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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