Compute Simple Return Calculation for Investment Other Than Stock

[ML2006]

I am trying to figure out how to compute simple return for the following investment (not a stock). The investment was also not sold:

contribution #1 $3,000,000 on July 10, 2014
contribution #2 $1,500,000 on November 30, 2014

dividend distribution #1 $75,000 made 11/15/14
dividend distribution #2 $101,000 made 2/1/15

I need to compute the return and to make sure the distributions satisfy a 6% per annum simple return.

Questions: How do you compute this step-by-step and how is the timing of this factored into the equation.

 

[Ishuda]

I am trying to figure out how to compute simple return for the following investment (not a stock). The investment was also not sold:

contribution #1 $3,000,000 on July 10, 2014
contribution #2 $1,500,000 on November 30, 2014

dividend distribution #1 $75,000 made 11/15/14
dividend distribution #2 $101,000 made 2/1/15

I need to compute the return and to make sure the distributions satisfy a 6% per annum simple return.

Questions: How do you compute this step-by-step and how is the timing of this factored into the equation.

Generally a yearly return is computed as though the interest is not compounded unless specifically stated. So the return is a 'simple interest' problem during a single year. Next, depending on just how accurate you need to be, you have to decide what is the minimum period you will work with. Generally this is a day and thus 'interest' (rate of return) for one day would be 1/365 or 1/360 times the yearly interest (depending on the institution or whatever).

I will do a step by step for you for a simple rate of return with a month step (you have to hold a complete month (30 days) to earn your 'interest'. If you hold it part of a month, it doesn't count). I will also assume record date is payment date. However, before we start, I'm not sure if this is the way this is taught or not but this is the way I would do it.

You have
$3,000,000 from July 10, 2014 to Feb 1, 2015 = 6 months
$1,500,000 from Nov 30, 2014 to Feb 1, 2015 = 2 months
Total earned earned $75,000 + $101,000 = $176,000

Let the annual rate of return be i, i.e. 0.06 or 6%. The
(6 * 3000000 * i + 2 * 1500000 * i) / 12 = 176000
or
21000 i / 12 = 176
or
i ~ 10.057%

Note that each amount is multiplied by the number of months held and the sum is divided by the number of months in a year. That is the general rule, i.e. if figuring for days, multiply by days held and divide sum by days in year. Also, so as not to have to carry around all those zeros, you can express you money as 1000's of dollars [drop three zeros off the end] or what ever you feel comfortable with.

 

[ML2006]

Thanks.

Thanks so much. You have no idea how much this has helped.

 

[ML2006]

Computing for Per Annum Simple Return

What if I needed to compute the per annum simple return. How do you do that?

 

[Ishuda]

What if I needed to compute the per annum simple return. How do you do that?

That is what you have calculated. Note that the formula could be written another way
(6 * 3000000 * i + 2 * 1500000 * i) / 12
=(6/12) * 3000000 * i + (2/12) * 1500000 * i
=3000000 * ((6/12) i) + 1500000 * ((2/12) i) = 176000

or the interest for the 3000000 was for 6 out of 12 months which is 1/2 the annual rate and the interest for the 1500000 was for 2 out of 12 months or 1/6th the annual rate. Another way to look at the original formula is that first you are figuring a monthly rate by multiplying by the number of months and then you are converting it to a yearly rate by dividing by 12 (the number of months in the year).

In the same way for computing down to the day, you would first use the number of days for the daily rate, then divide by the number of days in the year to convert it to an annual rate.

Notice that, as requested, this is for a simple rate of interest for a year. That is you get interest (income) proportional to the number of months (or days) held. The interest is not compounded at the monthly (daily) rate. Using monthly or daily computations is not for the purpose of compounding but because of 'what standard do you use'. Unless you have 'several times' [depending on amount held for the 'several'] you missed getting that extra month by a 'few' days, the difference will probably not be much. You might want to do the daily computation just so you wouldn't have to worry about that number of times.

Or maybe do the hourly so you don't have to worry about the times you missed the days by a 'few' hours or maybe by the minute so ...

 

[ML2006]

Thanks so much.

 

[ML2006]

Return for distribution period.

contribution #1 $3,000,000 on July 10, 2014
contribution #2 $1,500,000 on November 30, 2014

dividend distribution #1 $75,000 made 11/15/14
dividend distribution #2 $101,000 made 2/1/15

How would the return be calculated not for the entire period of the investment but just for for the distribution made on February 1, 2015.

 

[Ishuda]

contribution #1 $3,000,000 on July 10, 2014
contribution #2 $1,500,000 on November 30, 2014

dividend distribution #1 $75,000 made 11/15/14
dividend distribution #2 $101,000 made 2/1/15

How would the return be calculated not for the entire period of the investment but just for for the distribution made on February 1, 2015.

Again, it depends on just what you mean but if you are computing just the return itself and not a return per period (that is, for example, not a return of a particular percent per year), then basically just use the formula Denis gave
a=the money invested
b=what the money it is now worth
return (%) = (b/a-1)*100 = 100*(b-a)/a
so
return = [(75+101)/(3000+1500]*100 = 176/45 ~ 3.9%

 

[ML2006]

Return for distribution period.

The computation included both distributions. The distribution for $75,000 and the second distribution for $101,000. Is there a way to compute the return for the distribution for $101,000 on February 1.

Would the below be correct?.

101/(3000+1500)= 2.24%

And if I wanted to compute the return for the February 1, 2015 distribution which is after the November 15, 2014 distribution. Would the following be correct?:

(101*365 days)/[78 days from Nov 15 thru Feb 1*(3000+1500)]=10.5028%

Again, it depends on just what you mean but if you are computing just the return itself and not a return per period (that is, for example, not a return of a particular percent per year), then basically just use the formula Denis gave
a=the money invested
b=what the money it is now worth
return (%) = (b/a-1)*100 = 100*(b-a)/a
so
return = [(75+101)/(3000+1500]*100 = 176/45 ~ 3.9%

 

[Ishuda]

...

Would the below be correct?.

101/(3000+1500)= 2.24%

And if I wanted to compute the return for the February 1, 2015 distribution which is after the November 15, 2014 distribution. Would the following be correct?:

(101*365 days)/[78 days from Nov 15 thru Feb 1*(3000+1500)]=10.5028%

Yes, if you use the 78 days and 365 days in a year. I would probably use 77 (not count both ends of the period) and, depending on just what this is for a 'financial number of days in a year' might be 360, see
http://en.wikipedia.org/wiki/360-day_calendar
for example.

 

[ML2006]

Yes, this is confusing, that is why I need help. Thank you all. Contribution #2 is not tied to distribution#2. Distribution #2 is from both contributions.

This is all quite confusing...

You posted this:

"contribution #1 $3,000,000 on July 10, 2014
contribution #2 $1,500,000 on November 30, 2014

dividend distribution #1 $75,000 made 11/15/14
dividend distribution #2 $101,000 made 2/1/15"

Is contribution#2 tied to dividend#2,
or is dividend#2 applicable to both contributions?

Or is this what you mean:

$3,000,000 is invested on Jul10/14.
On Nov15/14, a dividend of $75,000 is paid.
What simple annual rate does this represent?

$1,500,000 is invested on Nov30/14.
On Feb1/15, a dividend of $101,000 is paid.
What simple annual rate does this represent?