Week 1and 2 - 2/25/2009 Week 1 and 2 Introduction to...

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2/25/2009 1 Week 1 and 2 Introduction to Financial Mathematics Cameron Truong 2 Objectives & learning outcomes of week 1 Appreciate the difference between nominal and real interest rates. Understand the concepts of present value, future value and their applications. Identify the differences between perpetuities, growing perpetuities and annuities. Understand the notion of Net Present Value (NPV). Demonstrate how the NPV rule can maximize the value of the firm. 3 Intuitions behind time value of money Why is a dollar today worth more than a dollar tomorrow? Inflation Suppose the inflation rate is 10% p.a. for all goods. Thus, a Ford car that costs $10,000 today will cost $11,000 in a year
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2/25/2009 2 4 Intuitions behind time value of money Individuals prefer present consumptions to future consumptions Suppose the bank’s saving rate is 10% p.a., thus allowing you to buy the Ford car in one year at $11,000 (provided you save $10,000 today). Would you choose to buy the car today at $10,000 or wait (i.e. save $10,000 in the bank) and buy the car in one year? Uncertainty (risk) associated with future cash flows 5 Future value Simple interest - Interest earned only on the original investment (principal) Suppose you save $100 today in the bank which offers a simple interest rate of 10% p.a. You save for 3 years. How much will your investment grow in 3 years? T=0 T=1 T=2 T=3 Interest earned 0 Value 100 10 110 10 120 10 130 6 Future value Compound interest : Interest earned on previous interest Suppose you save $100 today in the bank which offers an interest rate of 10% p.a compounded annually . You save for 3 years. How much will your investment grow in 3 years? T=0 T=1 T=2 T=3 Interest earned 0 100 10 110 11 121 12.1 133.1
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2/25/2009 3 7 Future value The beauty (and the beast) of compounding 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% 8 Future value Example (again): Suppose you save $100 today in the bank which offers an interest rate of 10% p.a compounded annually . You save for 3 years. How much will your investment grow in 3 years? 9 Future value FV = PV(1 + r) t (1) where FV = future value; PV = present value; r = interest rate (usually quoted as x % p.a.) t = year Solution: FV = 100 (1+ 0.1) 3 = 133.10
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2/25/2009 4 10 Future value Another example: Suppose you win a lottery today. You are given two options: Option A: receive a lump-sum of $1000 today Option B: receive $1140 in 1.5 years Which option would you prefer? Don’t know! 11 Future value Implications: Cash flows at different points in time cannot be compared to each other. They have to be brought to the same point in time before comparisons can be made. Must consider opportunity cost (i.e. interest rate) 12 Future value Example continues: Suppose the bank’s saving rate is 10% p.a.
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This note was uploaded on 10/08/2011 for the course FINANCE 101 taught by Professor Jannis during the Three '11 term at Monash.

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Week 1and 2 - 2/25/2009 Week 1 and 2 Introduction to...

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