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02%20time%20value%20of%20money%20part%202%202011.02.03%2015.30

02%20time%20value%20of%20money%20part%202%202011.02.03%2015.30

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of money part 2 - 1 FNAN 301 Financial Management Time value of money Part 2
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of money part 2 - 2 Topics Covered Multiple cash flows Present value General patterns, perpetuities, ordinary annuities, annuities due, and delayed perpetuities and annuities Current (today) and non-current reference point Finding the payment amount, number of payments, and rate Future value General patterns, ordinary annuities, and annuities due Finding the payment amount, number of payments, and rate The appropriate period and rate APR, EAR, and periodic rate
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of money part 2 - 3 Present Value with Multiple Cash Flows The present value of multiple cash flows at different points in time is the sum of the present values of each individual cash flow 0 1 2 t t-1 C 0 C 2 C 1 C t C t-1 Cash flow Time PV 0
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of money part 2 - 4 PV with Multiple Cash Flows: Equation PV 0 = C 0 + [C 1 / (1+r) 1 ] + [C 2 / (1+r) 2 ] + … + [C k / (1+r) k ] + … + [C t-1 / (1+r) t-1 ] + [C t / (1+r) t ] PV 0 denotes present value as of the reference point (often today) Often referred to as PV C k denotes the cash flow (or potential cash flow such as a value) as of k periods from the reference point (typically today) k is the length of time (number of periods) until cash flow from reference point r is the discount rate Sometimes called the opportunity cost of capital or cost of capital Note: for a given source of cash flows, different discount rates can apply to different periods, but we will assume the same r for all time periods
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of money part 2 - 5 Present Value with Multiple Cash Flows Solving problems Good first step is to map out the cash flows (often with timeline) and identify point in time for which you are trying to compute value Especially helpful with complex problems Relevant for not just present value problems, but all problems such as future value ones as well
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of money part 2 - 6 PV with Multiple Cash Flows – Example What is the value of a store that is expected to produce cash flows of $50,000 later today, $108,000 in 1 year, and $933,120 in 2 years if the cost of capital (or discount rate) is 8%? Solution – formula PV = C 0 + [C 1 / (1 + r) 1 ] + [C 2 / (1 + r) 2 ] C 0 = 50,000; C 1 = 108,000; C 2 = 933,120; r = .08 PV = 50,000 + [108,000 / (1.08) 1 ] + [933,120 / (1.08) 2 ] = 50,000 + 100,000 + 800,000 = $950,000 The store is worth $950,000 today Solution – financial calculator Year 0 CF: present value = 50,000 Year 1 CF: N = 1; FV = 108000; I% = 8; PMT = 0; PMT mode irrelevant; solve for PV = -100000, so present value = $100,000 Year 2 CF: N = 2; FV = 933120; I% = 8; PMT = 0; PMT mode irrelevant; solve for PV = -800000, so present value = $800,000 Total present value = 50,000 + 100,000 + 800,000 = $950,000 0 2 1 50,000 933,120 108,000 Cash flow Time r = 8% Present value = ?
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of money part 2 - 7 PV with Multiple Cash Flows – Example What is the present value of the cash flows associated with the purchase of your computer if you receive a rebate of $200 in 1 year, owe $2,000 in 2 years, and the discount rate is 6 percent ?
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