*This is a solution of Memo Solution Assignment Help** in which we discuss the concept of time value of money and its importance in the world of finance.*

# **Introduction**

The purpose of this memorandum (“hereinafter referred to as “memo”) is to understand the concept of time value of money and its importance in the world of finance. The memo will focus on the valuation of financial management and interpretation of the same taking into account the time value of money.

It is a common idea that money available at present is of more worth or value than the same amount of money available in the future. This notion outlines the concept of Time Value of Money. The time value of money demonstrates that it is better to have money sooner than later. The reason for this is that the money available today can be utilized for various investment purposes that would earn it interest overtime. Thus, a $100 now is equal to a $100 in 2 year; however, the sooner the $100 available, the better as the same can be invested to earn interest overtime. For instance, if the prevailing interest rate were 10 percent annually, the $100 available now would eventually become $121 at the end of 2 years. However, if the same $100 is available after 2 years, the investor is not left with sufficient time to invest the same. There are a number of uses of time value of money. It helps us to calculate the present value of money to be received in future as also future value of investment made now.

__Future Value:__

__Future Value:__

A basic illustration of time value of money is the computation of future value of an investment made today. This involves estimating the value that the current investment would grow to over a preset period of time and at a preset interest rate. Determination of future value of an investment involves compounding of interest, i.e. reinvesting the accumulated interest over the period of investment.To explain this, let us refer to problem #2 that assess the future value of $100,000 if invested for five years at a 5% annual interest rate. This is explained with the help of following flowchart:

Present Value Future Value

($100000 ($105000 ($110250 ($115762.5 ($121550.63 $100000 $105000 $110250 $115762.5 $121550.63 $127628.16

+Interest) +Interest) +Interest) +Interest) +Interest)* *

The above can also be formulated as follows:

Future Value (FV) = Present Value (PV) * [1 + Interest Rate (i)] ^{No. Of Compounding Periods (n)}

Thus, FV = $100000 * (1 + 0.05)^{5}

**FV = $127628.16**** **

The above calculation shows that the investment of $100000 for 5 years at an annual interest rate of 5% resulted in the growth of the same to $127628.16 at the end of 5 years. This growth is the result of interest accumulated each year and reinvested until the termination of the investment.

__Present Value:__

__Present Value:__

Another fundamentalpractice of time value of money is assessing the Present Value of return on an investment to be earned in future, i.e. what is the return on an investment now, if the amount is spent today. As stated above, the Future Value computation involves compounding of interest on investment, i.e. interest on principal as well as on interest earned over the time period. Present Value computation, however, involves discounting of future payment. To calculate the Present Value of a future return, we need to discount the same back till today in order to determine how much needs to be invested today. To explain this, let us refer to problem #1 that assess the present value of $100,000 to be received five years from now with a 5% annual interest rate.This is explained with the help of following flowchart:

Present Value Future Value

{$82270.25/ {$86383.76/ {$90702.95/ {$95238.10/ {$100000/$78352.62 $82270.25$86383.76$90702.95 $95238.10$100000

(1+Interest)}(1+Interest)}(1+Interest)} (1+Interest)} (1+Interest)}* *

The above can also be formulated as follows:

Present Value (PV) = Future Value (FV) / [1 + Interest Rate (i)] ^{No. Of Compounding Periods (n)}

Thus, PV = $100000 / (1 + 0.05) ^{5}

**PV = $78352.62**

The above calculation shows that the investment of $78352.62 today for 5 years at an annual interest rate of 5% would result in the growth of the same to $100000 at the end of 5 years. While calculation Future Value of money involves forward moving from present to future, Present Value of money entails backward calculation, i.e., discounting the future return to arrive at its value today.

__Variant to Future and Present Value – Annuities__

__Variant to Future and Present Value – Annuities__

Annuity basically, is a series of fixed payment made or received at a predetermined frequency over a fixed period of time.Annuities are also of 2 forms: Ordinary Annuity and Annuity Due. The difference between the two is very simple to understand. Under Ordinary Annuity, the payment is accounted for at the end of each period; however under Annuity Due, the payment is made at the beginning of each period. The Future and Present Value of Annuities are discussed in details below:

*Future Value of Annuity:*

If an investor invests a fixed amount of money at the end of each period for a certain time frame, Future Value of Ordinary Annuity helps in computing the value of return on that investment in the future, given a fixed interest rate. Let us understand this with the help of problem #4 that assess the future value of ordinary annuities of $100,000 if invested each year for five years at a 5% annual interest rate.

Present Value Future Value

$100000 $100000$100000 $100000 $100000

$100000 * [1 + 0.05] ^{0}

$100000 * [1 + 0.05] ^{1}

* * $100000 * [1 + 0.05] ^{2}

$100000 * [1 + 0.05] ^{3}

$100000 * [1 + 0.05] ^{4}

The above can also be formulated as follows:

FV = C * [{(1 + i) ** ^{n }**– 1}/ i]

Where, FV is Future Value;

C is Cash Flow each period;

i is Interest Rate;

n is No. of Compounding Period

Therefore, FV = $100000 * [{(1 + 0.05) ** ^{5}**– 1}/ 0.05]

**FV = $552563.13**

The above calculation shows that periodic investment of $100000 each year for 5 years at an annual interest rate of 5% resultsreturn of $552563.13 at the end of 5 years.

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*Present Value of Annuity:*

If an investor receives a series of fixed payment at the end of each period for a certain time frame, Present Value of Ordinary Annuity helps in computing the value of the same today, given a fixed interest rate. Let us understand this with the help of problem #3 that assess the present value of ordinary annuities of $100,000 to be received each year for five years with a 5% annual interest rate.

Present Value Future Value

$100000 $100000 $100000 $100000 $100000

$100000 / [1 + 0.05] ^{1}

$100000 / [1 + 0.05] ^{2}

$100000 / [1 + 0.05] ^{3}

$100000 / [1 + 0.05] ^{4}

$100000 / [1 + 0.05] ^{5}

The above can also be formulated as follows:

PV = C * [{1 – 1/ (1 + i)** ^{n}**}/ i]

Where, PV is Present Value;

C is Cash Flow each period;

i is Interest Rate;

n is No. of Compounding Period

Therefore, PV = $100000 * [{1 – 1/ (1 + 0.05) ** ^{5}**}/ 0.05]

**PV = $432947.67**

The above calculation shows that the periodic receipt of $100000 each year for 5 years at an annual interest rate of 5% is of $432947.67 value as of today.

__Perpetual Return__

__Perpetual Return__

Another variant to time value of money is perpetual return, i.e., a fixed amount of payment received infinitely at a fixed interest rate. Let us understand this with the help of problem #5 that assess the present value of$100,000 to be received each year forever with a 5% annual interest rate.

*Formula:*

Present Value of Perpetuity (PV) = Payment each period (PMT)/ Interest Rate (i)

Therefor, PV = $100000/ 0.05

**PV = $2000000**

__Conclusion: __

__Conclusion:__

The above explanations validate that time is one of the crucial player in any moneymaking decisions. This is because the value of money today is not the same as it will be in the future. Thus, it is important to factor in the importance of time while making investment decisions that provide yields at different time period. * *

*See more :Personal Finance Assignment Help *

*References:*

www.investopedia.com

www.financeprofessor.com/notes-for-classes/time-value-of-money-overview/

www.adawnjournal.com/economy-mortgage-101/what-is-time-value-of-money

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