Assignment:
1. Given an interest rate of 6% per year compounded yearly, how much will you have after 5 years if you invest $100 at this rate?
2. Starting next year, John will deposit $1,400 each year into an account that pays him 6% per year interest compounded yearly. He wants to have $30,000 saved up after 10 years. How many dollars short will he be of this goal?
3. At 10% annual interest rate, compounded annually, how much was $500 worth 4 years ago?
4. How much money should you be willing to pay now for a guaranteed $600 per year for 9 years starting next year, at a rate of return of 16%?
5. Given an interest rate of 18% per year compounded quarterly, what is the effective yearly rate?
6. Given an interest rate of 18% per year compounded semi-annually, what is the effective yearly rate?
7. A part's diameter is assumed to be normally distributed. What proportion, in %, of diameters will be within three standard deviations of the mean?
8. The weights of bags of crisps follow a normal distribution with a mean of 12.8 ounces and a standard deviation of 0.6 ounces. If the manufacturer wants to keep the mean at 12.8 ounces but adjusts the standard deviation so that only 1% of bags weigh less than 12 ounces, what will the new value of the standard deviation need to be, in ounces?
9. What nominal annual rate is equivalent to an effective rate of 16% per year, compounded semi-annually?
10. University Endowment, At 2% interest per year, what was the initial endowment amount (PW) that would permit $1 million dollars in interest to be generated each year, forever?
11. The weight of a certain product is normally distributed with a mean equal to 100 grams and a standard deviation equal to 12 grams. What is the probability that a sample of 64 of these products will have a mean weight that is less than 101 grams?
12. A company currently pays employees $0.56 per mile to drive personal car on business. The company is considering whether to provide cars employees instead.
• Purchase price is $25,000
• 3 year life
• Salvage value of $8,000
• Taxes & insurance cost $1,200 per year
• Operating & maintenance cost is $0.30 per mile
• Estimated annual travel is 30,000 miles
• If the interest rate is 10% per year, what equivalent cost mile for supplying cars?
13. A variable is normally distributed with a mean of 120 and a standard deviation of 5. Six scores are randomly sampled. What is the probability that the mean of the six scores is above 127?
14. A company produces a large lights. Fixed costs are $60,000 a month. Revenue is $12 per fixture. Variable cost is $X per light. They produce 10,000 of these lights each month. What would the variable cost ($) per light have to be in order for the company to break even?
15. The Government raised the average fuel efficiency standard to 35.5 mpg for new cars and new light trucks by the year 2016. The rules cost consumers an average of $926 extra when they buy a new car or truck. Assume a person purchases a new car in 2002 that gets 35.5 mpg and keeps it for 2 years (which is 24 months). If the person uses 28 gallons less each month from this new standard, how much will the gasoline have to cost, per gallon, in order for the buyer to recover the extra investment in 2 years? Use an interest rate of 1% per month.
16. The fixed costs at a publisher are $2,134 each year. Each book they sell results in a revenue of $4.21. They produce 4718 books each year. What is the variable cost ($) per text that allows the publisher to break even?
17. A business has taxable income of $150,000.
• What is its marginal tax rate?
• How much will the business pay in federal corporate tax?
• What is this amount as a percentage of the business' taxable income?
18. An asset with a first cost of $350,000 three years ago is sold for 385,000. The was depreciated by the MACRS method and has a book value of $100,800 at time sale.
• Determine if there are any instances of CG, DR or CL.
19. A MACRS-depreciated asset with a 5 depreciated asset with a 5-year recovery period has been sold after 8 years at an amount equal year recovery period at an amount equal to 20% of its first cost, which was $150,000.
• Determine if there are any instances of CG, DR or CL.
• If there are, use an effective tax rate of 30% to determine the amount income effect.
20. An 7-year property asset was removed from service and sold for $500 in year 6. When purchased, the asset was entered into the book with a basis of I= $180,000, S = 5,000. MACRS depreciation was used was used for the entire 7-year recovery period.
• Determine if there are any instances of CG, DR or CL.
• If there are, use an effective tax rate of 35% to determine the amount of income tax effect.
21. Find the combined marginal tax rate for a corporation that has a federal tax rate of 35% and a state tax rate of 5%.
22. Annual operating revenue is $1.2 million with expenses of $0.4 million and $350,000 depreciation on assets. The state imposed a flat rate of 6% on all taxable income.
• Use approach #1 (separate state and federal tax rates) to find:
i. State taxes due
ii. Federal taxes due
iii. Total taxes due
• Use approach #2 (combined marginal tax rate) to find:
i. Combined marginal tax rate tm
ii. Combined taxes due using tm
• What is the effective (average) tax rate?