1. You have a credit card with a balance of $4,000. The card carries an interest rate of 22%, compounded monthly. You decide to cut up the card, and pay it off by paying the minimum payment due each month, which is a constant $84. a. Calculate your EAR for the card. (5 points) b. Calculate how long (in months and then in years) it will take you to pay off the card. (5 points) c. Calculate your monthly payment if you want to pay the card off in 2 years. (5 points) 2. At age 30, you are evaluating several savings plans to fund your retirement at age 65 (in 35 years). You can earn 3% (compounded annually) on your investments. a. Calculate the amount you will have accumulated at retirement if you start making deposits of $1,000 per year at the end of this year (Hint: draw a cashflow diagram). (5 points) b. You decide the amount you would end up with is not enough: you need at least $1,000,000 at retirement to support in the style to which you have grown accustomed, during your anticipated 30 year retirement (you plan to die at age 95, leaving nothing to your heirs). i. Calculate how much you will be able to withdraw at the end of each year for the 30 years of your retirement, (starting at age 66) if you fund the account with $1,000,000. (5 points) ii. Calculate the amount you will have to deposit in an account today in order to have $1,000,000 at retirement in 35 years. (Hint: draw a cashflow diagram). (5 points) c. You think, Thats too much to have to put in right now. You figure you have three separate choices (value each choice ignoring the others): i. Defer retirement. Calculate how much you would have to deposit today to have 1,000,000 at age 70 (in 40 years). (5 points) ii. Earn more interest. Calculate what the interest rate would have to be to deposit $100,000 today, but still have $1,000,000 at age 65. (5 points) iii. Make annual deposits. Calculate how much you would have to deposit at the end of each year to have $1,000,000 in 35 years, if you could invest at 3% per year. (5 points) 3. Your favorite athlete has just been offered a $25 million, 7-year contract. Their salary for the year will be paid at the end of that year. You know from their investing blog that they can earn an average of 5% per year on their investments. a. Calculate the constant annual payment the athlete would have to receive for the contract to actually be worth $25 million. (5 points) b. Suppose the salary is actually going to be paid at the end of each year, according to one of the following two schedules: Year Schedule 1 Schedule 2 1 $2,000,000 $6,000,000 2 2,000,000 5,000,000 3 3,000,000 4,000,000 4 3,000,000 3,000,000 5 4,000,000 3,000,000 6 5,000,000 2,000,000 7 6,000,000 2,000,000 i. Calculate the true value of the contract, based on Schedule 1 (HINT: You can find an easy way to do this on your calculator on tvmcalcs.com). (5 points) ii. Calculate the true value of the contract, based on Schedule 2. (5 points) iii. Explain whether Schedule 1 or 2 is better (explain why its better, not just that its worth more why is it worth more?). (2 points) c. Calculate how much of a bonus the team would have to give the athlete today to make them indifferent between the two choices. (5 points) 4. You purchased 100 shares of John Deere (DE) stock on October 31, 2016. On October 31, 2017, you decide to assess your investment. You have the following information: the purchase price was $87.17; the closing price on October 31, 2017 was $106.25, and the stock paid a dividend of $2.40 during the year. a. Compute the holding period return for the DE stock. (4 points) b. You are considering buying more DE stock. You have projected DEs returns over the next year the following three scenarios. Calculate the expected return and standard deviation for the DE stock. (10 points) Scenario Probability Return CAT Invents a New Tractor 0.2 -25% Status Quo 0.5 10% Mowing Your Own Lawn is In 0.3 35% c. You decide that past data is better for predicting the future, so you decide to use the last 4 years of DEs returns to do your analysis. Calculate the expected return and standard deviation for the DE stock. (10 points) Year Return 2014 38.7% 2015 -20.2% 2016 -26.2% 2017 79.5% d. Suppose you found a different stock that had a higher expected return and standard deviation than DE, and whose returns had a correlation with DE of +0.10. As a risk-averse investor, explain the benefit (in terms of return and risk) of combining the two securities together to make a portfolio. (no calculations necessary). (2 points) 5. The beta of DE is 1.5. a. Suppose the risk-free rate (measured by 3-month US Treasury Bills) is 2%, and the stock market (measured by the return on the S&P 500 Index) expected return is 10%. Compute the required return for DE. (3 points) b. State whether you would purchase DE based on your Scenario Analysis (answer to 4b); or your Historical Return Analysis (answer to 4c). (2 points) c. Explain why choosing a method to calculate expected return can affect an investment decision. (2 points)