University of California
Type of paper: Thesis/Dissertation Chapter
The Present and Future Price of Money
One of the most important concepts about saving and investing is the time value of money. It can be used to compare investment alternatives and to solve problems involving loans, mortgages, leases, savings, and annuities. This means money paid out or received in the future is not equivalent to money paid out or received today because inflation erodes money’s buying power. Basically, the power of time is on a person’s side and the premise that cash in hand today is more valuable than the same amount in the future due to its capability of earning interest. There are three factors affecting how much an investment will grow: time, money, and interest rate. Time Value of Money is a concept that is very important in financial management. It affects business, personal, and government finance (Harvey, 2012) Within this paper we will discuss the definition of Time Value of Money and identifies the importance of financial managers understanding the concept.
Time, Money and Interest Rates
Time has an important impact on the future value of money. Time is referred to as “N”, or “number,” and signifies the number of times something happens to your money. The earlier an individual invests, the more time their investment has to compound interest and increase in value. The effects of time on the value of money need to be taken into account when assessing investments. Investments (Money) with interest rates compounding frequently will yield higher returns. The higher the interest rate, the more money an individual will earn. However, and individual must understand an investment with a higher interest rate generally has a greater risk. Risk is the uncertainty the yield on an investment will deviate from what is expected. Generally, having a savings or investment plan with a fixed interest rate guarantees a specific return but can provide a moderate risk. The last item to take into consideration with interest rates is ensuring the interest rate is higher than the rate of inflation. Inflation is the steady rise in the general level of prices of a market basket of goods. If the average interest rates rise, the amount a person earns from this type of investment will not increase. Another consideration with interest rates is ensuring the interest rate is higher than the rate of inflation.
Need for Financial Managers
Anyone who manages finances in a company setting , deals with consumer finance or running their own business is a financial manager and needs to understand the concept of Time Value of Money. A financial manager’s job it to compare the cost and benefits of alternatives that occur at different times. This is done by restating money values through time in Time Value of Money calculations. These calculations estimate what effect time will have on money.
For these professionals to make decisions that will assist a client in taking advantages of low interest rates or investing wisely a comprehensive knowledge and understanding of the Time Value of Money is needed. Understanding this concept allows them to make better decisions. If they don’t understand the concept then they could make an unfavorable decision resulting in loss of money for the client or their business (Time Value of Money, 2013)
Future Value and Present Value
As an investor, you cannot control the rate of return on an investment. The actual yield is determined by the market as a whole, in the form of people buying and selling the investments at a price that, coupled with the investment’s payouts, determines the yield. There are two fundamental formulas used to calculate the time value of money; the “future value” and the “present value” formulas. They’re basically the same formulas, but rearranged to solve for different values. The future value formula can answer the question, ‘how much money will I have if I invest a certain amount now, at a given rate of return”? The formula is FV=PV*(1+R)N, where FV is the future value (how much you’ll have later), PV is the present value (how much you’ll have now), R is the periodic rate of return or the percentage that your money will grow in each unit period of time. N is the number of unit periods of time in the overall time span. The following are examples of the calculation of future values: a) Solve for FV $150,537.19 invested for seven years at an interest rate of 5% will yield a future value of $211,820.94. FV = 150,537.19 (1+ .05)7 =
150,537.19 (1.05) 7 = 150,537.19 (1.40710042265625) = $211,820.94 b) Solve for FV $237,891.22 invested for eight years at an interest rate of 3% will yield a future value of $301.353.48. FV = 237,891.22 (1 + .03) 8 =
237,891.22 (1.03) 8 = 237,891.22 (1.266770081387616) = $301,353.48 c) Solve for FV $320,891.12 invested for 10 years at an interest rate of 11% will yield a future value of $911,144.98. FV = 320,891.12 (1 + .11) 10 =
320,891.12(1.11) 10 = 320,891.12 (2.839420986069016) = $911,144.98
