Institute of International Education 2 3 The Basic Tools of Finance ▪ The financial system coordinates saving and investment ▪ Participants in the financial system make decisions regarding the allocat[.]
2.3 The Basic Tools of Finance ▪ The financial system coordinates saving and investment ▪ Participants in the financial system make decisions regarding the allocation of resources over time and the handling of risk ▪ Finance is the field that studies such decision making Institute of International Education Finance: Questions ▪ Q: Which would you rather have: $100 today or $100 ten years later? ▪ Q: Would you rather have $100 today or $115 a year from today? ▪ Q: Would you rather have $100 or a lottery ticket that has a 60% chance of winning nothing and a 40% chance of winning $150? Institute of International Education Present Value: The Time Value of Money ▪ To compare a sums from different times, we use the concept of present value ▪ The present value of a future sum: is the amount today that would be needed, at current interest rates, to produce that future sum ▪ The future value of a sum: the amount of money in the future that an amount of money today will yield, given current interest rates Institute of International Education EXAMPLE 1: A Simple Deposit ▪ Deposit $100 in the bank at 5% interest per year What is the future value (FV) of this amount? • Interest rate = r = 0.05 • Suppose that interest is paid annually and that it remains in the bank account to earn more interest - a process called compounding Institute of International Education EXAMPLE 1: A Simple Deposit ▪ Future value = … • After year: (1+0.05) ˣ $100 = $105 • After years: (1+0.05) ˣ (1+0.05) ˣ $100 = (1+0.05)2 ˣ $100 = $110.25 • After years: (1+0.05)3 ˣ $100 = $115.76 ➔ After N years: (1+0.05)N ˣ $100 Institute of International Education EXAMPLE 1: A Simple Deposit Deposit $100 in the bank at 5% interest What is the future value (FV) of this amount? ▪ In N years, FV = $100(1 + 0.05)N In this example, $100 is the present value (PV) ▪ In general, FV = PV(1 + r )N where r denotes the interest rate (in decimal form) ▪ Solve for PV to get: Institute of International Education PV = FV/(1 + r )N EXAMPLE 1: A Simple Deposit If the interest rate is 5%, the present value of $200 to be paid in 10 years is PV = 200/(1 + 0.05 )10 = $123 ➔This means that $123 deposited today in a bank account that earned 5% would produce $200 after 10 years ➔This process is called discounting Discount factor: 1/(1 + r )N Institute of International Education EXAMPLE 2: Investment Decision Present value formula: PV = FV/(1 + r )N ▪ Suppose r = 0.06 Should Ford spend $100 million to build a factory that will yield $200 million in ten years? Solution: Institute of International Education EXAMPLE 2: Investment Decision ▪ Instead, suppose r = 0.09 Should Ford spend $100 million to build a factory that will yield $200 million in ten years? Solution: PV helps explain why investment falls - hence, Qd of loanable fund fall - when the interest rate rises Institute of International Education The Rule of 70 ▪ The Rule of 70: If a variable grows at a rate of x percent per year, that variable will double in about 70/x years ▪ Example: ▪ If interest rate is 5%, a deposit will double in about 14 years ▪ If interest rate is 7%, a deposit will double in about 10 years Institute of International Education ... value ▪ The present value of a future sum: is the amount today that would be needed, at current interest rates, to produce that future sum ▪ The future value of a sum: the amount of money in the. .. Institute of International Education PV = FV/(1 + r )N EXAMPLE 1: A Simple Deposit If the interest rate is 5%, the present value of $20 0 to be paid in 10 years is PV = 20 0/(1 + 0.05 )10 = $ 1 23 ➔This... investment falls - hence, Qd of loanable fund fall - when the interest rate rises Institute of International Education The Rule of 70 ▪ The Rule of 70: If a variable grows at a rate of x percent per year,