The required discount rate is 7 7 what is the value

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Unformatted text preview: year 5? What is the value of the cash flows today? What is the value of the cash flows at year 3? 15 15 Annuities and Perpetuities Annuities Defined Defined Annuity – finite series of equal payments that Annuity occur at regular intervals occur If the first payment occurs at the end of the period, it If is called an ordinary annuity is If the first payment occurs at the beginning of the If period, it is called an annuity due period, Perpetuity – infinite series of equal payments 16 16 Annuities and Perpetuities – Annuities Basic Formulas Basic Perpetuity: PV = C / r Annuities: 1 1− (1 + ) t r PV = C r 1 + )t − ( r 1 FV = C r 17 17 Annuity – Example 6.5 You borrow money TODAY so you need to You compute the present value. compute 48 N; 1 I/Y; -632 PMT; CPT PV = 23,999.54 48 ($24,000) ($24,000) Formula: 1 1− (1.01) 48 PV = 632 .01 = 23,999.54 18 18 Annuity – Sweepstakes Annuity Example Example Suppose you win the Publishers Clearinghouse Suppose $10 million sweepstakes. The money is paid in equal annual installments of $333,333.33 over 30 years. If the appropriate discount rate is 5%, how much is the sweepstakes actually worth today? today? PV = 333,333.33[1 – 1/1.0530] / .05 = 5,124,150.29 19 19 Buying a House You are ready to buy a house and you have $20,000 You for a down payment and closing costs. Closing costs are estimated to be 4% of the loan value. You have an annual salary of $36,000 and the bank is willing to allow your monthly mortgage payment to be equal to 28% of your monthly income. The interest rate on the loan is 6% per year with monthly compounding (.5% per month) for a 30-year fixed rate loan. How much money will the bank loan you? How much can you offer for the house? for 20 20 Buying a House - Continued Bank loan Monthly income = 36,000 / 12 = 3,000 Maximum payment = .28(3,000) = 840 PV = 840[1 – 1/1.005360] / .005 = 140,105 Total Price Closing costs = .04(140,105) = 5,604 Down payment = 20,000 – 5604 = 14,396 Total Price = 14...
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