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Question 2 (1 point) An invention costs an initial amount of $10 million to develop along with $3 million operating costs paid continuously throughout each year for the first five years
Question 2 (1 point) An invention costs an initial amount of $10 million to develop along with $3 million operating costs paid continuously throughout each year for the first five years. After the first five years, is anticipated that the invention will generate $4 million per year in perpetuity, received annually, with the first payment received at the beginning of the sixth year. Given an annual effective interest rate of 10%, calculate the net present value of the invention (in millions). a) -2.10 b) 2.90 c) 10.39 d) 5.39 e) 13.12
Expert Solution
Please select option d) 5.39
PV of all the costs = C0 + PV of C as annuity = C0 + C/r x [1 - (1 + r)-n] = 10 + 3/10% x [1 - (1 + 10%)-5] = 21.37
PV of all inflows at the end of year 5 = PV of perpetuity in advance = C x (1 + r) / r = 4 x (1 + 10%) / 10% = 44.00
PV today = PV at the end of year 5 x (1 + r)-n = 44 x (1 + 10%)-5 = 27.32
Hence, NPV = PV of all inflows - PV of all costs = 27.32 - 21.37 = $ 5.95 million
Please select option d) 5.39
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