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# Assignment - vestment 4 1 a Total beneﬁts are maximized...

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ECON 560 Spring, 2011 Managerial Economics Professor Bae Assignment 1 Solution 1. Option 1 (lease): PV = 8 , 000 1 . 06 + 8 , 000 (1 . 06) 2 + 8 , 000 (1 . 06) 3 = \$21 , 384 Option 2 (purchase): PV = \$20 , 000 So it is better to buy rather than lease. 2. What is the present value of the following series of cash ﬂows at an interest rate of 7%: \$1,000 today, \$2,000 at the end of year 1, \$4,000 at the end of year 3, and \$6,000 at the end of year 5? PV = 1 , 000 + 2 , 000 (1 . 07) + 4 , 000 (1 . 07) 3 + 6 , 000 (1 . 07) 5 = \$ 10,412 3. The net present value of the investment is NPV = \$15 , 000 (1+0 . 20) 1 - \$10 , 000 = \$12 , 500 - \$10 , 000 = \$2 , 500. Since the net present value is positive, the investment should be under- taken. Cash ﬂow considerations are irrelevant, in this case. Your ﬁrm could secure a \$ 10,000 one-year loan from the bank at 20 percent. Since the net present value is positive, in one year the \$ 15,000 generated from the investment will be more than enough to pay back the interest and principal on the loan. Thus, cash ﬂow is not really an issue in this case, and in present value terms, your ﬁrm will pocket \$ 2,500 from this in-

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Unformatted text preview: vestment. 4. 1 a. Total beneﬁts are maximized when MB ( Q ) = 100-4 Q = 0, which means Q = 25. b. The total costs of recycling are minimized when Q equals zero. c. Setting MNB ( Q ) = 100-4 Q-2 = 0 and solving, we see that the net beneﬁts of recycling are maximized when Q = 24 . 5. d. The optimal level of recycling is 24.5. At this level, the net beneﬁts are maximized. 5. a. 16 units, since 12 - 3(2) - 4(1) + 10 + 2(2) = 16. b. Complements, since the coeﬃcient of P y is a negative number (-4). This means an \$ 1 increase in the price of good Y decreases the demand for good X by 4 units. c. Normal, since the coeﬃcient of M is a positive number (1). This means a \$ 1 increase in income increases the demand for good X by 1 unit. d. The demand curve is Q d x = 12-3 P x-4(1) + 10 + 2(2) = 22-3 P x . The inverse demand curve is thus P x = 22 3-1 3 Q d x . 2...
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Assignment - vestment 4 1 a Total beneﬁts are maximized...

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