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# lecture 16 - Business Finance Lecture 16 Review of the...

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88 Business Finance Lecture 16 Review of the Previous Lecture z Annuities cash Flows { Present Value { Future Value z Annuities Due Topics under Discussion z Perpetuities z The Effect of Compounding Periods { Effective Annual Rate { Annual Percentage Rate z Loans { Pure discount Loans { Interest Only Loans { Amortized Loans Perpetuities z A special case of annuity, where the stream of cash flows continue forever. z The present value of a perpetuity is Perpetuity PV = C / r Perpetuities z Suppose we expect to receive \$1000 at the end of each of the next 5 years. Our opportunity rate is 6%. What is the value today of this set of cash flows? PV = \$1000 x (1 - [1/1.06 5 ]) / 0.06 = \$1000 x 4.212364 = \$4212.364 z Now suppose the cash flow will be \$1000 per year forever , making it a perpetuity . In this case, the PV is easy to calculate: PV = C/r = \$1000/.06 = \$16,666.67 Summary of Annuity and Perpetuity I. Symbols PV = Present value, what future cash flows bring today FV t = Future value, what cash flows are worth in the future r = Interest rate, rate of return, or discount rate per period t = Number of time periods C = Cash amount II. FV of C per period for t periods at r percent per period:

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89 FV t = C ° [(1 + r) t - 1] / r III. PV of C per period for t periods at r percent per period: PV = C ° (1 - [1/(1 + r) t ]) / r IV. PV of a perpetuity of C per period: PV = C / r Effective Annual Rates z If a rate is quoted as 10% compounded semiannually, then what this means is that the investment actually pays 5% every six months. z Is 5% every six months the same thing as 10% per year? { \$1 x 1.10 = \$1.10 { \$1 x 1.05 2 = \$1.1025 z 10% compounded semiannually is equivalent to 10.25% compounded annually.
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lecture 16 - Business Finance Lecture 16 Review of the...

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