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Econ 134A-100 (9:30 am) Winter 2013, Test 1

Econ 134A-100 (9:30 am) Winter 2013, Test 1. Solution sketches. Eber Extravagant.

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Econ 134A-100 (9:30 am) Winter 2013, Test 1

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  1. Econ 134A-100 (9:30 am)Winter 2013, Test 1 Solution sketches

  2. Eber Extravagant Eber Extravagant has just purchased $50,000 in furnishings for his living room. To do so, he charged all $50,000 spent on his American Slowpoke credit card, which charges 21% stated annual interest, compounded monthly. After getting home, he finds he has just been approved for a new Uncover credit card, which charges 18% stated annual interest, compounded monthly. The Uncover card charges a 4% fee for any balances that are transferred. If Eber is planning on making monthly payments of $1500 per month to pay off his furnishings, should he pay off his American Slowpoke credit card, or transfer his balance to the Uncover card today and pay off the higher balance? You need to completely justify your answer to get full credit. • First, find the number of payments needed to pay off American Slowpoke: , where 1.75% = 21% / 12 months. • Solving for T: , monthly payments.

  3. Eber Extravagant, continued • Repeat the process for Uncover, realizing that the balance would be 1.04 times $50,000, and the monthly rate 18%/12=1.5%: • Solving for T: , monthly payments. • He is able to pay off the Uncover card more quickly, so he should transfer the balance.

  4. Solve each of the following (a) The stated annual interest is r%, compounded continuously. How many years will it take to double an initial deposit made today? Assume that any interest earned gets re-invested. • Then,

  5. Solve each of the following (cont.) (b) Dan deposits $600 into a bank account today, and will receive $800 three years from today. What is the stated annual interest rate if the interest is compounded daily? You can assume there are 365 days per year. • , where . • Then the daily rate is • The annual rate is .

  6. Solve each of the following (cont.) (b) Danielle invests $600,000 into a new superconductor project today. She will receive $500,000 one year from now and $300,000 8 years from now. The effective annual discount rate is 9%. What is the profitability index of this project? • In thousands, . • The PI is

  7. Investments P and GP Investment P offers to pay $500 per year forever, starting today. Investment GP offers to pay $400 today, followed by 4% annual growth every year forever. For what effective annual discount rate would you be indifferent between the two investments? • Set the present values equal: • Getting rid of fractions, we get • Divide by 5 to get 5 4r + 1  (5r – 1) (r + 1) = 0  r = 0.2 or -1 (ignore -1) • Alternate way: = 0.2 or -1 • Ignoring the negative discount rate, the answer is

  8. Club 4321 Club 4321, Inc. pays quarterly dividends. The corporation will pay $4 in dividends per share over the next year. It will pay out $1 every quarter starting three months from now. The annual dividend will increase to $4.60 the following year, and remain there forever. (Remember that the $4.60 annual dividend also gets divided up into four quarterly payments.) The appropriate effective annual discount rate for this stock is 43.21%. What is the present value of Club 4321 stock? • First, we find the quarterly discount rate: • PV of the first year is • PV of the second year and beyond is • Adding these,

  9. Rain RainRain, Inc. Rain RainRain, Inc. specializes in umbrella production. In anticipation of a rainy season ahead, the executives decide to sell bonds to help fund additional umbrella production. Bonds sell today for $45 each, but the face value of the bond is $50. A 9% coupon is promised twice: One year from today and two years from today. The bond also matures two years from today. What is the yield to maturity, expressed as an effective annual rate? • The price of the bond should equal the two coupon payments and the face value, all properly discounted. • Ignoring the negative discount rate, the answer is

  10. Mountaintop Paving, Inc. Mountaintop Paving, Inc. needs to buy a new machine that paves roads in rural areas. If the company buys a machine today, the immediate cost is $60,000, and a one-time maintenance cost of $7,000 is required five years from today. The machine lasts for 8 years. The effective annual discount rate is 4%. (a) What is the equivalent annual cost of the machine? • PV of total cost is • EAC is found from

  11. Mountaintop Paving, Inc. (cont.) (b) Suppose instead that the executives at Mountaintop Paving decide to finance the machine so that the present value of the payments are the same as the present value of all costs of the machine (including maintenance) if purchased. The effective annual interest rate for the loan is 4%. Five payments will be made to pay back the loan. The first will be made today, and the remaining payments will be made 2 years, 4 years, 6 years, and 8 years from today. How much will each payment be?

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