Time Value of Money (Part 2)

Earlier we discussed about compounding by which we found out the future value of an amount deposited now.
Similar is the concept of discounting where we calculate the present value of a cash that is going to come in future.

PV - Present Value of an amount that will be received in the future, calculated after discounting. FV - Future Value of an amount invested now at a given rate of interest.

The rate used for compounding is the interest rate offered by the instrument in which the money is invested.
For discounting rate generally the cost of capital rate is used. This can be the rate which your money can grow with you.

Till now we had considered cash flow at one point of time and discussed ways to find its value at some other point of time. This kind of cash flow is known as lump-sum. What if the cash flow is divided and keeps on coming at different times. Four new terms are introduced for these:

Annuity - It is a regular cash flow for a fixed period of time.
Annuity Due- Cash flow occurs at the start of the period.
Annuity Ordinary- Cash flow occurs at the end of the period.
Perpetuity - It is a regular cash flow for a infinite period of time.

Generally, Annuity and Perpetuity are used for equal cash flows in each period.
If the cash flows are unequal it is called mixed stream.

The formula for future value of an ordinary annuity (FV) is:
where FVA(due) is future value of annuity due, A is equal cash flow per period for n periods compounded at interest rate r.
Similar formulae for present value are:
Present Value of a growing stream of cash flow:
Gordon Growth Model
g is growth rate of cash flow and if g < onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh7awFDFtnkqy-wTbUDBR2FLJDdcQDpfcIUeReymZnyAO7IqGLC2X9YeJaksDZ10WIrby-Y9zs9Rgzpeg7r-_1rQL8uTAoG2Jl1GS2CeQb6KHWTQuO3Uzu3lf-6ACKTsRaLejJAnCV8Ez0k/s1600-h/AnnuityGrow.jpg">
Change in Compounding interval