Industrial Economics Homework
Problem 1: A typical bank offers you a Visa credit card that charges interest on unpaid balance at 1.5% per month compounded monthly. This means that the nominal interest (annual percentage) rate for this account is A and the effective annual interest rate is B. Suppose your beginning balance was $500 and you make only the required minimum monthly payment (payable at the end of each month) of $20 for the next 3 months. If you made no new purchases with this card during this period, your unpaid balance (after your 3rd payment) will be C at the end of 3 months. What are the values of A, B, and C?
Problem 2: In January 1989, C&S, the largest mutual saving bank in Georgia, published the following information: interest, 7.55%; effective annual yield, 7.842%. The bank did not explain how the 7.55% is connected to the 7.842%, but you can figure out that the compounding scheme used by the bank should be ________.
Problem 3: How many years will it take an investment to double if the annual interest rate is 12% compounded (a) annually, (b) semiannually, (c) quarterly, (d) monthly, (e) weekly, (f) daily?
Problem 4: Suppose that $1500 is placed in a bank account at the end of each quarter over the next 10 years. Determine the total accumulated value (future worth) at the end of 10 years where the interest rate is 8% compounded quarterly.
Problem 5: What equal-payment series is required to repay the following present amounts?
a. $10,000 in 4 years at 10% interest compounded annually with 4 annual payments.
b. $80'000 in 30 years at 9% interest compounded monthly with 360 monthly payments.
c. $6,000 in 5 years at 8% interest compounded quarterly with 20 quarterly payments.
d. $5,000 in 4 years at 10% interest compounded semiannually with 8 semiannual payments.
Problem 6: Mendi wants to deposit $1000 in her bank account at Dai Bank at the end of each quarter over the next 5 years, but she doesn't know how to figure out the future worth at the end of 5 years. Help her figure it out when the interest rate is:
a. 12% compounded annually.
b. 12% compounded semi-annually.
c. 12% compounded quarterly.
d. 12% compounded monthly.
e. 12% compounded continuously.
Problem 7: Tim took out a loan from Dai Bank. What equal monthly payments will Tim be required to repay the loan of $50,000 over 10 years if the rate of interest is 5% compounded daily?
Problem 8: While snooping around in Professor Sadighian's office, Jason uncovered an equation that describes the conversion of a cash flow into an equivalent equal-payment series with n = 8. Help him figure out the original cash flow by drawing the original cash flow diagram. Assume an interest rate of 10% compounded annually.
Problem 9: For computing the equivalent equal-payment series (A) of the following cash flow with i = 10%, which of the following statements is (are) correct?
a. A=100(F/A, 21%, 4)(A/F, 10%, 8)
b. A=[100(P/F, 10%, 2) + 100(P/F, 10%, 4) + 100(P/F, 10%,6) + 100(P/F, 10%, 8)](A/P, 10%, 8)
c. A=100(A/F, 10%, 2)
d. A=[100(F/P, 10%, 2) + 100(F/P, 10%, 4) + 100(F/P, 10%,6) + 100(F/P, 10%, 8)](P/F, 10%, 10)(A/F, 10%, 8)
e. A=100(F/A, 10%, 4)(A/F, 10%, 8)
f. A=100(P/A, 21%, 4)(A/P, 10%, 8)
g. A=100(P/A, 10%, 4)(A/P, 10%, 8)
Problem 10: A couple with a 7-year-old daughter wants to save for their child's college expenses in advance. Assuming that the child enters college at the age 18 (the couple has 11 year to collect the money). They estimate that an amount of $24,000 per year in terms of today's dollars will be required to support the child's college expenses for 4 years. The future inflation rate is estimated to be 8% per year and they can invest their savings at 12% compounded monthly.
a. Determine the equal monthly amounts the couple must save until they send their child to college.
b. If the couple has decided to save only $1,000 each quarter, how much will the child have to borrow each year to support her college education?
