Question 1.

(a) The cost of a new bike is $500 today, and this price will remain the same over the next 3 years. If the annual interest rate is 10%, how much would you have to set aside now to be able to buy the bike in three years? How would you answer change if the bike price would grow at 10% each year?

(b) You have to pay $1,000 a month in apartment rent at the end of each of the next 9 months. How much do you need to set aside today to cover these bills, if the monthly interest rate is 6%? (Note: there is no rent payment today.)

Question 2. You are the financial manager of a firm manufacturing headphones. You just announced that this year's profits are $2 million. Analysts predict your profits will grow at 5% each year for the next three years and then profit growth will slow to 3% per year and will continue growing at 3% in perpetuity. Assuming an opportunity cost of capital of 5% per year, what is the present value of your future (not counting this year) projected profits? what is the present of your future projected earning including this year's profits?

Question 3. Suppose you are the financial manager of a firm manufacturing light bulbs. You are thinking of upgrading the firm's equipment today. If you do so, this upgrade will save you $3,000 in the first year. The new equipment will then begin to wear out so that the savings decline at a rate of 2% per year forever. What is the present value of the savings if the interest rate is 5% per year?

Question 4. You receive an inheritance from your grandmother in the amount of $9 million. The inheritance will be paid in 3 equal installments and the first payment will arrive only in three years. How much is the inheritance really worth to you today if the discount rate is 10%? How would your answer change if the inheritance would be paid in 9 equal installments? (Note: to receive a credit for this question you need to use shortcut formulas)

Question 5.

(a) Assume that your savings account offers you an APR of 6% with quarterly compounding. What is the present value of $1, 000 to be received 3 quarters from today? (b) Your bank charges you 0.5% per month on your car loan. What APR must the bank report on your loan? What is the effective annual interest rate (EAR) on your loan? Explain why the EAR is higher than the APR.

(c) You have been given the once-in-a-lifetime opportunity to invest $2, 000 in a certificate of deposit paying an APR of 24% with monthly compounding. Exactly how many months will it take for your $2, 000 to grow to $10, 000?

Question 6.

You live in Pittsburgh, but your partner lives in Washington, DC. For the next year, you have agreed to commute every other weekend to visit your partner in DC. You are deciding whether to rent (and commute by a car) or to fly. The cost of communing by a car is $350 per trip, while the cost of commuting by a plane is $360 per trip. The annual percentage rate (APR) equals 4% (annually). Assume there are exactly 52 weeks in a year and your next trip is in exactly two weeks from now. Also assume that you incur all the costs at the end of the week you are traveling to DC.

(a) What is the PV of all costs from commuting by a car? By a plane?

(b) How much do you save in present value terms by commuting by a plane for the next year?