In this post, let us consider how to calculate returns from ‘dividend’ and ‘dividend reinvestment’ mutual funds.
This post represents an understanding of an issue which has always troubled me since the (first) manual version of mutual fund tracker (notice the frequent revisions).
I thought I finally had it right in the automated version, until Mr. Deepak Rao wrote in saying that the way dividends were handled for CAGR calculation in the tracker was wrong.
He was kind enough to share his understanding of how mutual fund dividends must be accounted for, and sent his account statements for me to work on.
The following post and the subsequent corrections to the automated tracker would not have been possible without his efforts.
Unfortunately, the bad news is that existing users of the tracker who use dividend option mutual funds will have to download the new one from trackers main page.
I apologize for this inconvenience.
Now, on with the explanations. This article is based on the NCFM Advanced Mutual Fund Module. The study material referred for this post is from here (Chapter 6, section 6.1)
Warning: The following is some heavy stuff. If you don’t find the following arguments confusing at first, something is wrong with you!
If you are not interested in details, then please proceed to downloading the latest version of the automated mutual fund and financial goal tracker.
If you are interested in how stock dividends should be accounted for while calculating returns, see: Understanding the Nature of Stock Market Returns
If you are interested in this subject matter, you have no option but to read and re-read the following to obtain clarity. I will be delighted if you could take the trouble of reading this and share your thoughts in the comments section.
I Mutual Funds with ‘dividend’ payout option
In this case, fund houses offer dividends from time to time when they have enough to disburse. When a dividend is declared, the net asset value (NAV) decreases by an amount equal to the dividend rate – (typically few rupees per unit).
This lower NAV is known as Ex-dividend NAV
(Ex-dividend NAV + Div. Rate = Cum-Dividend NAV)
There are many ways of calculation returns from dividends, and there is enough confusion and debate on this. However, SEBI has mandated that dividends should be deemed as reinvested at ex-dividend NAV for calculating returns.
So we will just use this convention.
The essential idea is that, while calculating returns only the actions of the investor must be accounted for explicitly. A dividend is an action by the instrument and should only be accounted for implicitly.
Since my understanding is entirely based on the NCFM module, I will simply use the dates they use. The discussion here is however considerably different from the one there.
Let us consider the following example.
Consider the following actions taken by an investor
- Rs. 14,000 invested in a fund at a NAV of 14 on 15-Jan. 2011. Units: obtained: 1000
- On 01-Jul-2011, the fund declares a dividend on Rs. 2 per unit. Dividend received Rs. 2000
- On 10-Dec.-2011, the fund declares a dividend of Rs. 1.5 per unit. Dividend received Rs. 1500
- On 01-Feb-2012, The 1000 units are sold at a NAV of 14.85. Amount received Rs. 14,850.
How do we calculate the return for such a scenario?
Now, there are two ways to do this:
- Using Excels XIRR function
- Using the formula for CAGR
return = [total-value/investment]^(1/duration in years) -1
Let us start with the XIRR function.
Let us recall that dividends are assumed to be reinvested. So
- On 15-01-2011, investment of Rs. 14,000. Total units = 1000.
- On 01-07-2011, a dividend at the rate of Rs. 2 per unit was declared. So dividend = 2 x total units = 2 x 1000 = Rs. 2000
- This dividend is assumed to be reinvested at ex-dividend NAV of 12.5 (on 01-07-2011). Units ‘purchased’ = 160. Total units 1160
- On 10-12-2011, a dividend at the rate of Rs. 1.5 per unit was declared. So dividend = 1.5 x total units = 1.5 x 1160 = Rs. 1740 (this is entirely imaginary used only for calculating returns)
- This is the key step that eluded me previously. Any dividend should be calculated by assuming all past dividends are reinvested. This should reflect in the total units
- So this imaginary dividend of Rs. 1740 is assumed to be reinvested at ex-dividend NAV of 13.594 (on 10-12-2011). Units ‘purchased’ = 127.998. Total units = 1160 + 127.998 = 1287.998
- On 01-02-2012, these (imaginary) units were redeemed at a NAV of 14.85. So redemption amount is 19126.77
Implementation in Excel using XIRR
This can be a bit tricky. Dividends are assumed to be reinvested and this must reflect in the maturity value. However, a dividend is considered as an action by the instrument and not by the investor. Therefore such actions should be not explicitly included as part of the cash flow!
I know that sounds confusing! Join the club.
Here are two ways to implement this in Excel. Both will give you the same answer for the return = 34.74%
On the left, an additional cash flow entry is include – the value today. On the right this term is omitted.
Since all the units have been redeemed, whether you calculate returns today or as on 01- Feb-2012, the answer is the same, as it should be. This is the advantage of XIRR.
Implementation using CAGR
Here again, we assume that dividends are reinvested but do not explicitly include in as as cash flow entries.
