The Time Value of Money

Future Value Investment Interest or Yield Yield 10% Investment $1, ___x ___ 10 =.1== $100 Annual Yield 10% = 50% = 8% = 6.5% = Compound Interest How often is interest added to investment principal Examples: annually, monthly, weekly, daily Annually 12% = $120 Annually 12% = $120 Monthly 12% = $ Monthly 12% = $ $1,000 x.12 /12 = $10 Month 1 $1,010 x.12 /12 = $10.10 Month 2 Monthly Interest = $10 Monthly Interest = $10 -- Interest earning interest $1,020 x.12 /12 = $10.30 Month The Time Value of Money

Future Value Computation Beginning of Year End of Year Investmentx$1,000=$1,0001 Incomex$1,000=.0880 _____ $1, x$1,000=$1, x$1,080=$1,166 (1 + Interest Rate) xInvestment= Future Value = (1 + int) x Present Value PV x (1 + int) 2 End of year 1 = Future Value End of year 2 PV x (1 + int) n = Future Value Number of Payment Periods 1 = 100% The Time Value of Money

FUTURE VALUE The Time Value of Money

FUTURE VALUE Future Value Computation Beginning of Year End of Year Investment x $100,000 =$100,0001 Income x $100,000=.088,000 _______ $108, x$100,000=$108, x$108,000=$116,640 The Time Value of Money

Click the ‘Insert Function’ (f x ) icon FUTURE VALUE EXCEL

The Time Value of Money FUTURE VALUE EXCEL The ‘Insert Function’ Box Appears

The Time Value of Money FUTURE VALUE EXCEL The ‘Insert Function’ Box Appears Type ‘fv’ Then click on the ‘Go’ icon Then click ‘OK’

The Time Value of Money FUTURE VALUE EXCEL The ‘Function Arguments’ Box Appears Type ‘.08’ Type ‘2’ Type ‘0’ Type ‘ ’ The ‘function’ formula Excel utilizes appears as you type Then click ‘OK’ The calculated answer appears here even before you click the ‘OK’ icon

Positive and Negative Numbers IN your pocket = type in a POSITIVE Number OUT of your pocket = type in a NEGATIVE Number Ask yourself “Does this financial transaction allow me to put money IN my pocket or require me to take money OUT of my pocket? If you take $100,000 and put it in an investment where did the $100,000 come from? OUT of your pocket After 2 years the investment gives you = -100,000 IN your pocket$116,640 The Time Value of Money

Positive and Negative Numbers

Future Value of a Stream of Payments Future Value Computation Beginning of Year End of Year Investment x $100,000 =$100,0001 Income x $100,000=.088,000 _______ $108,000 Investment + $100,000 =$208,000 Income x $208,000=.0816,640 _______ $224,640 The Time Value of Money

EXCEL Click on function icon (f x ) Type ‘fv’ (future value) Click on ‘OK’ Future Value of a Steam of Payments

The Time Value of Money EXCEL The ‘Function Arguments’ Box Appears Type ‘.08’ Type ‘2’ Type ‘-100,000’ Type ‘0’ Type ‘1’ Then click ‘OK’ Future Value of a Stream of Payments

The Time Value of Money EXCEL Type is a value representing the timing of the payment: Payment at the beginning of the period = 1 Payment at the end of the period = 0 or omitted Investment Contribution Debt Payment Future Value of a Stream of Payments First Pension Check Type

The Time Value of Money Compounding What if your money compounds monthly or payments are made monthly instead of annually? 12 percent interest annually =.12 monthly =.12/12 payments annually = 1 monthly = 1 * 12 quarterly =.12/4 quarterly = 1 * 4

PRESENT VALUE Present Value Computation Beginning of Year End of Year Investment / $100,000 =$92, $92,593 x 1.08 = $100,000 Investment / $92,593 =$85, The Time Value of Money

EXCEL Click on function icon (f x ) Type ‘pv’ (present value) Click on ‘OK’ PRESENT VALUE

The Time Value of Money EXCEL The ‘Function Arguments’ Box Appears Type ‘.08’ Type ‘2’ Type ‘0’ Type ‘100000’ Type ‘0’ Then click ‘OK’ PRESENT VALUE

Present Value Computation Beginning of Year End of Year Investment / $100,000 =$92, Investment / $100,000 =$85, Investment / $100,000 =$79, The Time Value of Money Present Value of a Stream of Payments

Present Value Computation Beginning of Year End of Year Investment / $100,000 =$92, Investment / $100,000 =$85, Investment / $100,000 =$79, $257,710 ________ The Time Value of Money Present Value of a Stream of Payments

The Time Value of Money EXCEL Click on function icon (f x ) Type ‘pv’ (present value) Click on ‘OK’ Present Value of a Stream of Payments

The Time Value of Money EXCEL The ‘Function Arguments’ Box Appears Type ‘.08’ Type ‘3’ Type ‘100,000’ Type ‘0’ Then click ‘OK’ Present Value of a Stream of Payments

Four Practice Problems The Time Value of Money

Future Value of a Lump Sum

The Time Value of Money Future Value of a Stream of Payments

The Time Value of Money Future Value of a Stream of Payments

The Time Value of Money Future Value of a Future Lump Sum