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Unformatted text preview: [(1 + .04)/(1 + .09)]40} PV = $52,861.98 Now, we can find the future value of this lump sum in 40 years. We find: FV = PV(1 + r)t FV = $52,861.98(1 + .09)40 FV = $1,660,364.12 This is the value of your savings in 40 years. 35. The relationship between the PVA and the interest rate is: PVA falls as r increases, and PVA rises as r decreases FVA rises as r increases, and FVA falls as r decreases The present values of $7,500 per year for 12 years at the various interest rates given are: PVA@10% = $7,500{[1 – (1/1.10)12] / .10} = $51,102.69 PVA@5% = $7,500{[1 – (1/1.05)12] / .05} = $66,474.39 PVA@15% = $7,500{[1 – (1/1.15)12] / .15} = $40,654.64 61 36. Here, we are given the FVA, the interest rate, and the amount of the annuity. We need to solve for the number of payments. Using the FVA equation: FVA = $30,000 = $250[{[1 + (.10/12)]t – 1 } / (.10/12)] Solving for t, we get: 1.00833t = 1 + [($30,000)(.10/12) / $250] t = ln 2 / ln 1.00833 = 83.52 payments 37. Here, we are given the PVA, number of periods, and the amount of the annuity. We need to solve for the interest rate. Using the PVA equation: PVA = $80,000 = $1,650[{1 – [1 / (1 + r)]60}/ r] To find the interest rate, we need to solve this equation on a financial calculator, using a spreadsheet, or by trial and error. If you use trial and error, remember that increasing the interest rate lowers the PVA, and decreasing the interest rate increases the PVA. Using a spreadsheet, we find: r = 0.727% The APR is the periodic interest rate times the number of periods in the year, so: APR = 12(0.727%) = 8.72% 38. The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $1,200 monthly payments is: PVA = $1,200[(1 – {1 / [1 + (.068/12)]}360) / (.068/12)] = $184,070.20 The monthly payments of $1,200 will amount to a principal payment of $184,070.20. The amount of principal you will still owe is: $250,000 – 184,070.20 = $65,929.80 This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be: Balloon payment = $65,929.80[1 + (.068/12)]360 = $504,129.05 39. We are given the total PV of all four cash flows. If we find the PV of the three cash flows we know, and subtract them from the total PV, the amount left over must be the PV of the missing cash flow. So, the PV of the cash flows we know are: PV of Year 1 CF: $1,200 / 1.10 = $1,090.91 PV of Year 3 CF: $2,400 / 1.103 = $1,803.16 PV of Year 4 CF: $2,600 / 1.104 = $1,775.83 62 So, the PV of the missing CF is: $6,453 – 1,090.91 – 1,803.16 – 1,775.83 = $1,783.10 The question asks for the value of the cash flow in Year 2, so we must find the future value of this amount. The value of the missing CF is: $1,783.10(1.10)2 = $2,157.55 40. To solve this problem, we simply need to find the PV of each lump sum and add them together. It is important to note that the first cash flow of $1 million occurs today, so we do not need to discount that cash flow. The PV of the lottery winnings is: $1,000,000 + $1,350,000/1.09 + $1,700,000/1.092 + $2,050,000/1.093 + $2,400,000/1.094 + $2,750,000/1.095 + $3,100,000/1.096 + $3,450,000/1.097 + $3,800,000/1.098 + $4,150,000/1.099 + $4,500,000/1.0910 = $18,194,308.69 41. Here, we are finding interest rate for an annuity cash flow. We are given the PVA, number of periods, and the amount of the annuity. We need to solve for the number of payments. We should also note that the PV of the annuity is not the amount borrowed since we are making a down payment on the warehouse. The amount borrowed is: Amount borrowed = 0.80($2,600,000) = $2,080,000 Using the PVA equation: PVA = $2,080,000 = $14,000[{1 – [1 / (1 + r)]360}/ r] Unfortunately, this equation cannot be solved to find the interest rate using algebra. To find the interest rate, we need to solve this equation on a financial calculator, using a spreadsheet, or by trial and error. If you use trial and error, remember that increasing the interest rate decreases the PVA, and decreasing the interest rate increases the PVA. Using a spreadsheet, we find: r = 0.593% The APR is the monthly interest rate times the number of months in the year, so: APR = 12(0.593%) = 7.12% And the EAR is: EAR = (1 + .00593)12 – 1 = .0735 or 7.35% 42. The profit the firm earns is just the PV of the sales price minus the cost to produce the asset. We find the PV of the sales price as the PV of a lump sum: PV = $135,000 / 1.133 = $93,561.77 63 And the firm’s profit is: Profit = $93,561.77 – 96,000.00 = –$2,438.23 To find the interest rate at which the firm will break even, we need to find the interest rate using the PV (or FV) of a lump sum. Using the PV equation for a lump sum, we get: $96,000 = $135,000 / ( 1 + r)3 r = ($135,000 / $96,000)1/3 – 1 = .1204 or 12.04% 43. We want to find the value of the cash flows today, so we will find the PV of the annuity,...
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This note was uploaded on 07/10/2010 for the course FIN 6301 taught by Professor Eshmalwi during the Spring '10 term at University of TexasTyler.
 Spring '10
 eshmalwi
 Finance, Corporate Finance

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