash inflows of $30,000 annually for five years. The discount rate is 10%.

Step 1: Present the Calculation

First, we need to calculate the present value of each cash inflow. The present value (PV) of a future cash flow can be calculated using the formula:

$$PV = \frac{CF}{(1 + r)^t}$$

where:

$CF$ = Cash flow in a given year
$r$ = Discount rate
$t$ = Year

Step 2: Calculate the Present Value of Each Cash Flow

For Year 1:

$PV_1 = \frac{30,000}{(1 + 0.10)^1} = \frac{30,000}{1.10} = 27,273$

For Year 2:

$PV_2 = \frac{30,000}{(1 + 0.10)^2} = \frac{30,000}{1.21} = 24,793$

For Year 3:

$PV_3 = \frac{30,000}{(1 + 0.10)^3} = \frac{30,000}{1.331} = 22,556$

For Year 4:

$PV_4 = \frac{30,000}{(1 + 0.10)^4} = \frac{30,000}{1.4641} = 20,448$

For Year 5:

$PV_5 = \frac{30,000}{(1 + 0.10)^5} = \frac{30,000}{1.61051} = 18,643$

Step 3: Sum the Present Values

Now we sum the present values to find the total present value of the cash inflows:

$$NPV = PV_1 + PV_2 + PV_3 + PV_4 + PV_5$$

$$NPV = 27,273 + 24,793 + 22,556 + 20,448 + 18,643 = 113,713$$

Step 4: Calculate NPV

Finally, calculate the NPV by subtracting the initial investment:

$$NPV = Total~PV - Initial~Investment$$

$$NPV = 113,713 - 100,000 = 13,713$$

Clarity Tips

Always include units when presenting numeric answers, e.g., 'The NPV is $13,713.'
Write each step clearly so that the grader can follow your thought process.

Stating Assumptions

Why Assumptions Matter

In essay prompts that allow for judgment, stating your assumptions explicitly is essential. This not only demonstrates critical thinking but also helps the grader understand the basis of your calculations.

Example 2: Assumptions in Discount Rate Selection

Assuming we continue with the above NPV example, let’s say the prompt allows us to state an assumption about the discount rate used.

When justifying the choice of a discount rate, you might say:

Assumption 1: The discount rate of 10% represents the firm's weighted average cost of capital (WACC), which is appropriate given the risk profile of the investment.

This assumption is important because it provides context for your calculations. If you had chosen a different discount rate without explanation, the grader may not understand the basis of your analysis.

Tips for Stating Assumptions

Be concise but thorough; clarify why you made specific choices.
Link assumptions directly to your calculations so that they support your reasoning.

Self-Grading Practice Essays

The Importance of Self-Grading

Self-grading encourages candidates to critically analyze their work against a given rubric, enabling them to identify areas of improvement and reinforce learning.

Example 3: Self-Grading Using a Rubric

Let’s assume you have written an essay response to a practice question. The model rubric has criteria like:

Clarity of calculations (30%)
Proper use of units (20%)
Justification of assumptions (20%)
Overall structure and coherence (30%)

Step 1: Grade Your Own Work

After completing your essay, reflect on each criterion:

Clarity of calculations: Did you show every step? Were your calculations easy to follow?
Proper use of units: Did you consistently use units in your answers?
Justification of assumptions: Did you clearly state and justify your assumptions?
Overall structure and coherence: Was your essay logically structured?

Step 2: Assign a Score to Each Criterion

For example:

Clarity of calculations: 25/30
Proper use of units: 20/20
Justification of assumptions: 15/20
Overall structure and coherence: 25/30

Example Self-Grade Summary

Total Score: 25 + 20 + 15 + 25 = 85/100

Reflect on areas for improvement based on your analysis, and adjust future responses accordingly.

Conclusion

Mastering the presentation of numeric work, stating assumptions, and engaging in self-grading are critical skills that will enhance your constructed response quality. Candidates who can articulate their thought processes clearly and justify their assumptions will stand out in the CFA Level III exam.

Study Notes

Prioritize presenting calculations with clarity and the correct units.
State any assumptions clearly when the prompt allows.
Practice self-grading using a rubric to analyze and improve your responses.
Reflect on your writing and identify areas of weakness for continuous improvement.