11 special cases constant growth annuities present

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Unformatted text preview: present value can be written as PV = C1 r− g for r > g Example: PV of a Growing Perpetuity • Consider an economy with a constant inflation at a rate of 3%. What is the present value of a perpetuity that pays $100 next year and its cash flow will grow thereafter at the inflation rate. Suppose r = 6%. 11 Special Cases: Constant Growth Annuities Present value (constant growth) 01 2 … T C C(1+g) … C(1 + g)T-1 PV = C [1 - (1+g)T/(1+r)T]/(r-g) PV = C [1 - 1/(1+r)T]/r for g = 0 The future value of an annuity is just the future value of the present value FV = PV(1+r)T = C [(1+r)T - (1+g)T]/(r-g) Example: PV of a Growing Annuity • Next year, John Q Public will begin receiving his social security benefit of $6,600 next year. In the past, cost of living and adjustments have averaged 3.5% while the U.S. government’s cost of capital has averaged 5% - both are assumed to continue at those rates into the future. Suppose the benefits to the average citizen are assumed to last 30 years. What is the present value of the social security benefit that John Q. Public will receive? Summary 12 Summary Summary Present value of a constant growth annuity PV = C [1 - (1+g)T/(1+r)T]/(r-g) Using Time Lines • EXAMPLE - Saving for Retirement Problem Suppose you are exactly 30 years old. You figured out that your income will be such that you will be able to save for the next 30 years, until age 60...
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This note was uploaded on 01/17/2011 for the course MGMT 107 taught by Professor ? during the Winter '08 term at UC Irvine.

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