Chapter 5 problems
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Feb 20, 2024
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Problem 1:
Gabrielle just won $2.75 million in the state lottery. She is given the option of receiving a total of $1,400,000 now, or she can elect to be paid $110,000 at the end of each of the next 25 years. If Gabrielle can earn 5% annually on her investments, from a strict economic point of view which option should she take?
Lump sum:
1,400,000 Annunity: Present value = Annuity * [1 - 1 / (1 +r)n] / r Present value = 110,000 * [1 - 1 / (1 + 0.05)25] / 0.05 Present value = 110,000 * [1 - 0.295303] / 0.05 Present value = 110,000 * 14.093945 Present value = $1,550,333.90 Problem 2:
Your firm has the option of making an investment in new software that will cost $278,367 today and is estimated to provide the savings shown in the following table over its 5-year life, Year Savings estimate 1 $76,000 2 $106,400 3 $98,800 4 $53,200 5 $30,400 Should the firm make this investment if it requires a minimum annual return of 9% on all investments?
Calculation of Net Present Value Cash flows P.V.F. @9% P.V. of cash flows Year 0 -278367 1 -278367.00 Year 1 76000 0.917431 69724.77 Year 2 106400 0.84168 89554.75 Year 3 98800 0.772183 76291.73 Year 4 53200 0.708425 37688.22 Year 5 30400 0.649931 19757.91 Net present value 293,017.38 Net present is positive $14,650.39. So, it should make investment. Problem 3. For the mixed stream of cash flows shown in the following table, Year Cash flow stream 1 $27,000 2 $22,500 3 $18,000 4 $9,000 5 $4,500 Determine the future value at the end of the final year if deposits are made into an account paying annual interest of 8%, assuming that no withdrawals are made during the period and that the deposits are made: a. At the end of each year. FV = 40500*(1+0.08)^4 + 33750*(1+0.08)^3 + 27000*(1+0.08)^2 + 13500*(1+0.08)^1 + 6750*(1+0.08)^0 = $150437.88 b. At the beginning of each year. FV = 40500*(1+0.08)^5 + 33750*(1+0.08)^4 + 27000*(1+0.08)^3 + 13500*(1+0.08)^2 + 6750*(1+0.08)^1 = $162472.91
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Calculate the Present value for each of the above options. Round all answers to the nearest dollar.
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$fill in the blank 1
Option 2
$fill in the blank 2
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$fill in the blank 3
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O
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Bha
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