# Time Value of Money Paper Essay

Introduction

Before dwelling on the various applications of Time Value of money paper, it is imperative to clearly understand what the whole concept of time value of money is all about. The whole concept is based on the premise that all investors prefer receiving a certain amount of money today rather than the same amount in future, while holding everything else constant. Money in actual sense has a time value, which is an economic theory brought about by three reasons that include inflation, liquidity and risk. (Tuller, Lawrence W.1997)

This is based on the argument that if the investor receives the money today, he/she can earn interest on that amount until the specified future date. For example earning $100 today is preferable than earning this same amount in one years time. This is because choice of either spending the money today or investing it for future. Thus if one chooses to earn $100 one year from now, spending is also deferred for a similar period and will miss out on the opportunity to invest it. (Tuller, Lawrence W.1997)

Financial application of the time value of money

The Time Value for money is a very fundamental principle of investing and budgeting and all standard calculations are based on the basic formula of the present value of a future sum that is discounted to the present. The concept is fundamental in many aspects of finance; this is because it has an impact on consumer finance, business finance and government finance. (DeThomas, A 1992).

The Time value of money concept has much valuable financial relevance. The concept finds some of its major and important uses in the measurement of various trade-offs in spending and saving (DeThomas, A 1992). On a personal budgeting level, it has important consequences. For example one may make the decision to invest because the time value of money is greater in the future if the market interest rates stand at say 6% which is considered a high rate, however if the rates are much lower than this say between 1%- 2%, one may opt to spend the money because the time value of money today is higher. (DeThomas, A 1992).

The time value of money is extremely useful in the following sectors of business:

Commercial banks

Credit card financial service companies

Insurance companies

d. State governments – lotteries

Retirement plan financial service providers

The basic concept of time value for money that includes compounding, discounting and annuities are frequently used in the retirement savings plan to determine the amount of the deposit that is needed to accumulate a certain future plan.

Commercial banks

Commercial banks extensively find great use of time value for money; on a daily basis they use various time value of money formulas. It is used to calculate the amortization of loans for home mortgages that is described as present value of an annuity. In the calculation of mortgages, the future value of the annuity formula is used to determine monthly payments that the borrower is supposed to make. The concept is also used in the calculation of the future value of all the savings in the fixed deposit ( Crosson, S.V. & Needles, B.E. 2008)

Credit card financial service companies

Under normal circumstances credit card financial services issue loans to the card holders, towards this end the time value of money formula is used to determine the schedules for loan repayment and also used in calculating the future value of the loan which is the ending balance. ( Crosson, S.V. & Needles, B.E. 2008)

Insurance Companies

To illustrate how the insurance companies make use of the time value of money is when and one buys a life insurance. He/she gives money to the insurance company which doesn’t have to pay the beneficiaries the sum accruing until the principal dies, this can translate into many years. On the other hand the insurance company decides to invest the money in various instruments with the hope there value will increase. The insurance company is bound to benefit greatly the longer it has to invest the money, which it uses to pay back the benefit. The longer the insured lives the more the time the insurance company has to invest the money before paying up. ( Crosson, S.V. & Needles, B.E. 2008)

Thus if you buy the insurance when you are older it means that your lifespan is shorter, this also applies to those people with ailments or are unhealthy. That is the reason why the older or unhealthy people pay more in premiums compared to the young and healthy; the time value of money is applied the insurance company earns more money the longer the premium stays. ( Crosson, S.V. & Needles, B.E. 2008)

State governments – lotteries

Lottery is one of the methods that the government utilizes to provide funding for education in America. However those oppose the government for raising such money through lottery argue that the government takes advantage of the ignorance of the laymen of the time value of money with lotteries that hit a million dollars. The winner of such a lottery does not get the million dollars upfront; rather one receives $ 50,000 per annum for the next 20 years. The state cannot pay that money upfront because of the time value of money where a million dollar now is more worth a million dollars in future. ( Crosson, S.V. & Needles, B.E. 2008)

Components of a discount/interest rates

A sum of five different components makes up the rate of return at which an investment trades in financial theory; the five components are discussed here below and include:

a) The real risk-free interest rate

This forms the basis at which all other investments are analyzed and compared. It is basically the rate of return an investor would expect to earn in risk less environment devoid of any form of inflation. (Carl S. W et al 2001)

b) An Inflation Premium

To adjust an investment’s expectation for a future inflation a certain rate is added towards this purpose; this is what is termed as the inflation premium. (Carl S. W et al 2001)

c) Liquidity Premium

Liquidity premium is required in circumstances where investors are not willing to pay for the full value of the stocks or assets especially if there is a possibility of not selling them as quickly as they would wish because of buyer scarcity. The liquidity premium serves the purpose of compensating the potential loss. How big a liquidity premium is, is dependent on the investors perception of the activity of the market. A good example of where the liquidity premium is required is in such investments as family controlled company with thinly traded investments like bonds and stock. (Carl S. W et al 2001)

d) Default risk premium

Default risk premium indicates how investors perceive the likelihood of a company defaulting to meet its obligation or the likelihood of it going bankrupt. In most cases when there are telltale signs of a company in trouble, the investors demand a default risk premium which eventually leads to the collapse of the company. (Carl S. W et al 2001)

e) Maturity Premium

The maturity premium commonly refers to the difference that exits between the interest rates of a short term default free bond and a longer maturity default free bond. The price fluctuation of the interest rates change is determined by how further in the future the bonds of the company have matured which in turn determine the price. (Carl S. W et al 2001)