Problem 11: Suppose you have the choice of investing in (1) a municipal bond that costs $1,000 today, pays $67 in interest semiannually, and matures at the end of 5 years or (2) zero-coupon bond that costs $525 today, pays nothing during its life, and then pays $1,000 after 5 years. Which bond would provide the higher yield to maturity (or return on your investment)?
Problem 12: NPI Corp., ice cube producer company, generates a continuous constant after-tax cash flow at the rate f(t) = $250,000 for a 10-year planning horizon.
a. Find the present value of this cash flow stream over 10 years at 12% compounded continuously.
b. The profit per year is expected to increase continuously because of increased productivity and the new cash flow rate can be expressed as f(t) = 250,000(2.0-e-0.2t) where t is time in year. Find the present value of this cash flow stream.
c. Productivity increases as in part b, but competition reduces the profit continuously by 8% per year. Find the present value of the cash flow.
Problem 13: State the immediate effect (increase, decrease, no effect) of the following transactions on:
a. Current Ratio (assume current ratio = 1 at start of each question)
b. Quick Ratio (assume current ratio = 1 at start of each question)
c. Working Capital
d. ROE
Transactions:
1. Shares of common stock worth $150,000 are issued.
2. Goods worth $40,000 were destroyed by fire. Salvage value of some of the partly burnt goods was $4,000, which is received in cash. The goods were not insured.
3. Equipment costing $90,000 with accumulated depreciation of $40,000 is sold for $30,000 in cash.
4. Inventory worth $130,000 is sold on account for $170,000.
5. A machine costing $150,000 is purchased. $30,000 is paid in cash, and the balance will be paid in equal installments for the next three years (and consider that the cost attributed the same year is $30,000, too).
6. Payments of $80,000 are made to suppliers.
Problem 14: Spectrum Associates' financial data is show as follows (figures in thousands):
|
|
Year 1
|
Year 2
|
Year 3
|
Year 4
|
|
Accounts Receivable
|
500
|
800
|
600
|
750
|
|
Cash
|
200
|
100
|
200
|
200
|
|
Other Current Assets
|
100
|
200
|
250
|
100
|
|
Inventories
|
400
|
800
|
1500
|
2150
|
|
|
1200
|
1900
|
2550
|
3200
|
|
Accounts Payable
|
600
|
700
|
825
|
800
|
|
Accrued Salaries
|
300
|
400
|
495
|
400
|
|
Other Current Liabilities
|
100
|
150
|
165
|
450
|
|
|
1000
|
1250
|
1475
|
1650
|
Compute the current and quick ratios for years 1 through 4.
Comment on the short-term liquidity position of Spectrum Associates.
Problem 15: Consider the discrete cash flow patterns shown in the accompanying illustrations
a. Compute the present value of each cash flow series using the conventional interest formulas at i = 10%
b. Compute the present value of each cash flow series using the discrete transform results at i = 10%
c. Compare the annual equivalent value of each cash flow series over 20 years.
Problem 16: Find the present value of the following quadratic cash flow at 10% interest compounded continuously, f(t) = $400 + 90t - 6t2
a. if 0 ≤ t ≤ 10
b. if 0 ≤ t ≤ ∞
Problem 17: Use the data from the financial statements of Dell and Gateway to answer the following questions.
a. Calculate the following ratios for the most recent period, 2003: ROE, ROC, ROA, Profit Margin, Total Asset Turnover, Receivable Turnover, Inventory Turnover, Payables Turnover Current, Quick Debt/Equity.
b. Calculate the common-size balance sheet and income statement for year 2003.
c. Comment on the financial health of the two organizations from the point of view of a lender who has been asked to make a $200 million loan to each of the companies.
d. Estimate Dell's and Gateway's 2003 net sales if sales were recognized as cash is collected rather than on the accrual basis. Comment on the significance of the difference between your estimate and reported sales.
e. Suppose you are interested in forecasting future sales for Dell and Gateway. Describe the methods that can be used. Forecast Dell's and Gateway's sales for 2006. Justify your answer.
Attachment:- Assignment File.rar