d) Solve for FV $520,520.22 invested for 13 years at an interest rate of 13% will yield a future value of $2,549,513.82. FV = 520,520.22 (1 + .13) 13 = 520,520.22(1.13) 13 = 520,520.22(4.898011103216606) = $2,549,513.82 The present value formula is based on the same fundamental formula, but it’s “solved” for the PV term and assumes you will know the FV amount. The present value formula can answer the question, ‘how much money would I have to invest now in order to have X dollars at a specific future date?’. That formula is PV = FV/(1 + R) n where all the terms mean the same thing, except that R in this formula is typically referred to as the “discounted rate”, because its purpose is to lower a future amount of money to show what it is worth to you now (McCracken, 2014). The following are examples of the calculation of present value: a) If you receive a dividend of $562,126.17 in 7 years at an interest rate of 5%. You initial investment would have been $399,492.57. PV = 562,126.17/(1 + .05) 7 = 562,126.17 / (1.05) 7 = 562,126.17/1.40710042265625 = $299,492.57 b) If you receive a dividend of $225,003.21 in 6 years at an interest rate of 6%. Your initial investment would have been $158,618.38. PV = 225,003.21/(1 + .06) 6 = 225,003.21/(1.06) 6 = 225,003.21/1.418519112256 =
c) If you receive a dividend of $321,567.35 in 5 years at an interest rate of 18%. Your initial investment would have been $140,560.05. PV = 321,567.35/(1 + .18) 5 = $140,560.05/(1.18) 5 = 321,567.35/2.2877577568 = $140,560.05 d) If your receive a dividend of $63,000.05 in 12 years at an interest rate of 5%. Your initial investment would have been $35,080.75. PV = 63,000.05/(1 + .05) 12 = 63,000.05/ (1.05) 12 = 63,000.05/1.795856326022129 = $35,080.79
An annuity is a series of identical payments occurring at equal time intervals. When the payments appear at the end of each time period, the annuity is said to be an ordinary annuity or an annuity in arrears. Present value calculations allow us to determine the amount of the recurring payments in an ordinary annuity if we know the other components: present value, interest rate, and the length of the annuity. Present value calculations involve the compounding of interest. This means that any interest earned is invested and will earn interest at the same rate as the principal. So, you earn interest on your interest. The compounding of interest can be very significant when the interest rate and the number of years are sizable. The present value of an annuity, represented by a series of equal payments, receipts or rents involve five components: (1) Present Value (2) Amount of each identical cash payments (3) Time between the identical cash payments (4) Number of periods that the payments will occur, length of the annuity and, (5) Interest rate or target rate used for discounting the series of payments. If you have any 4 of the 5 components, you have the information you need to calculate the unknown component.
Calculations of Annuity
Suppose you are to receive a stream of annual payments of $325,891.12 every year for 12 years starting at the end of this year. The interest rate is 6%. What is the present value of these 12 payments. PVA =PMT [( 1- (1 /(1 + r) n )) /r ]
= 325,891.22[(1- (1/(1 + .06) 12))/.06]
= 325,891.22[(1- (1/(1 .06) 12))/.06]
= 325,891.22[(1 – (1/20121964718355))/.06]
= 325,891.22 x 8.383843940383317
= $2,732,221.13 is the present value of the 12 payments.
Suppose you are to receive a payment of $437,891.24 at the end of each year for five years. You are depositing these payments in a bank account that pays 15% interest. Given these five payments and this interest rate, how much will be in your bank account in five years? FVA =PMT [((1 + r) n – 1) /r]
= 437,891.24 [((1 + .15) 5 – 1)/.15]
= 437,891.24 [((1.15) 5 – 1)/.15]
= 437,891.24 [(2.0113571875 -1) /.15]
= 437,891.24 [1.0113571875/.15]
= 437,897.24 x 6.74238125
= $2,952,429.69 will be in your bank account at the end of 5 years.
Present Value and Future calculations seem to be a simple way to compare money at different periods of time. Utilizing the future value calculation a person is able to determine the estimated future value of investments based on periodic, constant payments and constant interest rate. It ca also be used to calculate the future of loans payments.
Time Value Money is a basic tool in finance that is used every day. Utilizing this concept can help individuals and companies weight all the options so the best decision can be made to prosper in the future. Understanding and having the knowledge about saving and investing is very important to our generation, especially with the very bleak look of social security.
Biger, N. (2008). Explanation of present values and net present values.
Harvey, C. R. (2012). Time Value of Money. Retrieved January 16, 2013, from The Free Dictionary: http://financial-dictionary.thefreedictionary.com/Time+value+of+money McCracken, M., (n.d.) The time value of money. Retrieved January 2014 from http://www.teachmefinance.com/timevalueofmoney.html Time Value of Money Overview. (n.d.) Retrieved January 17, 2013, from University of West Florida: http://uwf.edu/rconstand/fin4424web/T2-TimeValue/T2-TimeValuePO1.htm