1. Introduction to Accounting I Professor Marc Smith CHAPTER 1 MODULE 1 Time Value of Money Module 4

2. In the present value of an ordinary annuity case, we want to know the value today of a series of equal payments to be made or received in the future. How much is a series of future payments occurring at the end of each period worth today? 01 234 Time Value of Money – Module 4

3. Present Value of an Ordinary Annuity = Payment x Present Value Annuity Factor KEY POINTS 1.The ‘payment’ in the above formula represents the amount of each individual, equal payment. Do not add the payments together. 2.The future value and present value of annuities are NOT reciprocal to each other (like the lump sums) and therefore can not be used interchangeably to solve problems. i,n Time Value of Money – Module 4

4. Periods 5% 8% 10% 12% 3 2.7233 2.5771 2.4869 2.4018 6 5.0757 4.6229 4.3553 4.1114 9 7.1078 6.2469 5.7590 5.3283 Present Value Annuity = Payment x PVA Factor Present Value Annuity = $10,000 x 2.4869 Present Value Annuity = $24,869 We must invest $24,869 today into a savings account that pays 10% interest compounded annually in order to be able to make payments of $10,000 at the end of each year for the next three years. 10% | 3 Time Value of Money – Module 4

5. Question: How much interest will M.T. Glass earn over the three year period? Answer: ($10,000 x 3) - $24,869 $5,131 Time Value of Money – Module 4

6. In the present value of an annuity due case, we want to know the value today of a series of equal payments to be made or received in the future. How much is a series of future payments occurring at the beginning of each period worth today? 01 234 Time Value of Money – Module 4 To find the present value of an annuity due table factor, multiply the ordinary annuity factor by (1 + i).

7. Periods 5% 8% 10% 12% 3 2.7233 2.5771 2.4869 2.4018 6 5.0757 4.6229 4.3553 4.1114 9 7.1078 6.2469 5.7590 5.3283 Present Value Annuity = Payment x PVA Factor Present Value Annuity = $5,000 x 5.0757 x 1.05 Present Value Annuity = $26,647 We must invest $26,647 today into a savings account that pays 10% interest compounded semi-annually in order to be able to make payments of $5,000 at the beginning of every six months for the next three years. 5% | 6 Time Value of Money – Module 4 x 1.05

8. Question: Is this a lump sum or an annuity problem? Answer: Annuity – since she will be making annual deposits (payments). Question: Is this a future value or present value problem? Answer: Future value – since the problem tells us how much she wants to have (not how much she needs/has today). Time Value of Money – Module 4

9. Future Value Annuity = Payment x FVAF $192,732 = $20,000 x FVA Factor x 1.08 FVA Factor = $192,732 ÷ $21,600 = 8.9228 8% | n Time Value of Money – Module 4 x 1.08 Periods 8% 4 4.5061 5 5.8667 6 7.3359 7 8.9228 The compounding is annual, thus: n = 7 years