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tvmpracticeset1solutions

tvmpracticeset1solutions - Solutions to TVM Practice Set I...

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Solutions to TVM Practice Set I 1. The future value is $12,000 in four years, so you wish to find the present value, at a discount rate of 4.5% per year. The timeline looks like this: 0 1 2 3 4 PV = ? 12,000 Using the PVIF, compute the PV as follows: t r PVIF ) 1 ( 1 + = . Therefore: 4 ) 045 . 0 1 ( 000 , 12 + = × = PVIF FV PV = $10,062.74 On your financial calculator: N I PV PMT FV 4 4.5 CPT 12,000 -10,062.74 2. For each period, multiply by (1 + r). The timeline looks like this: 0 1 2 3 4 1 + r = 1.04 0.948 1.085 0.95 100 104 98.59 106.97 101.62 Therefore: Ending value = Beginning value × 1.04 × 0.948 × 1.085 × 0.95 = $100 × 1.0162 = $101.62 3. a. You wish to find the annual rate that doubles an amount by the end of four years. The timeline looks like this: 0 1 2 3 4 -100 200 In FVIF terms, you must find r such that: FV = PV × FVIF 200 = 100 × (1 + r ) 4 => r = - 1 ) 100 200 ( 4 1 = .1892 or 18.92% F301 TVM practice set I solutions 1
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On your financial calculator, compute I: N I PV PMT FV 4 CPT -100 200 18.92 b. Find t , the number of periods, such that: 200 = 100 × (1.125) t . On your financial calculator, compute N: N I PV PMT FV CPT 12.5 -100 200 5.88 4. a. The total present value is the sum of the present values of the three payments, discounted at 7% per year. The timeline looks like this: 0 1 2 3 PV = ? 180,000 50,000 70,000 30 . 224 , 168 07 . 1 000 , 180 1 = = PV 94 . 671 , 43 07 . 1 000 , 50 2 2 = = PV 85 . 140 , 57 07 . 1 000 , 70 3 3 = = PV Sum = $269,037.09 b. The three equal payments must have a present value of $269,037.09. Therefore, find PMT such that PV = 269,037.09. Solve for the payment amount, C , in the annuity present value formula: + - × = r r C APV t ) 1 ( 1 1 ; - = ] 07 . ) 07 . 1 ( 1 1 [ 09 . 037 , 269 $ 3 C ; C = $102,517.03 On your financial calculator: N I PV PMT FV 3 7 -269,037.09 CPT 102,517.0 3 F301 TVM practice set I solutions 2
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5. a. The best option is the one with the highest present value. Therefore, you must calculate the present value of each option and compare them. In Option 1, the payments occur at
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