Lecture 15-16

# Lecture 15-16 - Interest Rates and Bond Pricing 1 Present...

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Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 15-16, spring 2010, page 1 Interest Rates and Bond Pricing 1. Present Value (PV) of Money: To make our discussions simpler, for this part of our lectures, when we talk about interest rates, we are assuming annual compounding unless specified. a) If you will receive \$7 next year, and the current interest rate is 40%, what is the value of this future income as of today? b) What is the formula? r C PV 1 c) If you will receive that \$7 in two years, and the current interest rate is 40% per year, what do you value this \$7 as of today? PV = d) What is the formula? 2 ) 1 ( r C PV The present value of cash C t received at time t is: t t r C C PV ) 1 ( 0 Notation: here the interest rate is constant . t r ) 1 ( 1 is called the discount factor --- discounting the future cash flow to obtain the current value/present value. It is the PV of \$1 received at time t. 2. Net Present Value a) If you receive \$1 in one year and another \$1 in two years, and the prevailing interest rate is 40%, do you have the equivalent of \$2 today? b) What do you value this cashflow as of today? PV = c) If you need to pay \$1 to get this cashflow, should you pay? d) If the interest rate is 80% a year, should you pay? NPV =

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Lily Qiu, Assistant Professor Economics Department, Brown University EC1710, Lecture 15-16, spring 2010, page 2 The Net Present Value with infinite cashflows: 0 2 2 1 0 ) 1 ( ... ) 1 ( 1 t t t r C r C r C C NPV The first cash flow C 0 is often negative, i.e., the investment you initially put down in order to receive all the future cash flows -> thus the “net” in the name 3. Future Value of Money: a) You invest \$55,000 at an interest rate of 350 basis points above the 5% annual interest rate. If the interest rate is annual compounded, what will you receive at the end of the year? If the interest rate is monthly compounded, and you reinvest monthly interest payments at the same interest rate, what will you have at the end of the year? 4. Perpetuities
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Lecture 15-16 - Interest Rates and Bond Pricing 1 Present...

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