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CHAPTER 1: EXERCISES

1. With r = 10%, calculate the present value of $100 a year for 10 years.

2. With r = 10%, calculate the present value of $1,000 ten years from now.

3. Explain why the answers to exercise 1 and 2 are different.

4. You have $100 and suppose you have the following investment opportunities.

i) Invest in a money market account paying 7% a year.

ii) Invest in a project paying $115 two years from now.

What will you do and why?

5. At 10%, compounded annually, how long will it take for $100 to double?

6. At 10%, compounded monthly, how long will it take $100 to double?

7. Suppose you want to buy a house in 5 years. The interest rate is 10%, and you forecast that the house will cost $250,000.

i) How much will you have to save every month to ensure being able to buy the house?

ii) If you plan on borrowing 60% of the cost then how much will you save every month to buy the house?

8. You own drilling equipment which you estimate will last 7 years if rented 11 out of 12 months each year. The equipment costs $350,000 and the interest rate is 10%. What monthly rental must you charge to break even?

9. You want to give just enough money to a charity so that it receives $5,000 a year for 20 years. If r = 10%, how much must you give?

10. You have $100, and can invest in one of two ways. Both the investments last for 10 years. The first pays an interest rate of 9%, and compounds annually. The second pays a rate of 6% but compounds semi-annually. Which one will you choose?

11. You are trying to decide whether to lease a car or buy it. The interest rate is 9%, and your options are:

a) Buy the car, borrowing the amount it costs, and paying back over 5 years.

b) Leasing the car for 5 years, at the end of which the dealer buys it back at a fixed price.

The car costs $10,000, your income is $30,000 a year, taxed at 30%, and suppose you can arrange your financing requirements so that interest payments are deductible while lease payments are not.

A. If you buy the car and throw it away after 5 years:

i) Calculate the annual payment.

ii) Calculate the interest paid each year.

iii) Calculate the taxes you pay each year.

iv) Calculate the present value of your after tax net of car payments.

B. If you lease the car, and the dealer buys it back for $3,000:

i) Calculate the annual payment.

ii) Calculate the taxes you pay each year.

C. Will you buy or lease (Provide support for your answer)?

 

D. Suppose that the way you arranged your financing is not accepted by the IRS and so you can no longer treat your interest payments as tax deductible. Will you buy or lease (provide support for your answer)?

E. Suppose you think you could sell the car after 5 years for $2,000. Would this change your answer to part C?

12. Your monthly income is $5,000, and you are in the market for a house. A bank will give you a mortgage as long as your monthly payments do not exceed 28% of your monthly income.

i) If 30 year mortgages are going for 9% what is the maximum amount you can borrow?

ii) What if r% = 10%?

iii) At 9%, what happens if your income goes up to $5,000?

13. You need to borrow $2,000. You discount future cash flows at 10% and have an income of $12,000 a year. You can take out a 3-year loan at 8% or a two year loan at 7.5%. Which one will you choose? Explain your answer.

14. Suppose you can rent your house for $1475 per month for ever. If the market rate of interest is 8.5%