in time you must discount it PV= C/ (1+r)n Valuing Streams of CF NPV= ∑Cn/ (1+r)n Perpetuity Stream of equal CF that last forever PV= C/r Annuity A stream of CF that occur at regular intervals for N periods Growing Perpetuities Stream of CF that occur at regular intervals and grow at a constant rate forever (growing dividend) NPV= C/ r – g g= growth rate Growing Annuities PV= C x (1/(r-g)) (1-((1+g)/(1+r))N What if g>r? * not possible for g to be greater
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= -1‚548 + 138/.09 = -14.67 (cost today plus the present value of the perpetuity) 7. PV = 4/(.14-.04) = $40 8. a. PV = 1/.10 = $10 b. Since the perpetuity will be worth $10 in year 7‚ and since that is roughly double the present value‚ the approximate PV equals $5. PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately) c. A perpetuity paying $1 starting now would be worth $10‚ whereas a perpetuity starting in year 8 would be worth roughly $5. The difference between these
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NPV = -1‚548 + 138/.09 = -14.67 (cost today plus the present value of the perpetuity) 7. PV = 4/(.14-.04) = $40 8. a. PV = 1/.10 = $10 b. Since the perpetuity will be worth $10 in year 7‚ and since that is roughly double the present value‚ the approximate PV equals $5. PV = (1 / .10)/(1.10)7 = 10/2= $5 (approximately) c. A perpetuity paying $1 starting now would be worth $10‚ whereas a perpetuity starting in year 8 would be worth roughly $5. The difference between these cash
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the difference between a perpetuity and an annuity? A cash flow stream that consists of the same amount being received or paid on a periodic basis is called an annuity. If the same payments are made periodically forever‚ the contract is called a perpetuity. 24 6.4 Define annuity due. Would an investment be worth more if it was an ordinary annuity or an annuity due? Explain. When annuity cash flows occur at the beginning of each period‚ it is called an annuity due. Annuity due will result in a bigger
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the perpetuity). Est time: 01-05 7. PV = 4/(.14 − .04) = $40. Est time: 01-05 8. a. PV = 1/.10 = $10. b. Since the perpetuity will be worth $10 in year 7‚ and since that is roughly double the present value‚ the approximate PV equals $5. You must take the present value of years 1–7 and subtract from the total present value of the perpetuity: PV = (1/.10)/(1.10)7 = 10/2= $5 (approximately). c. A perpetuity paying $1 starting now would be worth $10‚ whereas a perpetuity starting
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Multiple Choice Questions 1. An annuity stream of cash flow payments is a set of: A. level cash flows occurring each time period for a fixed length of time. B. level cash flows occurring each time period forever. C. increasing cash flows occurring each time period for a fixed length of time. D. increasing cash flows occurring each time period forever. E. arbitrary cash flows occurring each time period for no more than 10 years. 2. Annuities where the payments occur at the end of
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limited liability. They can lose their investment‚ but no more. Chapter 2 How to calculate Present values Question 6: Perpetuities An investment costs $1‚548 and pays $138 in perpetuity. If the interest rate is 9%‚ what is the NPV? Answer NPV = −1‚548 + 138/.09 = −14.67 (cost today plus the present value of the perpetuity). Question 7: Growing perpetuities A common stock will pay a cash dividend of $4 next year. After that‚ the dividends are expected to increase indefinitely at
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The PV of $100 received in years 1 to 12 is: PV = $100 [Annuity factor‚ 12 time periods‚ 9%] PV = $100 [7.161] = $716.10 The PV of $100 paid in years 1 to 2 is: PV = $100 [Annuity factor‚ 2 time periods‚ 9%] PV = $100 [1.759] = $175.90 Therefore‚ the present value of $100 per year received in each of years 3 through 12 is: ($716.10 - $175.90) = $540.20. (Alternatively‚ we can think of this as a 10‑year annuity starting in year 3.) 3. a. so that r1 = 0.136 = 13.6% b.
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CHAPTER 4 PART II: VALUATION AND CAPITAL BUDGETING Discounted Cash Flow Valuation The signing of big-name athletes is often accompanied by great fanfare‚ but the numbers are often misleading. For example‚ in late 2010‚ catcher Victor Martinez reached a deal with the Detroit Tigers‚ signing a contract with a reported value of $50 million. Not bad‚ especially for someone who makes a living using the “tools of ignorance” (jock jargon for a catcher’s equipment). Another example is the contract signed
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Questions 1. An ordinary annuity is best defined by which one of the following? A. increasing payments paid for a definitive period of time B. increasing payments paid forever C. equal payments paid at regular intervals over a stated time period D. equal payments paid at regular intervals of time on an ongoing basis E. unequal payments that occur at set intervals for a limited period of time 2. Which one of the following accurately defines a perpetuity? A. a limited number of equal
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