how to calculate return on investment

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!

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.

Using this rate you can now calculate PV.

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

Am afraid that would be incorrect

@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.