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# Lec8 - Lecture 8 page 52 Time Value of Money Part II...

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Lecture 8 page 52 Time Value of Money - Part II Annuities Perpetuities Amortizing Loans Annuities Question: Why can’t we just worry about lump sum payments? 1. Capital budgeting decisions 2. Mortgages 3. Planning for retirement ordinary annuity annuity due We want to know how to compute the PV and FV of any annuity. Why? We are taking a series of cashflows (the annuity) and converting them to an equivalent lump sum cash flow at the beginning (PV) or end (FV) of the payment stream. To do this, we need to know the following: PMT N* M* r/M * - note that these definitions are slightly different than when we computed lump-sum FVs and PVs. - Richard T. Bliss, Babson University and Terry D. Nixon, Miami University

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Lecture 8 page 53 PRESENT VALUE OF AN ORDINARY ANNUITY + - = M r M r PMT annuity ordinary of PV N / ) / 1 /( 1 1 \$ This is the Present Value Annuity Formula (PVAF) We use the PVAF to compute the lump-sum equivalent at the beginning, i.e., one period before the first cash flow, of the stream of annuity payments. TIMELINE: Example 9: You expect to receive \$1,000 per year at the end of each of the next five years. The market interest rate is 12%. What is the PV of these payments today? TIMELINE: PMT = M = r = N = + - = M r M r PMT annuity of PV N / ) / 1 /( 1 1 \$ = NOTE: This is the lump-sum equivalent (at t=0) to the five \$1000 payments. We can get the exact same answer by discounting each of the \$1,000 payments individually and summing them. PV {5 payments of \$1,000} = 1000/1.12 + 1000/1.12 2 + 1000/1.12 3 + 1000/1.12 4 + 1000/1.12 5 = - Richard T. Bliss, Babson University and Terry D. Nixon, Miami University
Lecture 8 page 54 Example 10: Your roommate asks for a loan, offering to make weekly payments of \$25 for one year. If the appropriate interest rate is 8.25% APR, compounded weekly, how much would you be willing to lend her today? Assume she will make her first payment of \$25 to you in one week. TIMELINE: PMT = M = r = N = + - = M r M r PMT annuity of PV N / ) / 1 /( 1 1 \$ = Practice: What amount would you lend if the payments are for three years? - Richard T. Bliss, Babson University and Terry D. Nixon, Miami University

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Lecture 8 page 55 Example 11: You win the Ohio Lottery and get to choose between receiving \$950,000 today, or \$100,000 at the end of each of the next 25 years (\$2.5 million in total payments). If the discount rate is 9.75%, which is the better option? TIMELINE: PV of lump-sum: PV of \$100,000 payments: PMT = M = r = N = + - = M r M r PMT annuity of PV N / ) / 1 /( 1 1 \$ = FUTURE VALUE OF AN ANNUITY - + = M r M r PMT ofAnnuity FV N / 1 ) / 1 ( \$ This is the Future Value of an Annuity Formula (FVAF) We use the FVAF to compute the lump-sum equivalent at the end (i.e., on the date of the last payment) of a stream of annuity payments.
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Lec8 - Lecture 8 page 52 Time Value of Money Part II...

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