Time Value of Money Paper Essay Example for Free

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 â€Å"value† that this money will hold at the end of two years so that we can devise an appropriate interest rate to recover the â€Å"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 â€Å"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 â€Å"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 â€Å"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/