Future Value Versus Present Value and Comparison of Annuity(TVM)

           Future Value Versus Present Value

Assume that you have an opportunity to spend $10,000 today
on some investment that will produce $15,000 spread out over the next 4 years as follows:

Year 1        $3,000
Year 2        $5,000
Year 3        $5,000
Year 4        $2,000

Is this a wise investment? It might seem that obvious answer is YES because you spend $10,000 and receive $15,000.But it is not clear that it is an obvious investment or not.Because we don't know the future value of cash outflow? and We also don't know the present value of Cash inflows.

Time value of money analysis helps manager answer question like this.The basic idea is that managers need a way to compare cash today versus cash in future.

For making the right investment decision, managers need to compare the cash flows at a single point in time.Typically, that point is either the end or beginning of the investment's life.The future value techniques use compounding to find the future value of each cash flow at the end of investment's life and then sums these value to find the investment's future value.Instead of the present value techniques use discounting to find the present value of each cash flow at time zero and then the sums these values to find the investment's value today.

When making the investment decision, managers usually adopt the present value approach.

Comparison of an Annuity Due with an Ordinary Annuity Present Value

Project A

If,

Annual Payment = $700

Annual rate of Interest, compounded annually = 8%

Number of years = 5

Then, 

Present Value of an Ordinary Annuity= $2,794.90

Present Value of an Annuity Due = $ 3,018.49

The present value of an annuity due is always greater than the present value of an ordinary annuity.We can see this by comparing the values of project A.

The reason is that the cash flow of the annuity due occurs at the beginning of the period rather than at the end, its present value is greater.

 Comparison of an Annuity Due with an Ordinary Annuity Future Value

Project A

If,

Annual Payment  = $1,000

Annual rate of interest,compounded annually= 10%

Number of years = 5

Then,

Future value of Ordinary Annuity= $ 6,105

Future value of Annuity Due= $ 6,716

The future value of an Annuity due is always greater than the future value of an Ordinary Annuity.We can see this by comparing the future values of Project A.

Because the cash flow of the annuity due occurs at the beginning of the period rather than at the end(that is, each payment comes one year sooner in the annuity due), its future value is greater. 

                 Basic Patterns of Cash Flow

The cash flows can be described by its general pattern.It can be defined as a single amount, an annuity, or a mixed stream.

Single amount: A lump-sum amount either currently held or expected at some future date.Examples include $1,000 dollar today and $650 to be received at the end of 10 years.

                                         Mixed cash flow stream

End of year                       A                              B   

    1                                $ 100                      -$ 50

    2                                   800                         100

    3                                 1200                           80

    4                                 1000                          -60

    5                                   500

    6                                   800

Note that A is a 6-year mixed stream and B is a 4-year mixed stream.

         

  Finding Interest or Growth Rates

       Sometimes we need to calculate the compound annual interest or growth rate of a series of cash flows.
Examples include finding the interest rate on a loan, the rate of growth in sales, and the rate of growth in earnings.In doing this we have to follow the following formula-

Interest Rates Formula 

                                  Math

# Suppose, Mr. A purchased an investment four years ago for $1,200.Now it is worth $1,500.What compound annual rate of return has Mr. A earned on this investment?

Solution:

                Given that, 

                   Present Value,PV  = $ 1,200

                   Fututre Value,FV  = $ 1,500

                 Number of years,n  = 4

                         Interest Rate, i =?