Problem 2-23 Annuities

1.)David and Helen Zhang are saving to buy a boat at the end of seven years. If the boat costs $21,000 and they can earn 9% a year on their savings, how much do they need to put aside at the end of years 1 through 7? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

2.) The annually compounded discount rate is 5.5%. You are asked to calculate the present value of a 11-year annuity with payments of $50,200 per year.

a. Calculate the PV if the annuity payments arrive at one-year intervals. The first payment arrives one year from now. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b.) Calculate the PV if the first payment arrives in six months. Following payments arrive at one-year intervals (i.e., at 18 months, 30 months, etc.). (Do not round intermediate calculations. Round your answer to 2 decimal places.)

3.) The $53 million lottery prize that you have just won actually pays out $8.5 million a year for 20 years. The interest rate is 10.0%.

a. If the first payment comes after 1 year, what is the present value of your winnings? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

b. What is the present value if the first payment comes immediately? (Do not round intermediate calculations. Enter your answer in millions rounded to 2 decimal places.)

5.) a. The cost of a new automobile is $10,200. If the interest rate is 8%, how much would you have to set aside now to provide this sum in eight years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. You have to pay $11,000 a year in school fees at the end of each of the next nine years. If the interest rate is 11%, how much do you need to set aside today to cover these bills? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. You have invested $99,000 at 11%. After paying the above school fees, how much would remain at the end of the nine years? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

7) If the interest rate is 10% compounded annually, what is the value of the following three investments?

a. An investment that offers you $160 a year in perpetuity with the payment at the end of each year. (Round your answer to 2 decimal places.)

b. A similar investment with the payment at the beginning of each year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

c. A similar investment with the payment spread evenly over each year. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

10.) Halcyon Lines is considering the purchase of a new bulk carrier for $7.0 million. The forecasted revenues are $6.6 million a year and operating costs are $5.6 million. A major refit costing $3.6 million will be required after both the fifth and tenth years. After 15 years, the ship is expected to be sold for scrap at $3.1 million.

a. What is the NPV if the opportunity cost of capital is 10%? (Enter your answer in dollars, not millions of dollars. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to the nearest whole dollar amount.)

b. Halcyon could finance the ship by borrowing the entire investment at an interest rate of 4.5%. Will this borrowing opportunity affect your calculation of NPV yes or no?