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# 2TVM - Time Value of Money People prefer to have a dollar...

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Time Value of Money People prefer to have a dollar today rather than a dollar tomorrow They must be compensated for waiting to consume So, markets form that allow some people to invest and earn interest for delaying consumption, and other people to borrow money and pay interest to be able to consume now Given some cash flows in the future, how do we find the “present value”, or how much people would be willing to pay for those future cash flows?

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Outline Discount cash flows: Lump sum Perpetuity Annuity Growing Perpetuity and Annuity Compounding interest rate: Nominal Interest rate Effective rate Asset valuation Bonds Preferred stock Common stock
Lump-Sum Cash Flows If we have a single cash flow t periods in the future, The future value analogue: t t r FV PV ) 1 ( 0 + = t t r PV FV ) 1 ( 0 + =

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Lump-Sum Example Your job promises a one-time retirement benefit of \$100,000 on the day of your retirement. You plan to work for 15 more years, and require a return of 8% on investments. What is this benefit worth?
Perpetuities A perpetuity is an infinite sequence of equal cash flows i.e. \$1 per year forever Present value of a perpetuity: Notice the timing of the present value and payments in the perpetuity formula r PMT PV t t 1 + =

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Perpetuities Example On January 3, 2007, Freddie Mac preferred stock, which pays an annual dividend of \$2.90, closed at \$46.86. What rate of return was required by investors of Freddie Mac preferred stock? On January 18, 2008, Freddie Mac preferred stock closed at \$42.75. What rate of return is required by Freddie Mac preferred stock investors?
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