AS/MATH2580 A Assignment AS/MATH2580 A Assignment #4
Due Wednesday, May 2, 2000

Make sure your name and student number are on your submitted assignment. Show your work on each question. Your answer to each question should be in sentence form.

1. A company has raised \$40 million with a stock offering. They wish to use the money to generate semiannual income for the next 10 years. Method 1: They can invest at j2 = 6.25% and withdraw equal semiannual payments (each payment part interest and part principal) for 10 years. Method 2: They can purchase 10-year par bonds with coupons at j2 = 9% priced to yield j2 = 6.5%, strip these bonds of coupons, and sell the strip bonds to yield j2 = 6%. If the bonds are \$1000 bonds, how many bonds can they purchase? Compare the semiannual revenue from Method 1 to the semiannual coupon revenue from Method 2.

2. A serial issue of \$1000 par bonds has 1000 bonds maturing July 1, 2009, 1000 bonds maturing Jan 1, 2010, 1000 bonds maturing July 1, 2010, and so on until the last group of 1000 bonds matures July 1, 2015. All bonds bear semiannual coupons at j2 = 8%. Find the price of the entire series on May 6, 2001 to yield j2 = 6%. [Hint: P = P0(1+ki).]

3. A mining property costs \$1,400,000 now and is expected to produce revenue of \$200,000 at the end of each year for the next 11 years. At the end of the 12th year, there will be a cost of \$300,000 for closing the mine and cleaning up the area and that cost combined with the revenue for the 12th year will result in a net loss of \$100,000 at the end of the 12th year.

1. Is this investment suitable for an investor who wishes to earn j1 = 7%?
2. Is it suitable for an investor who wishes to earn j1 = 8%?
3. What is the internal rate of return of this investment as a per cent rounded to two decimals?

4. A truck of type A can carry 39 tons of gravel, costs \$125,000, has annual operating cost of \$7,900 and has a lifetime of 9 years after which it is worth \$18,000. A truck of type B can carry 45 tons of gravel, costs \$175,000, has annual operating cost of \$9200 and has a lifetime of 12 years after which it is worth \$25,000. If money is worth j1 = 7% which truck is a better buy?

5. A machine costs \$21,000 and has a salvage value of \$5,000 after 9 years. Annual maintenance is \$1,000. If money is worth j1 = 6% how much can economically be spent on a special parts kit that will increase the machine's production rate by 10%, reduce the annual maintenance by 50%, and also extend its life from 9 years to 12 years. (Salvage value is unchanged by using the kit.)

6. A machine costing \$35,000 has a scrap value of \$7,000 at the end of 8 years. Find the depreciation during the machine's 5th year of operation using (a) the straight line method (b) the constant-percentage method.

7. A car costing \$36,000 new is expected to have a resale value of \$4,000 in 10 years. The owner intends to replace it after 4 years. She sets up a sinking fund at j12 = 6% with monthly payments to accumulate funds for a new car in 4 years. She estimates that new car prices will have risen 5% by then and she estimates her car's resale price in 4 years as the book value using the constant-percentage method of depreciation. What should her monthly sinking fund deposit be?

8. In April of 2001, a high school class has 23 students all aged 18. There are 10 females (of whom 5 are smokers) and 13 males (of whom 6 are smokers).

1. A school reunion is held in March of 2021. According to CIA 1982-1988 mortality what is the probability that at least one of the former students has died by that time?
2. For the school reunion held in March of 2081, what is the probability that at least one of the former students is still alive?

9. A loan company charges j12 = 9% to customers with a credit rating. For customers with no credit rating, they assume a 1% chance of default each month. (A loan default means no further payments will be made on the loan.) A customer with no credit rating wants to borrow \$10,000 for 4 years and make monthly amortization payments. What should the monthly payments be?

10. A male smoker aged 32 pays \$10,000 to an insurance company for an endowment payable when (and if) he reaches age 65.

1. If the insurance company uses an annual effective interest rate of 6%, what will be the size of the endowment?
2. If he were to have just invested the money at 6% effective in a bank, how much would he have at age 65?
3. What would the corresponding endowment be for a female nonsmoker?

File translated from TEX by TTH, version 1.98.
On 16 Apr 2001, 16:02.