Accounting 490 Professor Jeff Harkins1/14/2019The Time Value of MoneyInterest, the time value of money, implicitly derives from an individual’s preference for current consumption over future consumption. People prefer current consumption because people have present wants and needs and because there is a risk that they might not be around in the future if they forego consumption today. However, people will forego consumption today, if they are rewarded for doing so. The reward, which we will call interest, must reimburse the individual who sacrifices today’s consumption for the uncertainty associated with the deferral of present consumption. The model for evaluating the present and future values of monetary transactions is built from this basic need for a reward to sacrifice today’s consumption. In accounting and finance, the time value of money is used to measure and evaluate many business and economic transactions, including:- accounts and notes receivable- accounts and notes payable- long-term capital assets- stocks, bonds and other securities- long-term leases- pensions and retirement plans- investment analysis- depreciation- business combinations- capital budgeting decisions- mergers and acquisitionsIt is important that students of business, especially accounting and finance students, be comfortable with techniques for evaluating financial transactions using time value of money techniques. Future Values and Present ValuesFor an introduction to the basic structure and technique of determining the time value of money, consider that you have deposited $1,000 in a savings account at the bank today and that you will leave the money with the bank for one year. You might ask yourself if you would be willing to leave the money with the bank for the year, then at the end of the year, withdraw the funds ($1,000), with no additional compensation. If not, why not? Reflecting on your response may help you to understand the introductory paragraph. No, you probably expect to receive more than $1,000 from the bank at the end of the year.There are many ways to view the subtleties of this event. One perspective directs you to recognize that the bank is borrowing your money for one year - and because they are “using” your money, you expect to receive “rent” for the use of the funds for the year. Another way of thinking about this transaction is to consider that you are “investing” yourfunds in a relatively low-risk investment (the savings account) and that you expect to receive a “return” on your investment. In either case, you expect a reward for placing ; The Time Value of MoneyAccounting 490 Professor Jeff Harkins1/14/2019your funds at the disposal of the bank, thus the bank pays you a fee, called “interest”. Theinterest fee or “rent” is usually quoted as a “rate” or interest rate and refers to the percentage payment that will be paid on the principal for a period of time. Unless stated otherwise, the conventional means of quoting interest rates is to state the interest rate for an annual period or one year. Thus, if our $1,000 deposited at the bank earned interest at 9%, it would be assumed that the bank is paying us $90 for use of the money deposited forone year. To place the above scenario into a more structured argument and contemporary syntax, if we deposit $1,000 today (the present value) which will earn 9% per year (the compounding rate of interest per period); the funds on deposit in one year (the future value) total $1,090. This “future value” is calculated as follows:Future value (FV) = Present value (PV) + [Present value (PV) * Interest rate ( r )]orFV = PV + [PV * r]orFV = $1,000 + [$1,000 * .09] = $1,090Suppose we decided to leave the funds on deposit for two years instead of one year. This could be calculated as follows:FV = PV + [PV * r] + {[PV + (PV * r)] * r} = $1,000 + [$1,000*.09] + {[$1,000 + ($1,000 * .09)] * .09} = $1,000 + [$90] + [$1,090 * .09] = $1,000 + $90 + $98.10 = $1,188.10If you are comfortable with algebra, you might notice that the right hand side of the preceding equation can be simplified by factoring. Begin with:FV = PV + [PV * r] + {[PV + (PV * r)] * r}Clear the brackets, which produces:FV = PV + PVr + PVr + PVr2Then factor the term PV from the restated equation and collect terms:FV = PV (1+ r + r + r2)FV = PV (1+ 2r + r2); The Time Value of MoneyAccounting 490 Professor Jeff Harkins1/14/2019Then reduce the result to its simplest form:FV = PV (1+ r )2If we substitute the information from our earlier example for $1,000 earning 9% interest compounded annually for two periods, we get the result:FV = PV (1+ r )2FV = $1,000 (1+ .09 )2FV = $1,000 (1.09 )2FV = $1,000 (1.1881)FV = $1,188.81This is equivalent to the extended calculations rendered above. As you might have suspected, the calculation of the future value of a present amount is a geometric series and the formula can be generalized as follows:FV = PV (1 + r)nwhere: FV = Future value of a present amountPV = Present value of amountr = Interest rate per periodn = Number of compounding periodsThis generalized form serves as the basis of all calculations involving the time value of money. For instance, suppose that we were interested in determining the present value of an amount we wanted or expected to receive in the future. By solving the future value equation for the unknown PV, we can determine the present value. Consider that you want to buy a car in 4 years and you want to pay cash for the vehicle. You expect the car to cost $10,000. If you could earn 8% per year on a Certificate of Deposit at the local bank, how much would you have to deposit today in order to accumulate the $10,000? We can solve this problem by manipulating the equation for future value. We know that:FV = PV (1 + r)n$10,000 = PV (1 + .08)4$10,000 = PV (1.08)4PV = $10,000/(1.08)4PV = $10,000/(1.08)4PV = $10,000/1.3604889; The Time Value of MoneyAccounting 490 Professor Jeff Harkins1/14/2019PV = $7,350.30The result is that if you deposit $7,350.30 today in an interest-bearing investment that earns 8% annually for four years, you would accumulate $10,000 by the end of four years.If you wish to evaluate this, you might consider reviewing the table that reflects the extended form of calculation. Date Interest Rate Interest Earned Balance1/1/Year1 Deposit 7,350.3012/31/Year1 8% 588.02 7,938.3212/31/Year2 8% 635.07 8,573.3912/31/Year3 8% 685.87