Economics 201-4 Answers to Problems with Interest-Rate Calculations (1)Allen1. 2000(1.065) = 21302. 10000/1.06 = 9434 Using discount table, 10000 x .943 = 94303. Present value of 19 annual payments = 50000(12.805) = 604250 Value of right-how payment = 50000 Present value of all lottery winnings = 6542504. The key to this problem is to recognize that the house is being sold for its market value. This implies that the total value the seller receives will equal the present value of all the payments, now and in the future, that the buyer will make. Present value of annual payments = 6000(9.108) = 54648 Value of down payment made now = 20000 Value of [total payment for] house 74648 Answers to Problems with Interest-Rate Calculations (2)1. A. Present value of annual returns/scrap 30000(3.352) = 100560 Investment cost = 123000 Net present value NEGATIVE 22440 B. Present value of annual returns 50000(1.626) = 81300 Investment cost 89200 Net present value NEGATIVE 7900 C. Present value of annual returns/scrap 20000(3.352) = 67040 Investment cost = 56600 Net present value = 4140 D. Present value of 1996 returns 40000(0.870) = 34800 Present value of 1997 returns 20000(0.756) = 15120 Present value of 1998 returns 10000 (0.658) = 6580 Total 56500 Investment cost = 55800 Net present value 700 Unfortunately, I neglected to give you the discount factors for a single payment when the interest rate is 0.15. But there’s still another way to skin this particular cat. Turn the page.1. D. Present value of 10000 for 3 years 10000(2.283) = 22830 Present value of 10000 for 2 years 10000(1.262) = 16260 Present value of 20000 for 1 year 20000(0.870) = 17400 Total value of returns 56490 Investment cost 55800 Net present value 690 The difference is due to the rounding implicit in the discount factors.2. Since the internal rate of return is the rate of return that drives the net preset value to zero, the technique is to for the discount rate whose discount factor is closest to the project’s investment cost (I), divided by its annual dollar return (R). Project A I/R = 123000/30000 = 4.1 For 5 years this is closest to a discount rate of 0.07 (lecture tables) Project B I/R = 89,200/50000 = 1.784 For 2 years, this is closest to a discount rate of 0.08 (lecture table) Project C I/R = 56,600/20000 = 2.830 For 5 years, this is closest to a discount rate of > 0.21 (With more complete tables, it’s about 0.225.) 3. Interest Project Incremental Total Rate__ _____ Investment Investment .21 C 56,600 56,600 .16 D 55,800 112,400 .08 B 89,200 201,600 .07 A 123,000 324,000 The appearance of the demand “curve” will be demonstrated in
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