Chapter 14 Notes Page 1 Please send comments and corrections to me at [email protected] Capital Budgeting This chapter examines various tools used to evaluate potential projects or investments. Accountants advocate the use of the Simple Rate of Return, which is based upon the accounting concept of Net Income for this purpose. This return is also referred to as the Accounting Rate of Return. Financiers do not like to use Net Income as a basis for evaluating investments because of the discretion that accountants have in determining Net Income (e.g., estimates of various allowances, useful lives, and the choice of depreciation methods). Financiers prefer to use After-Tax Cash Flow as the basis for their analysis. Financiers advocate the use of the Payback Period, Net Present Value, and Internal Rate of Return for purposes of evaluating investments. Simple Rate of Return and Payback period are referred to as non-discounting models because they do not utilize the time value of money. Net Present Value and Internal Rate of Return are referred to as discounting models because the time value of money is part of their analysis. All of these tools are used to evaluate the merits of a particular project or investment. The way that the project or investment will be financed is not included in the evaluation (e.g., do not include interest costs). It is assumed that the project or investment is funded with available capital, and the source of that capital is not in issue. Present Value "I'll gladly pay you Tuesday for a hamburger today." Instinctively, you know that a dollar that Wimpy is willing to pay sometime in the future is not as valuable as a dollar in your hand today. This inequality arises because you can put the dollar that you currently have in the bank, earn interest on that deposit, and have more than one dollar (the dollar deposit plus the interest) in the future. The Present Value tells you what you have to put in the bank today in order to have a dollar in the future. While you can use your calculator, Excel or a Present Value table, you should be able to figure out the Present Value of one dollar to be receive at the end of a given period by using the following formula: PVIF = __1___ (1+ d)n where “d” is the discount rate (the interest rate) and “n” is the number of periods until you receive the one dollar. PVIF is the Present Value Interest Factor (PVIF) or discount factor that is reported on a Present Value table. If you treat “n” as the number of years Capitol Investment?Chapter 14 Notes Page 2 Please send comments and corrections to me at [email protected] and “d” as the annual interest rate, then your Present Value is based on simple interest. If you change the “n” to reflect the number of six-month periods, and the “d” to reflect the amount of interest that is paid in each six-month period, then you have Present Values that reflect semi-annual compounding of interest. By adjusting the “d” and “n” to reflect various time periods and interest rates, you can vary the extent of the compounding of interest. For example, if one dollar is to be received at the end of one year, and you can receive interest from your bank at the rate of 10% compounded annually, then you need to deposit the following to have one dollar at the end of the year: PVIF = (1/(1.10)1) PVIF = 90.909¢ You can test this: One Year's Interest Is .1 x 90.909¢ = 9.0909¢ Original Principal = 90.9090¢ 99.9999¢ We are a little off because of rounding. As another example, assume that one dollar is to be received at the end of a two-year period, and you can receive interest from your bank at the rate of 10% compounded annually, then you need to deposit the following to have one dollar at the end of two years: PVIF = (1/(1.10)2) PVIF = 82.6446¢ You can test this: One Year's Interest Is .1 x 82.6446¢ = 8.26446¢ Original Principal = 82.64460¢ Amount on Deposit After 1 year: 90.90906¢ Notice how this is similar to the Present Value of a dollar at the end of one year. The only difference is due to rounding. The Second Year's Interest Is .1 x 90.90906¢ = 9.090906¢ Balance At Start of Year = 90.909060¢ Amount on Deposit After 2 years: 99.999966¢ If you are to receive a dollar at the end of each year for a given period of time, this is called an annuity. You could figure out the Present Value of that annuity by calculating the Present Value of each dollar you are going to receive using the above formula. ThisChapter 14 Notes Page 3 Please send comments and corrections to me at [email protected] could get cumbersome if the annuity period is long. Alternatively, you could use the formula for calculating the Present Value of an Annuity. Conceptually, the Present Value of an Annuity is that amount that must be invested today at a given interest rate in order to produce sufficient funds to enable annual withdrawals of the annuity amount over the annuity period. PVIFannuity = 1 – 1/d[ __1___ ] (1+d)n For example, if one dollar is to be received at the end of each year for a two-year period, and you can receive interest from your bank at the rate of 10% compounded annually, then you need to deposit the following to be able to withdraw one dollar at the end of each year for two years: The Present Value of one dollar received a year from now is: 90.9090¢ The Present Value of one dollar received two years from now is: 82.6446¢ $1.735536 Using the Present Value of an Annuity formula: PVIFannuity = [1-(1/(1.10)2]/.1 PVIFannuity = $ 1.73553719 Again, the difference is due to rounding. If you deposit $1.73553719 with a bank at 10% interest, you can withdraw one dollar at the end of each year for two years: Initial Deposit: $1.735537190 One Year’s Interest: 17.355372¢ Amount On Deposit After One Year: $1.909091 Withdrawal of Annuity: -$1.000000 Amount On Deposit After Withdrawal of Annuity: 90.9091¢ Second Year’s Interest: 9.0909¢ Amount On Deposit After Two Years: $1.000000 Withdrawal of Annuity: -$1.000000 Amount On Deposit After Withdrawal of Annuity: 0 Net Present Value The problem when
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