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Unformatted text preview: your salary you must save each year. Since your salary is increasing at 3 percent, and the savings are increasing at 3 percent, the percentage of salary will remain constant. 56. Since she put $1,000 down, the amount borrowed will be: Amount borrowed = $25,000 – 1,000 Amount borrowed = $24,000 So, the monthly payments will be: PVA = C({1 – [1/(1 + r)]t } / r ) $24,000 = C[{1 – [1/(1 + .084/12)]60 } / (.084/12)] C = $491.24 69 The amount remaining on the loan is the present value of the remaining payments. Since the first payment was made on October 1, 2007, and she made a payment on October 1, 2009, there are 35 payments remaining, with the first payment due immediately. So, we can find the present value of the remaining 34 payments after November 1, 2009, and add the payment made on this date. So the remaining principal owed on the loan is: PV = C({1 – [1/(1 + r)]t } / r ) + C0 PV = $491.24[{1 – [1/(1 + .084/12)]34 } / (.084/12)] C = $14,817.47 She must also pay a one percent prepayment penalty and the payment due on November 1, 2009, so the total amount of the payment is: Total payment = Balloon amount(1 + Prepayment penalty) + Current payment Total payment = $14,817.47(1 + .01) + $491.24 Total payment = $15,456.89 57. The cash flows for this problem occur monthly, and the interest rate given is the EAR. Since the cash flows occur monthly, we must get the effective monthly rate. One way to do this is to find the APR based on monthly compounding, and then divide by 12. So, the preretirement APR is: EAR = .11 = [1 + (APR / 12)]12 – 1; And the postretirement APR is: EAR = .08 = [1 + (APR / 12)]12 – 1; APR = 12[(1.08)1/12 – 1] = 7.72% APR = 12[(1.11)1/12 – 1] = 10.48% First, we will calculate how much he needs at retirement. The amount needed at retirement is the PV of the monthly spending plus the PV of the inheritance. The PV of these two cash flows is: PVA = $20,000{1 – [1 / (1 + .0772/12)12(20)]} / (.0772/12) = $2,441,554.61 PV = $1,000,000 / (1 + .08)20 = $214,548.21 So, at retirement, he needs: $2,441,554.61 + 214,548.21 = $2,656.102.81 He will be saving $1,900 per month for the next 10 years until he purchases the cabin. The value of his savings after 10 years will be: FVA = $1,900[{[ 1 + (.1048/12)]12(10) – 1} / (.1048/12)] = $400,121.62 After he purchases the cabin, the amount he will have left is: $400,121.62 – 320,000 = $80,121.62 He still has 20 years until retirement. When he is ready to retire, this amount will have grown to: FV = $80,121.62[1 + (.1048/12)]12(20) = $646,965.50 70 So, when he is ready to retire, based on his current savings, he will be short: $2,656,102.81 – 645,965.50 = $2,010,137.31 This amount is the FV of the monthly savings he must make between years 10 and 30. So, finding the annuity payment using the FVA equation, we find his monthly savings will need to be: FVA = $2,010,137.31 = C[{[ 1 + (.1048/12)]12(20) – 1} / (.1048/12)] C = $2,486.12 58. To answer this question, we should find the PV of both options, and compare them. Since we are purchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $1. The interest rate we would use for the leasing option is the same as the interest rate of the loan. The PV of leasing is: PV = $1 + $520{1 – [1 / (1 + .08/12)12(3)]} / (.08/12) = $16,595.14 The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is: PV = $26,000 / [1 + (.08/12)]12(3) = $20,468.62 The PV of the decision to purchase is: $38,000 – 20,468.62 = $17,531.38 In this case, it is cheaper to lease the car than buy it since the PV of the leasing cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be: $38,000 – PV of resale price = $16,595.14 PV of resale price = $21,404.86 The resale price that would make the PV of the lease versus buy decision is the FV of this value, so: Breakeven resale price = $21,404.86[1 + (.08/12)]12(3) = $27,189.25 59. To find the quarterly salary for the player, we first need to find the PV of the current contract. The cash flows for the contract are annual, and we are given a daily interest rate. We need to find the EAR so the interest compounding is the same as the timing of the cash flows. The EAR is: EAR = [1 + (.05/365)]365 – 1 = 5.13% The PV of the current contract offer is the sum of the PV of the cash flows. So, the PV is: PV = $7,500,000 + $4,200,000/1.0513 + $5,100,000/1.05132 + $5,900,000/1.05133 + $6,800,000/1.05134 + $7,400,000/1.05135 + $8,100,000/1.05136 PV = $38,519,529.66 71 The player wants the contract increased in value by $1,000,000, so the PV of the new contract will be: PV = $38,519,529.66 + 750,000 = $39,269,529.66 The player has also requested a signing bonus payable today in the amount of $10 million. We can simply subtract this amount from the PV of the new co...
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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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