CHAPTER 1 MODULE 1 Time Value of Money

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

Time Value of Money – Module 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 ? TODAY FUTURE i, n

Time Value of Money – Module 2 Periods 3% 3 0. 9151 6 0. 8375 9 0. 7664 12 0. 7014 6% 0. 8396 0. 7050 0. 5919 0. 4970 9% 0. 7722 0. 5963 0. 4604 0. 3555 12% 0. 7118 0. 5066 0. 3606 0. 2567 Present Value = Future Value x PV Factor 6% | 6 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.

Time Value of Money – Module 2 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. DISCOUNTING ? TODAY FUTURE

Time Value of Money – Module 2 Periods 3% 3 0. 9151 6 0. 8375 9 0. 7664 12 0. 7014 6% 0. 8396 0. 7050 0. 5919 0. 4970 9% 0. 7722 0. 5963 0. 4604 0. 3555 12% 0. 7118 0. 5066 0. 3606 0. 2567 Present Value = Future Value x PV Factor 3% | 12 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.

Time Value of Money – Module 2 Periods 3% 3 0. 9151 6 0. 8375 9 0. 7664 12 0. 7014 6% 0. 8396 0. 7050 0. 5919 0. 4970 9% 0. 7722 0. 5963 0. 4604 0. 3555 12% 0. 7118 0. 5066 0. 3606 0. 2567 Present value factors can be calculated as follows: n 1 ÷ [(1 + i) ] 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 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 3% | 12 $25, 000 = Present Value x 1. 4257 Present Value = $17, 535

Time Value of Money – Module 2 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 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 Present Value = Future Value x PV Factor 3% | n $34, 440 = $70, 000 x PV Factor 3% | n Present Value Factor 3% | n= $34, 440 ÷ $70, 000 = 0. 4920 Periods 3% 22 0. 5219 23 0. 5067 24 0. 4920 25 0. 4776 However – the compounding is quarterly, thus: n x 4 = 24 periods; n = 24 ÷ 4 = 6 years

Time Value of Money – Module 2 Future Value = Present Value x FV Factor 3% | n $70, 000 = $34, 440 x FV Factor 3% | n Future Value Factor = $70, 000 ÷ $34, 440 = 2. 0325 3% | n Periods 3% 22 1. 9161 23 1. 9736 24 2. 0325 25 2. 0938 However – the compounding is quarterly, thus: n x 4 = 24 periods; n = 24 ÷ 4 = 6 years