Mastering CAGR and Holding Yield: Step-by-Step Excel Guide with RATE, XIRR Functions and ChatGPT Prompt

 

Understanding CAGR and Holding Yield in Finance

Introduction

The Compound Annual Growth Rate (CAGR) and Holding Period Yield (HPY) are crucial metrics used to evaluate investment performance. This blog explores their importance using a practical example of an investment in a fund, examining both the CAGR and HPY to highlight their differences and significance in financial analysis.

Investment Example

An investment of $117,976 was made on October 18, 2016, and grew to $276,318.30 by February 21, 2025. The reinvestment of unit distributions is already included in the final value.

Step-by-Step Calculations Using Excel Functions

1. Calculate the Holding Period in Days

• Start Date: October 18, 2016
• End Date: February 21, 2025
• Excel Formula: =DATEDIF("2016-10-18", "2025-02-21", "D")
• Total Days: 3,047 days

2. Calculate the Holding Period Yield (HPY) The formula is: =((FV - PV) / PV) * 100

• Final Value (FV): $276,318.30
• Initial Investment (PV): $117,976
• Excel Formula: =((276318.30 - 117976) / 117976) * 100
• Result: 134.19%

3. Calculate the Number of Years (n) Convert the holding period in days into years:

• Excel Formula: =3047 / 365
• Result: 8.34 years

4. Calculate the Compound Annual Growth Rate (CAGR) Using the RATE function in Excel:

• Syntax: =RATE(n, 0, -PV, FV)
• Formula: =RATE(8.34, 0, -117976, 276318.30)
• Result: 10.25%
• Note: The RATE function assumes a year consists of exactly 365 days.

5. Calculate CAGR Using the XIRR Function

• Create a table with dates and cash flows:
  • Row 1: 2016-10-18, -117976 (initial investment, negative because it's an outflow)
  • Row 2: 2025-02-21, 276318.30 (final value, positive because it's an inflow)
• Excel Formula: =XIRR(B2:B3, A2:A3)
• Result: 10.73%
• Explanation: The XIRR function considers the actual number of days in each year (365 or 366 for leap years), providing a slightly higher return than the RATE function.

Comparison: CAGR vs. Holding Period Yield

• CAGR (10.25% using RATE, 10.73% using XIRR) represents the annualized rate of return, smoothing out fluctuations and providing a clear picture of consistent growth.
• HPY (134.19%) reflects the total percentage increase over the entire holding period.

The difference between the RATE and XIRR results is due to the treatment of calendar days. RATE uses a simplified 365-day year, while XIRR accounts for leap years, making it more accurate for long-term investments.

Importance of CAGR in Finance

CAGR simplifies the comparison of investment performance over different periods. Key applications include:

• Evaluating Investment Performance: Provides a clear view of growth trends.
• Comparing Different Investments: Standardizes returns for fair comparisons.
• Forecasting Future Returns: Helps estimate potential future growth.

ChatGPT Prompt

As a certified financial planner, Calculate and compare the Compound Annual Growth Rate (CAGR) and Holding Yield for an investment initially valued at $117,976 on October 18, 2016, which grew to $276,318.30 by February 21, 2025 (including reinvested unit distributions). Provide the final comparative values for CAGR and Holding Yield rounded to two decimal places, formatted clearly in a concise table. Additionally, briefly interpret the meaning and practical implications of these two metrics for evaluating investment performance. This calculation serves as an alternative verification method to standard financial calculators and Excel.

Conclusion

In conclusion, both CAGR and HPY are essential for assessing investment performance. However, CAGR's annualized perspective makes it particularly valuable for long-term financial planning and comparative analysis, and using Excel functions like RATE and XIRR ensures accurate and efficient calculations.

Understanding and Calculating CAGR Using Different Methods

Introduction

The Compound Annual Growth Rate (CAGR) is a useful measure to determine the mean annual growth rate of an investment over a specified period, assuming the profits were reinvested at the end of each year. It provides a clear picture of an investment’s performance over time. Various methods can be used to calculate CAGR, including Excel's IRR, XIRR, TVM functions, and a standard mathematical formula.

Simple CAGR Calculation Example

Let’s assume you invested $10,000 in a portfolio on January 1, 2005. Over time, the investment grew as follows:

• $13,000 by January 1, 2006

• $14,000 by January 1, 2007

• $19,500 by January 1, 2008

If you liquidate your investment on January 1, 2008, the CAGR can be calculated using the following methods:

1) Excel IRR Method

• Define the cash flows, with negative values for outflows (initial investment) and positive values for inflows (returns).

• Ignore intermediate portfolio growth that does not contribute to cash flow; zeros should be explicitly stated where applicable.

• Use the IRR function for the selected range: =IRR(B4:B7).

2) Excel XIRR Method

• Define the cash flows, with the same convention of negative for outflows and positive for inflows.

• Assign transaction dates to each cash flow.

• Use the XIRR function to calculate the internal rate of return based on specific transaction dates: =XIRR(B12:B13,A12:A13).

3) Excel TVM (Time Value of Money) Method

• Use the RATE function with the formula:

  =RATE(n, pmt, PV, FV, mode)

  Where:

  • n = number of years

  • pmt = periodic payment (if applicable)

  • PV = present value (initial investment)

  • FV = future value (final value of investment)

  • mode = 0 or 1 (payment timing)

4) Mathematical Formula Method

• The CAGR formula:

  CAGR = (FV / PV)^(1/n) - 1

  Where:

  • FV = final value

  • PV = initial investment

  • n = number of years

Real-Life CAGR Calculation

In reality, investments involve multiple transactions, such as:

• Initial investment

• Additional top-up investments

• Dividend payouts

• Bonus issues

• Partial or full liquidation

Since these transactions occur at different times, the XIRR function in Excel is the most versatile method for computing CAGR. It considers the timing of cash flows, making it more precise for real-world applications.

Conclusion

Understanding CAGR is crucial for evaluating investment performance over time. While the mathematical formula provides a quick approximation, Excel’s IRR, XIRR, and TVM functions offer more flexibility for various scenarios. For real-life investment tracking, XIRR is the most reliable method as it accounts for irregular cash flows.