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Course notes RSM332 - Class 3

# Course notes RSM332 - Class 3 - The Time Value of Money...

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The Time Value of Money Suppose market interest rates are 10%/year. That means, if you invest 1000 today, in 1 year, you will have 1000(1.10) = 1,100 = 1,000 (your original principal) + 100 interest. We could also ask, what is the present value (PV) (the value NOW) of 1,100 to be received in 1 year, if market interest rates are 10%/year? Answer: PV = X such that X(1.10) = 1100 => X = 1100/1.10 = 1000. What is the PV of 1000 in 1 year, if the interest rate is 10%? Answer: X such that X(1.10) = 1000 => X = 1000/1.10 = 909.09 What would you rather have, 909.09 now or 1000 in 1 year? Example: If interest rates are 12%/year, what does 1500 grow to in 5 years? In 1 year, 1500 => 1500(1.12) = 1680 = 1500 + 180 of interest. In the second year, 1680 => 1680(1.12) = 1881.60. Note: 1881.60 –1500 = 381.60 and 180 x 2 = 360 and 381.60 – 360 = 21.60. 21.60 is the interest earned in the second year, on the interest earned in the first year. Benjamin Franklin: “Money makes money, and the money that money makes, makes more money.” In 5 years, 1500 => 1500(1.12)^5 = 1500(1.7623) = 2643.51. We say, 2643.51 is the future value (FV) of 1500 in 5 years if interest rates are 12% annually with annual compounding. In general: FV = C 0 (1+r) T where C 0 is the amount invested, r = the annual rate and T = the number of years it is invested for. Similarly, What is the PV of 2643.51 in 5 years if r = 12%? PV = X such that X(1.12) 5 = 2643.51 => X = 2643.51/(1.12) 5 = 1500. PV of an amount C 1 in 1 year: PV = C 1 /(1+r) PV of an amount C T in T years is PV = C T /(1+r) T Suppose we invest C 0 now in return for: C 1 in 1 year C 2 in 2 years C T in T years First note: If r is the appropriate annual interest rate, the PV of the future payments is given by: PV= C 1 /(1+r) + C 2 /(1+r) 2 + … + C T /(1+r) T And the Net Present Value (NPV) = -C 0 + C 1 /(1+r) + C 2 /(1+r) 2 + … + C T /(1+r) T

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