Posted: May 13th, 2018

Finance 10 Problems Assignment Set

1. A kind and caring politician offers to pay you $500 million in 300 short years. Because thispolitician is from the political party you vote for, you believe that the amount will be paid withcertainty.A. How much is this promise worth today if the appropriate discount rate is 10%?B. How much is this promise worth today if the appropriate discount rate is 0%?C. Explain why your answer to B, while mathematically correct, does not make sense inreality. In your (short) answer, include 2 reasons why interest rates are positive.2. You won the lottery, and can choose one of two (guaranteed) payments: Choice A pays $10,000three years from today; Choice B pays $1,000,000 exactly 100 years from now.A. If the discount rate is 8%, which option should you choose?B. If the discount rate is 4%, which option should you choose?C. At what discount rate would you be indifferent between these two choices? (Hint:When will the two choices have the same present value?)3.Bank A pays 6% simple interest annually. Bank B pays 5.9% interest, with annualcompounding. Bank C pays 5.8% interest, with monthly compounding.A. How long will it take for your money to double in each of the three banks? Pleasestate your answers in years, rounded to the nearest tenth of a year (e.g., 6.3 years).B. In one or two sentences, what does your answer to part A illustrate about compoundinterest?4. Maybepay Life Insurance Company is selling a annuity contract for $70,000. The contractwill make monthly payments of $350 for the next 35 years.A. What is the monthly interest rate on this contract?B. What is the APR?C. What is the effective annual return?5. Eight years from now you will begin to receive cash flows of $5,000 per year. These cash flowswill continue for twenty years. If the discount rate is 8%, what is the present value (today) ofthese cash flows?6. An investment will pay $3,600 per year for 10 years, with the first payment occurring today.If the interest rate is 7%, what is the value of this investment today? What would the value of theinvestment be if the cash flows last 20 years (again, with the first payment today!)? How comethe value of the investment IS NOT twice as much? (After all, you will receive twice as muchcash in the 20 year annuity: 3600 X 20 vs. 3600 X 10).7. You just opened a retirement account with a $5,000 deposit. Assuming that you can earn an8% annual return (and that you make no additional deposits), what will this account be worthwhen you retire in 35 years? Now, assume that you wait 15 years before making the initial (andonly) deposit to your retirement account. What will your account be worth when you retire (note,you are still retiring 35 years from today)? Does this suggest an optimal retirement strategy?8. If Debbies Drug Co. chooses to develop a new drug, it expects to receive cash flows of$150,000 in year 3, $300,000 in year 4, and $100,000 in year 5. The discount rate is 8%.A. What is the present value of the expected future cash flows?B. Assume that this project requires a $400,000 investment today (or else the future cashflows will not happen). Should the firm make this investment?9. Over the last three years, Sally the investor earned the following returns on her portfolio(assume that all dividends were reinvested in the portfolio, and are reflected in the stated returns):+35% (year 1), -20% (year 2), and +5% (year 3). What was Sallys effective, annual,(compounded) return over this three year period? If Sally requires an annual return of 5% to behappy, is she happy?10. You borrow $500,000 to purchase a house. The mortgage is a 30-year fixed rate mortgage,with monthly payments.A. Assume that you have good credit, and can borrow money at a 3.75% annualinterest rate. What will your monthly payment be?B. Now, assume that you have lousy credit, and must pay a 6.5% annual interest rateto obtain a mortgage. What will your monthly payment be?C. Having lousy credit can be costly. How much additional interest will you pay overthe 30-year period if you have bad credit, relative to what you would pay if youhave good credit? (Hint: Calculate the total interest over the 30-year period on theloan in Part A, and the total interest over the 30-year period for the loan in Part D.What is the difference between the two amounts?).D. Is it ethical for banks to charge people with poor credit histories higher interestrates? [After all, people with lousy credit will benefit more from lower interestrates than people with good histories & high paying jobs (who could afford to paymore interest)].

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