Lecture macroeconomics chapter 2 3 the basic tools of finance

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

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?

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

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.

EXAMPLE 1: A Simple Deposit

▪ Future value = …

• After 1 year: (1+0.05) ˣ $100 = $105

• After 2 years: (1+0.05) ˣ (1+0.05) ˣ $100

= (1+0.05)2 ˣ $100 = $110.25

• After 3 years: (1+0.05)3 ˣ $100 = $115.76

➔ After N years: (1+0.05)N ˣ $100

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,

where r denotes the interest rate (in decimal form)

▪ Solve for PV to get: PV = FV/(1 + r ) N

FV = PV(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

EXAMPLE 2: Investment Decision

▪ Suppose r = 0.06

Should Ford spend $100 million to build a factory that will yield $200 million in ten years?

Solution:

Present value formula: PV = FV/(1 + r ) N

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,

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