REFERENCES

Carl S. Warren, James M. Reeves, Philip E. Fess, James M. Reeve (2001): Financial and Managerial Accounting: South-Western College

Crosson, S.V., and Needles, B.E. (2008): Managerial Accounting (8th Ed). Boston: Houghton Mifflin Company.

DeThomas, Art (1992): Financing Your Small Business: Techniques for Planning, Acquiring & Managing Debt: Oasis Press,

Tuller, Lawrence W. (1997): Finance for Non-Financial Managers and Small Business Owners: Adams Media

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# Time Value of Money Paper Essay

Time value of money (“TVM”) is defined as the idea that money available at the present time is worth more than the same amount in the future, due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also often referred to as “present discounted value” (Answers Corporation, 2006). TVM concepts help people like managers or investors understand the benefits and the future cash flow to help them determine if the future benefits will justify the initial cost of the project or investment.

To recognize how annuities (a set of fixed payments over a specified length of time) affect the TVM, managers need to consider the factors of interest rates, opportunity cost, future and present values of the money, and compounding. In this paper, I will explain how annuities affect TVM problems and investment outcomes. I will also address the impact of the following on TVM; interest rates and compounding, present value, opportunity cost, and annuities as well as the Rule of 72.

How do annuities affect TVM problems outcomes? Annuities are an investment that promise a constant amount of cash over a certain period. Since annuities generally gain interest, the organization receiving the payments is gaining interest. Annuities can be calculated differently based on the terms of the agreement between the two parties (Brealey, Myers, & Marcus, 2006).

How do annuities affect TVM investment outcomes? Annuities affect TVM investments in a negative manner when the money is accumulating interest. If the money is paid with simple interest, the interest is calculated annually at the rate determined. If the interest is compounded, the interest is calculated annually on the existing balance and as the balance grows. When these investments are in favor of the loaner/bank, the compounded interest is the positive calculation since it earns more money for the loaner/bank (Brealey, et al., 2006).

What is the impact of interest rates and compounding on TVM? When compounding periods are more frequent, interest is received more often; thus, the future value is greater. In addition, when analyzing, the greater the interest rate equates to the greater the return on investment. Both of these, interest rates and compounding periods, can quickly increase the rate at which an investment grows or a debt increases (Brealey, et al., 2006).

What is the impact of present value on TVM (of a future payment received)? The present value of money is also known as discounting. The discount rate is sometimes called the opportunity cost of money. Money can be invested to earn interest. Because money is of more value when it is cash in hand, it has more value since the person holding the cash can invest the cash and, in return, earn interest. When payments are not received, cash flow is reduced; therefore, interest earned is reduced. The relationship between present value and time and interest rate is exponential, i.e.: the greater the interest rate, the smaller the present value (Brealey, et al., 2006).

What is the impact of future value on TVM (of an investment)? The future value of money is also known as compounding. Future value is calculated by understanding how much interest the money will ear, how long it will be earning the interest and if the money will be compounded annually or at another interval. The impact of future value on an investment most likely will be greater than the present value (Brealey, et al., 2006).

What is the impact of opportunity cost on TVM? Opportunity costs are benefits of lost or forfeited as a result of selecting one alternative course of action over another. When an organization makes a bad decision with its existing cash balance, and the choices are not clearly calculated and analyzed, money can be lost if the value can increase in one choice over the other and the lesser of the two are selected (Brealey, et al., 2006).

What is the impact of annuities and the Rule of 72? The Rule of 72 states that in order to calculate the number of years necessary to double your money at a particular interest rate, one must divide the interest rate into the number 72. For example, if you would like to know how long it will take to double your money at eight percent interest, divide eight into 72 and the result is nine years. When the investor/manager can quickly calculate the return on investment, they will be able to make a quicker decision in regard to the investment or budget decision (Brealey, et al., 2006).

TVM is clearly a useful financial concept for managers to apply in their business practices. Figuring present and future values of the firm’s annuities allows for executives to calculate an expected rate of return on financial dealings. Through the understanding of TVM, managers can have an enhanced image of how the company’s investment opportunities are working for the betterment of the firm.

References

Answers Corporation (2006). Time value of money. Retrieved November 1, 2006, from http://www.answers.com/topic/time-value-of-moneyBrealey, R., Myers, S., Marcus, A. (2004). Fundamentals of corporate finance (9th ed.). New York, NY; McGraw-Hill/Erwin.

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# Time Value of Money Paper Essay

INTRODUCTION

The concept of Time Value of Money Paper has sprung from the concept of the depreciation in the value of money paper with time. It is the concept of the reduction n the purchasing power of the same quantity of money in a future period. Put another way, it is the theory that a certain quantity of money held today will have a more purchasing power than the same quantity of money in a future period due to the depreciating value of money caused by the interest rate and inflation,

There are various financial applications for TVM. In fact, financial calculations, assumptions and business is primarily based on the concept of TVM. Because it is this factor which has to be taken into account during long-term loans, annual borrowings and lending, in order for the business to recover the time costs it incurred for the period.

[Ross E. (2006)]

APPLICATION 1

A football club is borrowing $1,000,000 from ABC Bank for the purchase of new training equipment. The entire loan is paid back in 4 semi-annual installments. The interest rate is 10% compounded semi-monthly.

We want to investigate the “value” that this money will hold at the end of two years so that we can devise an appropriate interest rate to recover the “lost value” as well as get some markup.

1st payment: 250,000 * (1-0.05) = 237,500

2nd payment: 250,000 * (1-0.05)2 = 225,625

3rd payment: 250,000 * (1-0.05)3 = 214,343.8

4th payment: 250,000 * (1-0.05)4 = 203,626.6

Total Value; $881,095.3125

We can see that the flat $1 million paid back is not worth the ‘original” amount due to the changes in “value with time”. Thus the bank can levy a higher interest rate to recover the money lent as well as some markup.

[http://www.executivecaliber.ws/sys-tmpl/timevalueofmoney/]

APPLICATION 2

A mother is saving for her daughter’s college education for 10 years from now. She knows that it will costs her $500,000 for her daughters’ entire college expenses. She does not know how much she should save today in order to get $500,000 after 10 years, if the interest rate is 8% compounded annually.

Using the formula: FV=PV(1 + r)t

FV=500,000

r=0.08

t=10

PV=?

Therefore, PV=FV(1+r)-t

PV=500,000(1.05)-10

PV=$306956.6

Thus, she has only to deposit $306,956.6 in her account for a period of 10 years compounded annually at 8% to be sure that she will be able to have the amount necessary for her child’s education when required.

APPLICATION 3:

You want to purchase a new car and you are willing to pay $20,000. If you can invest at 10% compounded annually and you currently can invest $15,000, how long will it take you to generate enough cash to pay for the car?

FV=20,000

PV=15,000

r=0.01

t=?

Rearranging the basic formula [FV={PV(1+r)t]

t = ;n (FV/PV) / (1+r)

t = ln(20,000 / 15,000) / ln(1.1) = 3.02 years

So, it will take approximately 3 years for this amount to be able to pay for the car through compounding.

COMPONENTS OF DISCOUNT/INTEREST RATE

As we saw in the previous applications that the value of money depreciates as time progresses forwards, financial lenders and institutions are always looking to earn back the exact “value” of the money that they lent over the period of lending plus a service charge, which will be the actual profit for the lender.

Therefore, there are two components in the interest rate:

The actual capital recovery factor

The profit factor

EXAMPLE

A Man borrows $1,000 from a bank. He pays it back in 10 monthly installments. What interest rate will the bank charge if the bank wants to make a net real 10% profit on the lent amount? The inflation rate is 5%.

Payment 1: 100 * (1-0.05/12)1=99.58

Payment 2: 100 * (1-0.05/12)2=99.17

Payment 3: 100 * (1-0.05/12)3=98.76

Payment 4: 100 * (1-0.05/12)4=98.34

Payment 5: 100 * (1-0.05/12)5=97.93

Payment 6: 100 * (1-0.05/12)6=97.53

Payment 7: 100 * (1-0.05/12)7=97.52

Payment 8: 100 * (1-0.05/12)8=96.72

Payment 9: 100 * (1-0.05/12)9=96.31

Payment 10: 100 * (1-0.05/12)10=95.91

Total = $977.37

There is a difference of $22.63 between the lent amount and the value of the recovered amount. To make the “value” equal, the bank has to adjust the interest rate so that they earn $22.63 more to break-even. Further they have to earn an additional $100 as profit. They need a net $1100. So, the difference is $123.63 which has to be adjusted into the monthly installment to result in the desired figures.

Therefore, with an effective interest rate of 13% compounded annually, this amount can be generated sufficiently.

There are various methods for determining this interest rate:

Implicit Rate

Return on Investment Method

Weighted Capital

Opportunity Cost

[Block, Hirt (2005)]

REFERENCES:

Block, Hirt (2005). Foundations of Financial Management (11th ed.) New York: McGraw-Hill. Chapters 9 and 14.

Ross, E. (2006). Fundamentals of Corporate Finance (6th ed.) New York: Westerfield and Jordan. Chapter 5.

Time Value of Money. Retrieved April 20, 2008, from Leasing and Time Value of Money Web site: http://www.executivecaliber.ws/sys-tmpl/timevalueofmoney/