Créer une présentation
Télécharger la présentation

Télécharger la présentation
## Chapter 3: The Time Value of Money

- - - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - - -

**Chapter 3:The Time Value of Money**Corporate Finance, 3e Graham, Smart, and Megginson**The Role of Financial Markets**• Voluntary transfer of wealth • Between individuals • Financial intermediaries • Across time • Future value • Present value • The chance to earn a return on invested funds means a dollar today is worth more than a dollar in the future.**FVn = PV (1+r)n**• Future Value depends on: • Interest Rate • Number of Periods • Compounding Interval Future Value The Value of a Lump Sum or Stream of Cash Payments at a Future Point in Time**Future Value**• Two key points: • The higher the interest rate, the higher the future value. • The longer the period of time, the higher the future value.**Present Value**• Compounding: • Finding the future value of present dollars invested at a given rate • Discounting: • Finding the present value of a future amount, assuming an opportunity to earn a given return (r), on the money**Present Value**Today's Value of a Lump Sum or Stream of Cash Payments Received at a Future Point in Time FVn = PV (1+r)n PV =**FV of a Mixed Stream**• The future value of any stream of cash flows measured at the end of a specified year is the sum of the future values of the individual cash flows at that year’s end. • Sometimes called the terminal value**FV of a Mixed Stream Equation**Future value of an n-year mixed stream of cash flows (FV) can be expressed as**FV of Annuities: Formulas**• FV of an ordinary annuity: • FV of an annuity due:**Present Value Of Perpetuity**Stream of Equal Annual Cash Flows that Lasts Forever or**Present Value of a Growing Perpetuity**The Gordon Growth model:**Compounding More Frequentlythan Annually**• Semiannually • Quarterly • Monthly • Continuous**Compounding Intervals**m compounding periods per year**For semiannual compounding, m = 2:**• For quarterly compounding, m = 4: Compounding More Frequently Than Annually FV at End of 2 Years of $125,000 Deposited at 5.13% Interest**Continuous Compounding**• Interest Compounded Continuously FVn = PV ern FV at End of 2 Years of $125,000 at 5.13% Annual Interest, Compounded Continuously**The Stated Rate Versus the Effective Rate**Stated Rate – The contractual annual rate (r) charged by lender or promised by borrower Effective Annual Rate (EAR) – The annual rate actually paid or earned**Calculating Deposits Needed To Accumulate A Future Sum**• Often need to find annual deposit required to accumulate a fixed sum of money in n years • Closely related to the process of finding the future value of an ordinary annuity**Loan Amortization**• Generalize the formula to more frequent compounding periods by dividing the interest rate by m and multiplying the number of compounding periods by m.**Implied Interest or Growth Rates: Lump Sums**• Lump sums: The interest or growth rate of a single cash flow over time can be found by solving for r in the following equation: • If we know the interest rate (r), we can calculate the number of periods (n) necessary for a present value to grow to a desired future value**Implied Interest or Growth Rates: Lump Sums**• Annuities and mixed streams: Very difficult to solve for r using formulas • Use an iterative trial-and-error approach. Spreadsheets and financial calculators can do this very quickly. • Often referred to as finding the yield to maturityor internal rate of return (IRR)**Number of Compounding Periods**Lump Sums/Annuities: