CFA CFA Level 1 how to calculate return on investment

# how to calculate return on investment

• Author
Posts
• 0

I am interested in calculating returns from a fixed no of periodic investments that is redeemed at a specific time after the last payment.

ex : periodic outflow of 3000 on a monthly basis for 8 months.

year 1 :

may – 3000 june – 3000 july – 3000 aug – 3000 sep – 3000 oct – 3000 nov – 3000 dec – 3000

year 2 :

year 3 :

redemption in may.

all outflows are at the beginning of the month.

I would like to know if the below approach is correct

total of all ouflows – 24000

redeemed amount – 32405.33

no of months held – 17 (year 2 jan to year 3 may)

assume Future Value as 32405.33, Present Value as 24000, calculate interest using FV = PV ( 1 + i)^17.

Interest rate will be determined for a month.

Using the rate calculated above, find present value of the outflows from may to dec at may of year 1.

pv@year1_may = 3000 [ ( 1 – (1 + i)^8 )/i ] .

now with pv@year1 and fv = 32405.33 (redeemed value), calculate for interest rate with no of terms as 24 using

FV = PV (1 + i)^24.

Please share any knowledge material that explains above scenario.

• 5

As I understood, the question to be answered is: what is the return on your investment in this particular situation? Except for his/her last sentence, I agree with @d3v1l_dare. However, the way I would approach this situation is to build my understanding in steps.

1) Consider first the much simpler case where the outflows (-24,000) all occur on May 1, 2014 (time t=0) and the payback (32,405.55) occurs on May 1, 2015 (time t=1). The ROI is 35.02% (=32,405.55/24,000 – 1) and it is an annual rate, since the holding period was 1 year. You would want to go ahead with this investment if this ROI were greater than your opportunity cost of capital (what you would get by investing in your next best project).

2) Next consider the case where the outflows still occur on May 1, 2014 (time t=0) but the payback (32,405.55) occurs on May 1, 2016 (time t=2), which is closer to your situation. The ROI is still 35.02% but this is now a 2-year figure. The equivalent annual rate of return on the investment is 16.20% [ = (32,405.55/24,000)^1/2 – 1]. It makes sense that the rate is much lower because now you have to wait twice as long to get your return. Again, if your required rate of return is less than this 16.2% figure, then it’s a go.

3) Finally, we want to consider the staggered cash outflows, as 8 monthly instalments of \$3,000 from May 1, 2014 to December 1, 2014, which is exactly the situation proposed. The problem here is that each piece of your total investment will be “tied up” for a different length of time, so you see how a similar calculation as with the 2 simpler cases above would be difficult. The best way to resolve this is to first figure out what is your opportunity cost of capital (or required rate of return). Suppose it is 10%. Then you calculate the PV of your cash flows using this rate; since the net result is positive (=3,435.56), it’s a go for the investment. (If it were negative, it would be a no go!)

Note that this more general methodology (used in case 3) will give exactly the same answer as what we got in cases 1 and 2 above for a 10% required rate of return.

Finally, if you want to know what is the maximum required rate of return for which the project would be accepted, then you would calculate the IRR for the cash flows, which is an annual rate of 19.18% (equivalent to a monthly rate of 1.4728%, as calculated by @d3v1l_dare). Of course, you should not discount the cash flows with this rate… if you did, you’d get a zero NPV (it’s the definition of the IRR).

Hope this helps!

• 4

OP,

You can’t add ‘Outflows’ of different time and assume it as present value.

Considering you are talking about the following Cash flows… based on that, your IRR should be 1.4728%

That’s your return on investment as well.

 Period CF 0 May -3000 1 June -3000 2 July -3000 3 August -3000 4 September -3000 5 October -3000 6 November -3000 7 December -3000 8 January 0 9 February 0 10 March 0 11 April 0 12 May 0 13 June 0 14 July 0 15 August 0 16 September 0 17 October 0 18 November 0 19 December 0 20 January 0 21 February 0 22 March 0 23 April 0 24 May 32405.55

Using this rate you can now calculate PV.

• 4

thank you @d3vll_dare and @edulima for the explanation.

• 3

You are making so many assumptions which may or may not be wrong. What is this question anyway?

• 1

Am afraid that would be incorrect

You cannot calculate the initial interest rate basis present value as outflows are staggered. Simple option would be to calculate the interest rate basis future value of annuity formula since u know the monthly payment no of periods and future value
• 1

@edulima‌ nice elaboration. Great effort!! I agree fully. Just wanted to clarify what I meant

What the OP wanted to know, I assume, how to calculate return on investment when you know your cash outflows in first 8 months (each \$3000) and then you know your final lump sum return is \$32405.33. So, I guess ROI would be same as Internal rate of return.

Then OP wanted to know the PV of the outflow stream, which was for 8 periods!!

Anyways.. it’s solved now.