2. 125/139 = .899 3. PV = 374/(1.09)9 = 172.20 4. PV = 432/1.15 + 137/(1.152) + 797/(1.153) = 376 + 104 + 524 = $1‚003 5. FV = 100*1.158 = $305.90 6. 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)
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Times per Year Annual Compounding FVn = PV( 1 + i )n 2 FV 1 i PV = Present Value of a Lump Sum. (PVIFi‚n) -n Future Value of an Annuity. (FVIFAi‚n) FVAn = CF 4 Present Value of an Annuity. (PVIFAi‚n) 1 - ( 1 + i )-n PVAn = CF i 5 Present Value of Perpetuity. (PVA ) 6 Effective Annual Rate given the APR. 7 The length of time required for a PV to grow to a FV. 8 The APR required for a PV to grow to a FV. 9 Present Value of a
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1. PV = FV x [ 1 ÷ (1 + i)n ] PV = $11mil x [ 1 ÷ (1 + 0.06)2 ] PV = $11mil x [ 1 ÷ (1.06)2 ] PV = $11mil x [ 1 ÷ 1.1236 ] PV = $11mil x [ 0.88999644] ← PV factor PV = $9‚789‚960.80 If I were chose between alternative 2 and the first $10min alternative I would go with alternative 1. It reflects a bigger present value than alternative with an opportunity interest rate of 6%. PV = FV x [ 1 ÷ (1 + i)n ] PV = $11mil x [ 1 ÷ (1 + 0.12)2 ] PV = $11mil x [ 1 ÷ (1.12)2 ] PV = $11mil
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1. How does Ben’s age affect his decision to get an MBA? This document is the property of Management Development Institute‚ Gurgaon. Ben passed out from college six years ago with a finance undergraduate degree. He is 28 years of age and his goal I to become an investment banker. Ben’s age can affect his decision to get an MBA due to the following reasons: o His age determines the time period wherein he can be productively employed. The time window available to Ben keeps on reducing with age
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CHAPTER 3 How to Calculate Present Values Answers to Practice Questions 1. a. PV = $100 0.905 = $90.50 b. PV = $100 0.295 = $29.50 c. PV = $100 0.035 = $ 3.50 d. PV = $100 0.893 = $89.30 PV = $100 0.797 = $79.70 PV = $100 0.712 = $71.20 PV = $89.30 + $79.70 + $71.20 = $240.20 2. a. PV = $100 4.279 = $427.90 b. PV = $100 4.580 = $458.00 c. We can think of cash flows in this problem as being the difference between two separate streams
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3 percent per year‚ so the present value of his after tax salary is: PV = C PV = $857‚343.20 Wilton MBA: The direct costs of attending Wilton are the costs of tuition‚ books and other supplies‚ health insurance costs‚ and the increased room and board expenses. The present value of the direct costs is: PV of direct expenses = ($65‚000 + 2‚500 + 3‚000 + 2‚000)
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of money concept is used to determine present and future values of money. “The time value of money refers to the relationship between time‚ money‚ and the rate of interest.” (Letsche‚ 2011). The formula consist of four components FV = Future Value‚ PV = Present Value‚ i = the interestrate per period and n= the number of compounding periods (TeachMeFinance.com). In business‚ TVM is used to evaluate expected returns on investments and monitoring the company’s cash flow. “However‚ understanding the
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initial input values. To calculate share value‚ we have to estimate a horizon value at 2010 and add its PV to the PV of dividends from 2005 to 2010. Using the constant-growth DCF formula‚ The PV of dividends from 2005 to 2010 is $3.43 in 2004‚ so share value in 2004 is: The spreadsheet also calculates the PV of dividends through 2012 and the horizon value at 2012. Notice that the PV in 2004 remains at $16.82. This makes sense‚ since the value of a firm should not depend on the investment
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back to end mode after finishing your calculations in begin mode. Time Value of Money calculations: FV of a Lump Sum: FV = PV(1+r)n FV of $300‚ 5 yrs‚ 10% FV = 300 (1+.10)5 = 300 * 1.61051 = 483.153 Using the Calculator: [Gold] [Clear All] (Clears all of the registers in the calculator) 1 [Gold] [P/Yr] (Sets # payments per period to 1) 300 [+/-] [PV] (Enters -300 as the PV) 5 [N] (Enters 5 as the number of compounding periods) 10 [I/YR] (Enters 10% and the interest rate) Hit [FV] = 483.15
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Equations Mechanics velocity Δ s v= Δ t ds v= dt acceleration Δ v a= Δ t dv a= dt equations of motion v = 0+at v x =x0+v 0 +½ 2 t at weight W =m g momentum p =m v dry friction ƒ μ =N centrip. accel. v2 ac = r 2 ac =−ω r impulse J =F Δ t impulse–momentum F Δ= Δ t m v J =⌠ dt F ⌠ dt =Δ F p ⌡ kinetic energy potential energy ⌡ K =½ mv 2 gravitational p.e. Δ g =mgΔ U h Δ =−⌠ · U F ds ⌡ F =−∇U v 2= 0 +2
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