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# chap5 - Ch 5 Time Value of Money 1 Topics Covered Future...

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1 Ch. 5 - Time Value of Money

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2 Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Non-annual interest compounding Effective Annual Interest Rate
3 The Time Value of Money Compounding and Discounting Single Sums

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4 Future Values Future Value - Amount to which an investment will grow after earning interest. Compound Interest - Interest earned on interest. Simple Interest - Interest earned only on the original investment.
5 Example: Simple vs. Compound Interest Compare \$100 invested at 10% interest compounded annually vs. 10% simple annual interest for 3 years.

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6 Future Value of Single Cash Flow n i PV FV ) 1 ( + × =
7 0 1000 2000 3000 4000 5000 6000 7000 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 Number of Years FV of \$100 0% 5% 10% 15% Future Values of \$100 with Compounding Interest Rates

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8 Example: Futurama Value? Fry is frozen in the year 2000 with \$0.93 in his checking account that pays 2.25% compounded annually. How much does Fry have in his account when he “awakes” a thousand years later in the year 3000?
9 Present Value Today's value of a lump sum received at a future point in time: ( 29 n n i PV FV + × = 1 n n i FV PV ) 1 ( + =

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10 Example: Paying for Baby’s MBA Just had a baby. You think the baby will take after you and earn academic scholarships to attend college to earn a Bachelor’s degree. However, you want send your baby to a top- notch 2-year MBA program when baby is 25. You have estimated the future cost of the MBA at \$102,000 for year 1 and \$107,000 for year 2.
11 Example: Paying for Baby’s MBA Today, you want to finance both years of baby’s MBA program with one payment (deposit) into an account paying 6.5% interest compounded annually. How large must this deposit be?

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12 The Power of High Discount Rates Periods Present Value of One Dollar (\$) 0 2 4 6 8 10 12 14 16 18 20 22 24 0.5 0.75 1.00 0.25 10% 5% 15% 20% 0%
13 Implied Interest Rates Internal Rate of Return Time necessary to accumulate funds Time Value of Money (applications)

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14 Example : Finding Rate of Return or Interest Rate A broker offers you an investment (a zero coupon bond) that pays you \$1,000 five years from now for the cost of \$740 today. What is your annual rate of return?
15 The Time Value of Money Compounding and Discounting Cash Flow Streams 0 1 2 3 4

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16 Annuities Annuity : a sequence of equal cash flows, occurring at the end of each period. This is known as an ordinary annuity. 0
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chap5 - Ch 5 Time Value of Money 1 Topics Covered Future...

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