Future value of the following uneven cash flow stream

CFA Level I Quant
#1

Find the future value of the following uneven cash flow stream. Assume end of the year payments. The discount rate is 12%.

Year 1 -2,000 Year 2 -3,000 Year 3 6,000 Year 4 25,000 Year 5 30,000

Explanation

N = 4; I/Y = 12; PMT = 0; PV = -2,000; CPT → FV = -3,147.04

N = 3; I/Y = 12; PMT = 0; PV = -3,000; CPT → FV = -4,214.78

N = 2; I/Y = 12; PMT = 0; PV = 6,000; CPT → FV = 7,526.40

N = 1; I/Y = 12; PMT = 0; PV = 25,000; CPT → FV = 28,000.00

N = 0; I/Y = 12; PMT = 0; PV = 30,000; CPT → FV = 30,000.00

Sum the cash flows: $58,164.58.

In the explanation, how are they getting the N values? Why is the first year’s payment N=4? (and not N=1?)

Thanks in advance for any clarification.

#2

You want the value at time t = 5. A payment at time t = 1 will be invested for 5 − 1 = 4 years.

And so on.

It might be easier to calculate the NPV, then compute the future value of that amount after 5 years. If you do that, make sure that you put in CF0 = 0.

#3

Personally I always found it easier to draw out a timeline for questions like this to help keep things straight in my mind. The reason why the first year’s payment has an N of 4 applied to it is that you are calculating the future value here, not the present value (ie what the value of the t=1 cashflow is at t=5). The perspective here is that you are essentially sitting hypothetically at t=5 working out what the prior years’ cash flows are worth to you at that point in time. In this way, you need to know what the -2,000 cash flow is worth when compounded over 4 periods at 12% --> 2,000(1 + 0.12)4.

Hopefully that helps a little - can’t stress how useful drawing out the timelines really is. Once you get the hang of it they’re very quick to put together, and you’ll never get a question like this wrong again.

#4

This is waaaaaay faster than rolling up individual CFs!!! :+1: :bulb: