Posted: May 12th, 2015

Time value for money

Part One

Introduction

Time value of money can be used to explain how money over time loses value mainly due to inflation rates combined with interest rate in a given economy. It holds the idea that a coin today is more than the same in in the near future. Time value of money holds that any amount of money is worth more the sooner it’s received as you should receive the same amount today than wait to receive it at a later date when its value will have depreciated. Time value of money helps investors to understand the risk involved when lending money due to factors like changes in inflation rate where the money losses value over time and changes in loan borrowing rates from federal reserve for banks. This business risk must be mitigated by calculating the time value of money. Time value of money is applied in mortgages as they are timely payments and thus the present value and the future value of the money must be calculated for good returns. Mortgages are fixed timely payments made by clients to home developers to own a home and at the same time the developers must get good returns for their investment. The mortgage payers must also be offered a competitive price to pay for the mortgage. The payments are usually made on a monthly basis and thus may also be seen as perpetuity. Time value of money can also be used to calculate annual growth rates taking the formula of calculating the future value of a single sum of money. Time value of money is also used when amortizing a loan using the amortization schedule which is a payment combined with interest charged over a loan until the whole loan is paid off. The schedule revolves around making timely payments until the loan is paid off together with the interest charged over a given period of time (Correia, 73).

Future Value of single sum

A future value can be explained to mean the amount of cash that will be accrued by a given time resulting from an earlier single sum that has been invested. When a single amount is invested for a period of time it is referred to as a future value of a single sum. The single sum accrues interest each period of investment. The future value generally tells us of how something will be worth in the future or a future date. To calculate the future value of a single sum we use the formula (Correia, 25).

FV= PV (1 + i)n

Future value= present value (1 + i)ⁿwhere i represents interest rate and n represent the number of compounding periods.

 

For example,

FV = 50, I = 0.08, n = 3

Thus FV = PV(1 + i)ⁿ = 50(1 + 0.08)³ = 62.99

Present value of single sum

PV = FV [ 1/ (1 + i)n ]

Present value of a single sum of money is the amount of money that is equivalent to a future money payment. It can also be used to mean the amount of money if invested on a given date with a specific rate of interest will be equal to the same amount invested and the compounding interest earned.

 

 

Where PV = Present value, FV = Future Value, i = interest rate per period, n = Number of compounding periods (Correia, 45).

For example: you want to buy a house 5 years from now for $ 150000. Assuming a 6 % interest rate compounded annually, how much should you invest today to yield $ 150,000 in 5 years?

FV = 150000, I = 0.6, n = 5

PV = 150,000 [ 1 / (1 + 0.6)⁵ ] = 112088.73

Ordinary annuity

The term ordinary annuity can be used to mean an amount of money made as payment at the end of a given period of time. The payments are usually done on a timely interval for example on a monthly basis or quarterly or even half yearly. The present value of an annuity heavily depends on the prevailing interest rate in the country or even on the economy. Usually the opposite of an ordinary annuity is an annuity due which is to be paid at the beginning of the payment period for example on the start of the month (Besley et al., 47).

Present value of an annuity

PVoa = PMT [(1 – (1 / (1 + i)n)) / i]

An annuity is a payment made or cash received in series for a given period of time and thus the present value of an annuity is the value of stream of expected future payments to be made with a kind of discounted interest.

 

Where;

PVoa = Present Value of an ordinary annuity, PMT =Amount of each payment, i = Discount Rate per period and n = Number of periods

For example; PMT = 50 I = 0.07, n = 3

Future value of an annuity

Future value of an annuity is used to calculate the accumulated growth for a series of payments made at an interval and how the stream of payments will be worth in a given time in future. It calculates the future value of each annuity payment made at a given time interval so as to know its worth in future. It differs from the present value in terms that it must be an indication of how a certain investment will be worth in future with its payment made at a fixed time series. Future value of an annuity uses the following formula to arrive at the future value of a given timely payment (Besley et al., 46).

Where FV = Future Value, PMT = Payment made, i = interest rate, n = number of compounding periods

For example; PMT = 25, I = 0.09, n = 3

 

Amortization

Amortization is a term used to refer to the timely payment made to pay off a loan a client had borrowed from a financial institution over a given period of time combined with the interest rate attached to the loan. In the payment of a loan we use an amortization schedule which combines a list of each monthly payment made together with the balance that remains and an addition interest rate charged. Amortization follows a process of decreasing an amount over a given period of time where the amount is allocated over the whole paying period. Amortization is also done on capital deduction of assets in a business premise and thus a measure of this deduction is crucial in determining the value of the asset over time (Estes et al., 85).

Cash flow

Cash flow can be defined to mean the movement of money in and out of a business venture. It can also be referred to as a change in the revenue or expense account over a given time. Cash flow normally arises from the following cash inflow and out flow due to financing, investing and operations activities in the business. As a business student it better to learn how to derive a statement of cash flows that occur as a result of an amount generated and used by a business premise in a given period of time. A business must take in to account any cash flow attributed in the course of doing business as it checks how solvent a business is and will it be able to pay for its expenses. The statement of cash flow is used by business owner and stakeholder to assess the financial position of a business. Without a statement of account it’s not possible for a business owner to gauge its performance and use the information to make decision about investing. For a business growth and to access credit from financial institution it must have a favorable statement of cash flow as collateral to guarantee its loan service in a given period of time. A cash flow statement can be used as a measure of the financial health of a given business premise. It is calculated by adding all the cash receipt in the business over a given period of time minus all the cash payments at the same time. Another way to derive a cash flow statement is by adding the net profit with cash amounts charged off for depreciation, amortization and depreciation (Friedlob, 48).

Present value of an unequal cash flow

Cash flow can be defined to mean the movement of money in and out of a business venture. It can also be referred to as a change in the revenue or expense account over a given time. Cash flow normally arises from the following cash inflow and out flow due to financing, investing and operations activities in the business. ThusPresent value of an unequal cash flow is the calculation of the present value of cash flows that are not regular over a given period of time (Friedlob, 56).

Simple interest

Interest can be defined as the cost charged for borrowing money by a money lender for the use of money by a borrower. It serves as compensation to the lender by the borrower for the loan awarded over a given period of time. An interest can also be used to mean the compensation that a borrower is charged over a given period of time for use of the money taking into account that inflation rate also play a role in lowering the initial value of money over time. Whereas the rate of interest is the percentage of the principal amount that is charged over the principal for borrowing money over a given period of time may it be a month or quarter yearly or even annually (Besley et al., 46).

For example, if $50 were charged to borrow $1000 principal for one year, the interest rate is 5%.

I = 50/1000 = 5 %

Compound interest

Compound interest is a type of interest earnedon interest. Usually when compounding on annual interval there is no compounding effect as interest is earned once in the year. If compounding is done monthly then interest earned each month and thus the future value is greater as compared to the one earned on annual basis as in the monthly compounding the interest is earned monthly (Besley et al,. 48).

For example the value of $100 invested for one year at 8%

Annual compounding = 100(1 + 0.008)1 = 108

Monthly compounding = 100 (1 + 0.008/12)12 = 108.3

Discount rate

Discount rate is the interest rate charged on the discounted cash flows where it is used to calculate the present value of future cash flows that a business enterprise may wish to invest in. it can also mean the rate that a financial institution borrows money from the central bank over a given period of time. For example a bank borrowing money from the Federal reserve as a loan where the rate of borrowing is subsidized by the Federal reserve according to amount and duration of pay. The discount rate is controlled by monetary policy of the given country as a control of money demand and supply.

Perpetuities

Perpetuities are equal payments made regularly for a considerable duration of time and most of the time it has no end and the payment is made forever without cease. The payments are usually fixed. The payments are characterized with no end and thus the future value of perpetuity is finite. For example, to get the future value of perpetuitywe divide the payment with the interest rate of the perpetuity. Present Value = Payment/ interest rare. Given payment = $1000 and interest rate = 3%.

Thus PV = $1000/0.03 = $33,333

Part Two

Application of time value of money

The present value is used to calculate and help in determining the various amounts in the valuing the retirements payments for a citizen or a civil servant. Present value can also be used to calculate the pricing of coupons bearing bond and the return of a single sum at maturity of the bond. Present values are used to determine the value of periodic payment to an insurance company by a single party as premium over a given time. Also the concept of present value can be used to establish the amount of money that a single client will be required to pay for purchase of an investment that will be paid in installments. Time value of money helps investors to understand the risk involved when lending money due to factors like changes in inflation rate where the money losses value over time and changes in loan borrowing rates from federal reserve for banks. This business risk must be mitigated by calculating the time value of money. Time value of money is applied in mortgages as they are timely payments and thus the present value and the future value of the money must be calculated for good returns. Mortgages are fixed timely payments made by clients to home developers to own a home and at the same time the developers must get good returns for their investment. The mortgage payers must also be offered a competitive price to pay for the mortgage. Time value of money can also be used to calculate annual growth rates taking the formula of calculating the future value of a single sum of money. Time value of money is also used when amortizing a loan using the amortization schedule which is a payment combined with interest charged over a loan until the whole loan is paid off. The schedule revolves around making timely payments until the loan is paid off together with the interest charged over a given period of time (Estes et al., 85 – 100).