We invested Rs. 14, 000 and we got Rs. 19,126.77, 382 days later
So using, CAGR = [total-value/investment]^(1/duration in years) -1
We get CAGR = [19126.77/14000]^(365/382) -1 = 34.74%
So we obtain the same answer as the XIRR function. Well, not quite! This is the return 382 days after investment. That is on 01-Feb-2012.
Try answering, what is return today (11 Apr 2014), that is after 1182 days after the investment?!
You will immediately agree that XIRR is a better and simpler choice! In any case, if the investor makes multiple purchases or redemptions, only XIRR can used.
Summary: For mutual funds with ‘dividend’ payout option, the dividends are assumed to be reinvested at ex-dividend NAV. Such ‘reinvestments’ must reflect in the ‘value’ of the investment. However, dividends are considered to be actions on part of the instrument and not the investor. Therefore, they should not be accounted for explicitly in the cash flow.
II Mutual Funds with ‘dividend reinvestment’ option
For such instruments, the dividends are actually reinvested by the investor on the dividend date at ex-dividend NAV!
So we have two actions here:
- The dividend: action by the instrument and to be taken into account implicitly as above
- The dividend reinvestment: action by the investor. This results in an actual increase in number of mutual fund units held. Therefore, this must be explicitly taken into account in the cash flow.
Consider the following actions taken by an investor
- Rs. 14,000 invested in a fund at a NAV of 14 on 15-Jan. 2011. Units obtained: 1000
- On 01-Jul-2011, the fund declares a dividend on Rs. 2 per unit. Dividend received = 2 x 1000 = Rs. 2000 as dividend.
- This is (actually) reinvested in the fund at ex-dividend NAV of 12.5. Units received: 160; Total number of units: 1160
- On 10-Dec.-2011, the fund declares a dividend of Rs. 1.5 per unit. Dividend received = 1.5 X 1160 = Rs. 1740 as dividend.
- This is (actually) reinvested in the fund at ex-dividend NAV of 13.594 Units received: 127.998; Total number of units: 1160 =127.998 =1287.998
- On 01-Feb-2012, All 1287.998 units are sold at a NAV of 14.85. Amount received = Rs. 19126.77
In this situation, there are 3 actual purchases. So the CAGR formula cannot be used. One will have to use only the XIRR function.
Here is how the above investor actions will be accounted for, when we set out to calculate returns (take a deep breath!)
- 15-Jan. 2011: Rs, 14,000 invested. Units obtained: 1000
- 01-Jul-2011: Dividend of Rs. 2 per unit declared. Dividend received: Rs. 2000
- This dividend is assumed to be reinvested on the same day at ex-dividend NAV of 12.5. Units ‘purchased’ = 160. Total units 1160.
- The dividend reinvestment done on the same day is an action by the investor leading to purchase of actual units. Therefore, this has to be explicitly accounted for.
- Dividend reinvestment: Rs. 2000 at NAV of 12.5. Actual units purchased = 160. Total units: 1160 + 160 = 1320.
- 10-12-2011: Dividend of Rs. 1.5 per unit declared. Dividend ‘received’: 1320 X 1.5 = 1980 (notice that this imaginary dividend is different from actual dividend of 1740).
- This dividend is assumed to be reinvested on the same day at ex-dividend NAV of 13.594. Units ‘purchased’ = 145.652. Total units: =1320 + 145.652 = 1465.652.
- Again the dividend reinvestment is an investor action. So we will have to use the real dividend value of 1740 for the investment
- Dividend reinvestment: Rs. 1740 at NAV of 13.594. Actual units purchased = 127.998. Total units: 1465.652. + 110.343 = 1593.650
- 01-02-2012: Since the investor redeemed all units, all the imaginary units are assumed to be redeemed at NAV of 14.85. Redemption amount: 23665.705
Again, here are two ways to implement this in Excel. Both give the same answer for the return = 36.84%
On the left, an additional cash flow entry is included – the value today. On the right this term is omitted.
Since all the units have been redeemed, whether you calculate returns today or as on 01- Feb-2012, the answer is the same, as it should be.
Summary: For mutual funds with ‘dividend reinvestment’ option, we will need to deal with dividends and dividend reinvestments separately.
- Dividends are actions by the instruments and are assumed to be reinvested. They are not explicitly taken into account as a cash flow entry
- The dividend reinvestment is an actual investment leading to an increase in the number of units held. So this has to be explicitly accounted for as a cash flow entry.
- Both dividends and dividend reinvestments must be taken into account for XIRR calculation.
This method of accounting for dividends and dividend reinvestments has been incorporated in the current version of the automated mutual fund and financial goal tracker.
I would appreciate your feedback on this post. If you are an expert and disagree with any of the above, please do spare a few moments to let me know your concerns.
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