Econ 134 A Test 1 Spring 2016 Based on Form A

Q1 Tanner bought a sunflower today for $5. The sunflower produces $1 in seeds every 12 months forever, starting 4 months from today. If Tanner’s effective annual discount rate is 9%, what is the profitability index of purchasing the sunflower? PV of cash flows: ×(1.09)2/3 = $11.77 PI= $11.77/$5 = 2.3536

Q2 Ashley runs her own small business at home. She is expected to earn $60,000 five years from today, and $100,000 per year for 10 years. (Note: The first $100,000 cash flow will occur 6 years from today.) What is the present value of all earnings if Ashley’s effective annual discount rate is 10%? PV= $60,000/(1.1)5 +($100,000/0.1) ×[1-1/1.110](1/1.15) =$37,255+381,529 =$418,784

Q3 Lincoln buys a machine today for $500. The machine lasts for 8 years. What is the equivalent annual cost of the machine if the effective annual interest rate is 7%? 500= [1-1/1.078] 500=5.9713×C C=$83.73

Q4 Alice borrows $5,000 today from her local bank. She makes monthly payments of $125 for 48 months, starting one month from today. She makes one additional payment 49 months from today to pay off the loan. How much will this payment be if the stated annual interest rate of the loan is 13.2%, compounded monthly?

Q4 PV of 48 payments: [1-1/1.01148]=$4,642.20 Remaining payment has PV: 5000-4,642.20= $357.80 PV49 months = 357.80×1.01149=$611.56

Q5 Calvin invests $10,000 into a bank account earning 12% annual interest, not knowing whether interest is compounded monthly or yearly. After one year, what is the difference in the amount of interest earned between the two types of compounding?

Q5 Yearly: .12 ×10,000 = $1,200 Monthly: [(1.01)12-1]×10,000 = $1,268.25 Diff = $1,268.25-$1,200 = $68.25

Q6 Today is April 22, 2016. Suppose that you are advising a couple just about to get married about how much they need to save for retirement. The couple will retire in 35 years. They will need to withdraw $2 million per year each year on April 22 of the years 2051-2075. When you ask the couple how they plan to save for retirement, they tell you they want to make 20 equal deposits of $X each year, starting one year from today. The total of these deposits will be exactly enough to cover all of their retirement expenses. Find X if the effective annual interest rate is 6%.  

Q6 PV of withdrawals: (in $1 millions): [1-1/1.0625]×(1/1.0634) = 3.5259 Amount of each deposit X calculated as follows: 3.5259 = [1-1/1.0620] 3.5259 = 11.4699X .307404 = X (in millions of dollars) Each deposit needs to be $307,404

Q7 Summer is considering purchasing a gold mine. The gold mine can be purchased for $10 million today, and she must pay $24 million to satisfy environmental regulators 10 years from now. The gold mine will produce $33 million in gold 5 years from now. If there are no other cash flows, find all annual internal rates of return.  

Q7 Let X be 5-year rate : -10 + 33/(1+X) − 24/(1+X)2 = 0 ( in $1 millions) Let Y = 1+X -10 +33/Y -24/Y2 = 0  -10Y2 + 33Y -24 = 0 Y= = (-33±11.3578) / (-20) Y = 1.08211 , 2.21789 = 1.015908 , 1.172703 IIR’s = 1.59083% 17.2703%