Unformatted text preview: ves us: PVA = $1,883,696.06 = C[1 – {1 / [1 + (.08/12)]300} / (.08/12)] C = $1,883,696.06 / 129.5645 = $14,538.67 withdrawal per month 24. Since we are looking to quadruple our money, the PV and FV are irrelevant as long as the FV is four times as large as the PV. The number of periods is four, the number of quarters per year. So: FV = $4 = $1(1 + r)(12/3) r = .4142 or 41.42% 25. Here, we need to find the interest rate for two possible investments. Each investment is a lump sum, so: G: PV = $75,000 = $135,000 / (1 + r)6 (1 + r)6 = $135,000 / $75,000 r = (1.80)1/6 – 1 = .1029 or 10.29% PV = $75,000 = $195,000 / (1 + r)10 (1 + r)10 = $195,000 / $75,000 r = (2.60)1/10 – 1 = .1003 or 10.03% H: 58 26. This is a growing perpetuity. The present value of a growing perpetuity is: PV = C / (r – g) PV = $215,000 / (.10 – .04) PV = $3,583,333.33 It is important to recognize that when dealing with annuities or perpetuities, the present value equation calculates the present value one period before the first payment. In this case, since the first payment is in two years, we have calculated the present value one year from now. To find the value today, we simply discount this value as a lump sum. Doing so, we find the value of the cash flow stream today is: PV = FV / (1 + r)t PV = $3,583,333.33 / (1 + .10)1 PV = $3,257,575.76 27. The dividend payments are made quarterly, so we must use the quarterly interest rate. The quarterly interest rate is: Quarterly rate = Stated rate / 4 Quarterly rate = .07 / 4 Quarterly rate = .0175 Using the present value equation for a perpetuity, we find the value today of the dividends paid must be: PV = C / r PV = $5 / .0175 PV = $285.71 28. We can use the PVA annuity equation to answer this question. The annuity has 23 payments, not 22 payments. Since there is a payment made in Year 3, the annuity actually begins in Year 2. So, the value of the annuity in Year 2 is: PVA = C({1 – [1/(1 + r)]t } / r ) PVA = $5,000({1 – [1/(1 + .08)]23 } / .08) PVA = $51,855.29 This is the value of the annuity one period before the first payment, or Year 2. So, the value of the cash flows today is: PV = FV/(1 + r)t PV = $51,855.29 / (1 + .08)2 PV = $44,457.56 29. We need to find the present value of an annuity. Using the PVA equation, and the 15 percent interest rate, we get: PVA = C({1 – [1/(1 + r)]t } / r ) PVA = $750({1 – [1/(1 + .15)]15 } / .15) PVA = $4,385.53 59 This is the value of the annuity in Year 5, one period before the first payment. Finding the value of this amount today, we find: PV = FV/(1 + r)t PV = $4,385.53 / (1 + .12)5 PV = $2,488.47 30. The amount borrowed is the value of the home times one minus the down payment, or: Amount borrowed = $450,000(1 – .20) Amount borrowed = $360,000 The monthly payments with a balloon payment loan are calculated assuming a longer amortization schedule, in this case, 30 years. The payments based on a 30year repayment schedule would be: PVA = $360,000 = C({1 – [1 / (1 + .075/12)]360} / (.075/12)) C = $2,517.17 Now, at time = 8, we need to find the PV of the payments which have not been made. The balloon payment will be: PVA = $2,517.17({1 – [1 / (1 + .075/12)]22(12)} / (.075/12)) PVA = $325,001.73 31. Here, we need to find the FV of a lump sum, with a changing interest rate. We must do this problem in two parts. After the first six months, the balance will be: FV = $6,000 [1 + (.024/12)]6 = $6,072.36 This is the balance in six months. The FV in another six months will be: FV = $6,072.36 [1 + (.18/12)]6 = $6,639.78 The problem asks for the interest accrued, so, to find the interest, we subtract the beginning balance from the FV. The interest accrued is: Interest = $6,639.78 – 6,000 = $639.78 32. The company would be indifferent at the interest rate that makes the present value of the cash flows equal to the cost today. Since the cash flows are a perpetuity, we can use the PV of a perpetuity equation. Doing so, we find: PV = C / r $150,000 = $13,000 / r r = $13,000 / $150,000 r = .0867 or 8.67% 60 33. The company will accept the project if the present value of the increased cash flows is greater than the cost. The cash flows are a growing perpetuity, so the present value is: PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t} PV = $18,000{[1/(.11 – .04)] – [1/(.11 – .04)] × [(1 + .04)/(1 + .11)]5} PV = $71,479.47 The company should accept the project since the cost is less than the increased cash flows. 34. Since your salary grows at 4 percent per year, your salary next year will be: Next year’s salary = $60,000 (1 + .04) Next year’s salary = $62,400 This means your deposit next year will be: Next year’s deposit = $62,400(.05) Next year’s deposit = $3,120 Since your salary grows at 4 percent, you deposit will also grow at 4 percent. We can use the present value of a growing perpetuity equation to find the value of your deposits today. Doing so, we find: PV = C {[1/(r – g)] – [1/(r – g)] × [(1 + g)/(1 + r)]t} PV = $3,120{[1/(.09 – .04)] – [1/(.09 – .04)] ×...
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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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