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Unformatted text preview: Chapter 8 HW Assignment: E84, 5, 7, 9, 12, 14, 16, 17, 19, 21, 22; P83, 4, 10, 11, 14, 16, 17, 22; Case 81, 2 Solutions E84 a. The future value of a sevenyear, 5%, $2,000 annuity is computed as follows: FVA = A × IF = $2,000 × 8.14201 = $16,284.02 b. Amount resulting from deposits: Amount resulting from interest: $2,000 × 7 deposits = $14,000 Ending balance $16,284.02 Amount from deposits 14,000.00 $ 2,284.02 E85 a. $1,829,252 Future value of a fouryear, 9%, $400,000 annuity: FVA = Amount × Interest Factor = $400,000 × 4.57313 = $1,829,252 b. $3,680,172 Future value of a sevenyear, 9%, $400,000 annuity: FVA = Amount × Interest Factor = $400,000 × 9.20043 = $3,680,172 c. The future value of an annuity grows from the contribution of additional deposits and by the compounding of interest on the existing balance. As the length of the annuity increases, the compounding of interest on the existing balance begins to contribute more to the annuity’s value than do the additional deposits. Therefore, the length of an annuity does not need to double in order for the annuity balance to double. E87 $925.93 $1,000 ÷ 1.08 = $925.93 (or $1,000 × 0.92593) $917.43 $1,000 ÷ 1.09 = $917.43 (or $1,000 × 0.91743) $909.09 $1,000 ÷ 1.10 = $909.09 (or $1,000 × 0.90909) As the rate of return increases, the present value of a future cash flow de creases. E89 $952.38 $1,000 ÷ 1.05 = $952.38 (or $1,000 × 0.95238) $907.03 $1,000 ÷ (1.05) 2 = $907.03 (or $1,000 × 0.90703) $863.84 $1,000 ÷ (1.05) 3 = $863.84 (or $1,000 × 0.86384) As the time until expected cash flow is received increases, the present value of a future cash flow decreases. Chapter 8 HW Solutions Page 1 E812 $798.54 $200 × 3.99271 (from Table 4, 8%, 5 years) = $798.54 $758.16 $200 × 3.79079 (from Table 4, 10%, 5 years) = $758.16 E814 a. No. The present value of the net cash inflows to be received is less than the present value of the investment made to obtain those cash inflows. Proof: Expected additional cash inflow per year $50,500 Expected additional cash outflow per year 30,200 Net new cash inflow $20,300 The present value of an annuity of $20,300 for six years at 8% is: PVA = Amount × IF (Table 4) PVA = $20,300 × 4.62288 PVA = $93,844.46 Since the present value of the expected net cash inflows ($93,844.46) is less than the investment required ($100,000), this was not a wise business decision. b. $21,631.54 Proof: To earn exactly 8%, the present value of the future net cash flows must be equal to the $100,000 investment. Therefore, the present value of the annuity (future cash flows) = $100,000 at 8% for six years. PVA = Amount × IF (Table 4) $100,000 = Amount × 4.62288 Amount = $100,000 ÷ 4.62288 Amount = $21,631.54 c. $1,331.54 Current expectations Expected new cash inflows $50,500.00 Expected new cash outflows 30,200.00 Net expected cash flow $20,300.00 Cash flow needed to earn 8% 21,631.54 Amount of additional cash inflows needed $ 1,331.54 Chapter 8 HW Solutions Page 2 E816...
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This note was uploaded on 09/04/2008 for the course ACC 310F taught by Professor Verduzco during the Spring '07 term at University of Texas at Austin.
 Spring '07
 Verduzco
 Financial Accounting

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