4-1

Exercises and Shortcuts in Time Value of Money

4-2

Net Present Value of an Investment Opportunity

4-3

Perpetuities, Annuities, and Other Special Cases

• Perpetuities • Annuities • Growing Cash Flows

– Growing Perpetuity– Growing Annuity

4-4

Short Cuts

Perpetuity – A fixed amount of cash is received forever.

Examples: Preferred stock, consol bond

Note: Mathematically, we have a declining geometric series, which has a finite value

4-5

Short Cuts

Perpetuity – A fixed amount of cash is received forever.

Examples: Preferred stock, consol bond

Note: Mathematically, we have a declining geometric series, which has a finite value

r

CPV 1

ratediscount

flow cash FlowCash of PV

4-6

Perpetuity - example

• Suppose that as a successful TCU graduate you decide to establish an endowed chair in finance that will pay $250,000 a year in perpetuity. How much money do you need to donate to the school to establish this endowment? Assume the prevailing interest rate is 10%

4-7

Short Cuts

Annuity - An asset that pays a fixed sum each year for a specified number of periods.

Example: mortgage payments, car payments, car insurance, rent

4-8

Short Cuts

trrrC

1

11annuity of PV

4-9

Present Value of a Lottery Prize Annuity

4-10

Retirement Savings Plan Annuity

4-11

Future Value of an Annuity

4-12

Growing Perpetuity

• Suppose you change your wish and decide that the salary that the professorship pays should grow at 4% annually. How much money do you need now?

4-13

Growing Perpetuity

4-14

Retirement Savings with a Growing Annuity

4-15

Present Value of a Growing Annuity