Lecture 2 - Time Value of Money

Lecture 2 - Time Value of Money - Required Reading TIME...

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Finance - I (MGCR 341) – Prof. de Mot a TIME VALUE OF MONEY Finance - I (MGCR 341) – Prof. de Mot a 2 Required Reading Chapter 4 , “ Time Value of Money ” from Berk and De Marzo , Corporate Finance . Finance - I (MGCR 341) – Prof. de Mot a 3 Corporate Finance Valuation of real and financial assets Valuation of cash flows generated by real and financial assets: - Size of Cash Flows - Timing of Cash Flows - Risk of Cash Flows Finance - I (MGCR 341) – Prof. de Mot a 4 Question Assume that the interest rate is 5% per year. How much would you be willing to pay for a bond that pays $105 in one year? Solution If I invest $100 today at the current interest rate, I can get $105 next year -100 +105 time 0 1 Finance - I (MGCR 341) – Prof. de Mot a 5 Question (Cont) This means that: $105 is the FUTURE VALUE of $100 received today. $100 is the PRESENT VALUE of $105 received in one year. I am willing to pay up to $100 dollars for a bond that pays $105 in one year. I would be indifferent between receiving $100 today or $105 in one year. $100 dollars today are worth $105 next year. Finance - I (MGCR 341) – Prof. de Mot a 6 Question Assume that the interest rate is 10% per year. If you invest $100, how much will you have in three years? And how much will you have in 100 years? Solution At the end of the first year: $100 + $100 x 0.1=$100 x (1+0.1) =$110 Principal Interest
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Finance - I (MGCR 341) – Prof. de Mot a 7 Solution (cont) At the end of the second year: $100 x (1+0.1) x (1+0.1)= $ 121 After 1 year After 2 years At the end of the third year: $100 x (1+0.1) x (1+0.1) x (1+0.1)=$ 133.1 After 100 years: Millionaires !!!! $1,378,061 0.1) (1 x $100 100 = + Finance - I (MGCR 341) – Prof. de Mot a 8 Question: Why do we have $133.1 instead of $130 by the end of the third year? Answer: Because we are earning interest on the interest earned in previous years. This is what we called COMPOUNDING. Compounding : The process of accumulating interest in an investment over time to earn more interest. Compound Interest : Interest earned on both, the initial principal and the interest reinvested from prior periods. Simple Interest : Interest earned on the original amount invested. Finance - I (MGCR 341) – Prof. de Mot a 9 How Big a Deal is Compounding? Let’s go back to our example of $100 and 10% interest rate. Simple Interest Interest on Interest Compound Interest 1 st Year 110 0 110 2 nd Year 120 1 121 5 th Year 150 11 161 10 th Year 200 59 259 20 th Year 300 373 673 40 th Year 500 4026 4526 100 th Year 1100 1,376,961 1,378,061 Finance - I (MGCR 341) – Prof. de Mot a 10 The Power of Compounding 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 1st Year 2nd Year 5th Year 10th Year 20th Year 40th Year Simple Interest Interest on Interests Compound Interests Finance - I (MGCR 341) – Prof. de Mot a 11 Future Value & Compounding where n: Number of periods r:
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This note was uploaded on 12/10/2011 for the course MGCR 341 taught by Professor Trainor during the Winter '08 term at McGill.

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Lecture 2 - Time Value of Money - Required Reading TIME...

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