Question

Describe in detail how to calculate the future value and the present value of a series of cash flows.

Answer 1

There can be two types of series of cash flows - Equal and Unequal. I'll show the calculation for both.

Future value

In case of unequal cash flows -

In this case you have to compute the future value of each individual cash flow and add them up. Future value of an individual cash flow can be computed as follows -

FV = Cash flow x (1 + r)ⁿ

where, r = rate of interest, n = no. of years remaining

Consider this - r = 10%, Cash flows - Year 1 = $1000, Year 2 = $2000, Year 3 = $3000. Compute future value till year 3. All cash flows occur at year end.

FV of year 1 cash flow = $1000 x (1 + 10%)² = $1210

FV of year 2 cash flow = $2000 x (1 + 10%)¹ = $2200

FV of year 3 cash flow = $3000 x (1 + 10%)⁰ = $3000

Total future value = $6410

In case of equal cash flows

These will be a form of annuity. Future value of an annuity can be computed as -

where, r = rate of interest, n = no. of years

Consider this - r = 10%, n = 3, Cash Flows = $1000 per year. Compute future value. All cash flows occur at year end.

In case of beginning of the year cash flows, multiply the above formula by (1+r).

Present value

In case of unequal cash flows -

Same as future value, i.e., compute the present value of each cash flow individually and add them up.

PV = Cash Flow / (1 + r)ⁿ

where, r = rate of interest, n = no. of years after which cash flow is received

Ques - r = 10%, Cash flows - Year 1 = $1000, Year 2 = $2000, Year 3 = $3000. Compute present value today. All cash flows occur at year end.

PV of year 1 cash flow = $1000 / (1 + 10%)¹ = $909.09

PV of year 2 cash flow = $2000 / (1 + 10%)² = $1652.89

PV of year 3 cash flow = $3000 / (1 + 10%)³ = $2252.94

Total = $4815.93

In case of equal cash flows -

where, r = rate of interest, n = no. of years

Ques - r = 10%, n = 3, Cash Flows = $1000 per year. Compute future value. All cash flows occur at year end.

Bonus - You must have the noticed the very similar formulas of future value of present value. Their is this relationship between present value and future value -

FV = PV x (1 + r)ⁿ

So, if you're given PV = 2486.85, r = 10%, n = 3

FV = $2486.85 x (1 + 10%)³ = $3309.99 or $3310 (See the future value for equal cash flow answer).