1. Introduction to Accounting I Professor Marc Smith CHAPTER 1 MODULE 1 Time Value of Money Module 2

2. In the present value of a lump sum case, we know the value of some amount in the future and we want to know the value today. How much is a dollar received in the future worth today? Present Value = Future Value x Present Value Factor i,n ? TODAY FUTURE Time Value of Money – Module 2

3. Periods 3% 6% 9% 12% 3 0.9151 0.83960.7722 0.7118 6 0.8375 0.70500.5963 0.5066 9 0.7664 0.59190.4604 0.3606 12 0.7014 0.49700.3555 0.2567 Present Value = Future Value x PV Factor Present Value = $25,000 x 0.7050 Present Value = $17,625 If you invest $17,625 today in a savings account that pays 12% interest compounded semi-annually, you will have $25,000 in your account at the end of 3 years. 6% | 6 Time Value of Money – Module 2

4. Figuring out how much a future amount is worth TODAY is called DISCOUNTING. Thus, we discounted the $25,000 to determine it is worth $17,625 today. ? TODAY FUTURE DISCOUNTING Time Value of Money – Module 2

5. Periods 3% 6% 9% 12% 3 0.9151 0.83960.7722 0.7118 6 0.8375 0.70500.5963 0.5066 9 0.7664 0.59190.4604 0.3606 12 0.7014 0.49700.3555 0.2567 Present Value = Future Value x PV Factor Present Value = $25,000 x 0.7014 Present Value = $17,535 If you invest $17,535 today in a savings account that pays 12% interest compounded quarterly, you will have $25,000 in your account at the end of 3 years. 3% | 12 Time Value of Money – Module 2

6. Periods 3% 6% 9% 12% 3 0.9151 0.83960.7722 0.7118 6 0.8375 0.70500.5963 0.5066 9 0.7664 0.59190.4604 0.3606 12 0.7014 0.49700.3555 0.2567 Present value factors can be calculated as follows: 1 ÷ [(1 + i) n ] Thus, the present value factor at 3% and 12 periods: 1 ÷ [(1 +.03) 12 ] = 1 ÷ [(1.03) 12 ] = 0.701379 In answering quiz and exam question, always use the table factors provided. Time Value of Money – Module 2

7. KEY POINT The present value of a lump sum and the future value of a lump-sum are reciprocal (opposites) of each other - they can be used interchangeably to solve problems. Future Value = Present Value x FV Factor $25,000 = Present Value x 1.4257 Present Value = $17,535 3% | 12 Time Value of Money – Module 2

8. Question:As the compounding frequency increases, what happened to the present value? Answer: It decreases (exactly opposite of future value). PV Semi-Annual Compounding $17,625 PV Quarterly Compounding $17,535 Question:Why does this happen? Answer:The more frequent the compounding, the more interest is earned on interest thus you need less money up front (today). Time Value of Money – Module 2

9. Interest Earned in Part A [semi-annual compounding] $25,000 - $17,625 = $7,375 Interest Earned in Part B [quarterly compounding] $25,000 - $17,535 = $7,465 Time Value of Money – Module 2

10. Periods 3% 22 0.5219 23 0.5067 24 0.4920 25 0.4776 Present Value = Future Value x PV Factor $34,440 = $70,000 x PV Factor Present Value Factor = $34,440 ÷ $70,000 = 0.4920 However – the compounding is quarterly, thus: n x 4 = 24 periods; n = 24 ÷ 4 = 6 years 3% | n Time Value of Money – Module 2

11. Periods 3% 22 1.9161 23 1.9736 24 2.0325 25 2.0938 Future Value = Present Value x FV Factor $70,000 = $34,440 x FV Factor Future Value Factor = $70,000 ÷ $34,440 = 2.0325 However – the compounding is quarterly, thus: n x 4 = 24 periods; n = 24 ÷ 4 = 6 years 3% | n Time Value of Money – Module 2