CH3 - CHAPTER 3 How to Calculate Present Values Answers to...

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CHAPTER 3 How to Calculate Present Values Answers to Practice Questions 1. a. PV = $100 × 0.905 = $90.50 b. PV = $100 × 0.295 = $29.50 c. PV = $100 × 0.035 = $ 3.50 d. PV = $100 × 0.893 = $89.30 PV = $100 × 0.797 = $79.70 PV = $100 × 0.712 = $71.20 PV = $89.30 + $79.70 + $71.20 = $240.20 2. a. PV = $100 × 4.279 = $427.90 b. PV = $100 × 4.580 = $458.00 c. We can think of cash flows in this problem as being the difference between two separate streams of cash flows. The first stream is $100 per year received in years 1 through 12; the second is $100 per year paid in years 1 through 2. The PV of $100 received in years 1 to 12 is: PV = $100 × [Annuity factor, 12 time periods, 9%] PV = $100 × [7.161] = $716.10 The PV of $100 paid in years 1 to 2 is: PV = $100 × [Annuity factor, 2 time periods, 9%] PV = $100 × [1.759] = $175.90 Therefore, the present value of $100 per year received in each of years 3 through 12 is: ($716.10 - $175.90) = $540.20. (Alternatively, we can think of this as a 10-year annuity starting in year 3.) 11
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3. a. = + = 0.88 r 1 1 DF 1 1 so that r 1 = 0.136 = 13.6% b. 0.82 (1.105) 1 ) r (1 1 DF 2 2 2 2 = = + = c. AF 2 = DF 1 + DF 2 = 0.88 + 0.82 = 1.70 d. PV of an annuity = C × [Annuity factor at r% for t years] Here: $24.49 = $10 × [AF 3 ] AF 3 = 2.45 e. AF 3 = DF 1 + DF 2 + DF 3 = AF 2 + DF 3 2.45 = 1.70 + DF 3 DF 3 = 0.75 4. The present value of the 10-year stream of cash inflows is (using Appendix Table 3): ($170,000 × 5.216) = $886,720 Thus: NPV = -$800,000 + $886,720 = +$86,720 At the end of five years, the factory’s value will be the present value of the five remaining $170,000 cash flows. Again using Appendix Table 3: PV = 170,000 × 3.433 = $583,610 5. a. Let S t = salary in year t - - = = = 30 1 t t 1 t 30 1 t t t (1.08) (1.05) 20,000 (1.08) S PV - = = = 30 1 t t 30 1 t t (1.029) 19,048 1.05) / (1.08 05) (20,000/1. $378,222 (1.029) (0.029) 1 0.029 1 19,048 30 = × - × = b. PV(salary) x 0.05 = $18,911. Future value = $18,911 x (1.08) 30 = $190,295 c. Annual payment = initial value ÷ annuity factor 20-year annuity factor at 8 percent = 9.818 Annual payment = $190,295/9.818 = $19,382 12
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6. Period Discount Factor Cash Flow Present Value 0 1.000 -400,000 -400,000 1 0.893 +100,000 + 89,300 2 0.797 +200,000 +159,400 3 0.712 +300,000 +213,600 Total = NPV = $62,300 7. We can break this down into several different cash flows, such that the sum of these separate cash flows is the total cash flow. Then, the sum of the present values of the separate cash flows is the present value of the entire project. All dollar figures are in millions. Cost of the ship is $8 million PV = -$8 million Revenue is $5 million per year, operating expenses are $4 million. Thus, operating cash flow is $1 million per year for 15 years. PV = $1 million
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CH3 - CHAPTER 3 How to Calculate Present Values Answers to...

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