{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Time value of money

# Time value of money - EC150 Financial Economics Slide Set 2...

This preview shows pages 1–10. Sign up to view the full content.

EC150: Financial Economics EC150: Financial Economics Slide Set 2: Time Value of Money Based on RWJ Chapter 4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Money has “time value” Money has “time value” Why? Because interest rates (and expected returns) are positive. Implies that: A dollar today is worth more than a dollar tomorrow (e.g, power of compounding) Cash flows at different points in time cannot be added together. (see DowTheory Letters on web-site)
To illustrate the basics: To illustrate the basics: Bank account accumulations. Bank account accumulations. You place PV = \$1000 in an account that earns r = 8% interest, paid at the end of each year. Let FV n denote the balance after n periods. n = 1. FV 1 = 1000 + 1000(.08) = 1000(1.08) = \$1080.00 n = 2. FV 2 = 1080 + 1080(.08) = 1080(1.08) = 1000(1.08) 2 = \$1166.40 n = 3. FV 3 = 1166.4 + 1166.4(.08) = 1166.4(1.08) = 1000(1.08) 3 = \$1259.71 In general, the balance after n periods can be determined from the initial balance and the interest rate as: FV n = PV(1+r) n

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
0 2 4 6 8 10 12 14 16 18 0 2 4 6 8 10 12 14 16 18 20 Year r = 5% r = 10% r = 15% r = 5% r = 10% r = 15% Accumulated (Future) Values FUTURE VALUE Year 1 2 5 10 20 5% 1.050 1.103 1.276 1.629 2.653 10% 1.100 1.210 1.331 2.594 6.727 15% 1.150 1.323 2.011 4.046 16.37 0 2 4 6 8 10 12 14 16 18 20 20 15 10 5 0 Future value of \$1 Years
Interest Rates and Future Interest Rates and Future Value Value Peter Minuit bought Manhattan Island from the Native Americans in 1621 for \$24. How much is that worth today? FV n = PV (1+r) n n=379, PV=24, and let’s have r=.06 per year FV = 24 (1.06) 379 = \$93.57 billion. Sensitivity Analysis: r=.05 and .07 FV = 24 (1.05) 379 = \$2.58 billion. FV = 24 (1.07) 379 = \$3.29 trillion.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Present Values (Discounting) Present Values (Discounting) The same basic formula can be used to determine the current amount that is equivalent to (i.e. can grow to) a stated future amount, since: PV = FV n /(1+r) n Example: You need \$20 million five years from now to fund a capital investment. If R = 6%, what amount can be set aside now to fund the investment? PV = 20.0/(1.06) 5 = 20.0/1.33823 = \$14.945 million. Terminology: Here, r is referred to as the discount rate , and PV is referred to as the present value of FV n .
PRESENT VALUES Present value of \$1 0 0.2 0.4 0.6 0.8 1 0 2 4 6 8 10 12 14 16 18 20 r = 5% r = 10% r = 15% PRESENT VALUE Year 5% 10% 15% 1 .952 .909 .870 2 .907 .826 .756 5 .784 .621 .497 10 .614 .386 .247 20 .377 .149 .061 Years

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Intuition Intuition Again, the higher the discount rate, the less you value a future cash flow relative to cash today.
Present Value Of A Series of Future Cash Present Value Of A Series of Future Cash Flows Flows In general, the present value of a stream of cash flows can be found using the following general valuation formula: PV C r C r C r C r C r N N N t t t t N = + + + + + + + + + = 1 1 2 2 2 3 3 3 1 1 1 1 1 1 ( ) ( ) ( ) ... ( ) ( ) = In words:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 62

Time value of money - EC150 Financial Economics Slide Set 2...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online