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Homework II

December 29, 2020
(20)1.Common stocks A, B, C, and D had the following quarterly returns.
A B C D
0.06 0.09 0.12 0.07
0.10 0.08 0.15 0.13
0.05 0.16 -0.06 0.04
-0.09 -0.10 0.08 0.09
0.12 0.05 0.11 0.15
0.08 0.12 0.14 0.12
0.11 0.13 0.09 0.08
-0.06 0.03 0.08 0.10
0.07 -0.04 -0.07 0.06
0.08 0.07 0.13 0.09
a) Determine the expected quarterly return, and standard deviation of each stock.
b) Determine the correlations among them.
c) What is the expected return and standard deviation of a portfolio comprised of 25% stock A, 15% stock B, 30% stock C, and 35% stock D.

(10)2a. Given the information that follows, prepare a cash budget for the XYZ Store for the first six months of 2012.
• All prices and costs remain constant.
• Sales are 85% for credit and 15% for cash.
• With respect to credit sales, 45% are collected in the month after the sale, 35% in the second month, and 20% in the third. Bad-debt losses are insignificant.
• Sales, actual and estimated, are:
October 2011 $275,000 March 2011 $340,000
November 2011 350,000 April 2011 300,000
December 2011 320,000 May 2011 375,000
January 2011 250,000 June 2011 280,000
February 2011 300,000 July 2011 370,000
• Payments for purchases of merchandise are 80% of the following month’s anticipated sales.
• Wages and salaries are:
January 2012 $40,000 April 2012 $65,000
February 2012 45,000 May 2012 55,000
March 2012 50,000 June 2012 52,000
• Rent is $4,000 a month.
• Interest of $7,500 is due on the last day of each calendar quarter, and no quarterly cash dividends are planned.
• A tax prepayment of $50,000 for 2012 income is due in April.
• A capital investment of $50,000 is planned in June, to be paid for then.
• The company has a cash balance of $100,000 at December 31, 2011, which is the minimum desired level for cash. Funds can be borrowed in multiples of $5,000. (Ignore interest on such borrowings.)

(10)2b. Use the cash budget worked out in Part (a) and the following additional information to prepare a forecast income statement for the first half of 2012 for the XYZ Store. (Note that the store maintains a safety stock of inventory.)
• Inventory at 12/31/11 was $180,000.
• Depreciation is taken on a straight—line basis on $240,000 of assets with an average remaining life of 10 years and no salvage value.
• The tax rate is 40 percent.

(10)2c. Given the following information and that contained in Parts (a) and (b), construct a forecast balance sheet as of June 30, 2012, for the XYZ Store. (Assume that accounts payable stay the same as at December 31, 2011.)

XYZ Store balance sheet at December 31, 2011
ASSETS LIABILITIES AND EQUITY
Cash $100,000 Accounts payable $100,000
Accounts receivable 427,500 Bonds 500,000
Inventory 180,000 Common stock and retained earnings
Fixed assets, net 240,000 347,500
$947,500 $947,500

(10)3. In order to increase sales from their present annual $35 million, ABC Company, a retailer, is considering more liberal credit standards. Currently, the firm has an average collection period of 30 days. It believes that with increasingly liberal credit standards, the following will result:
Credit Policy
A B C D
Increase in sales from previous level (in millions) $5.5 $4.5 $2.3 $1.1
Average collection period for incremental sales (days) 45 60 90 150
Bad-debt losses on incremental sales 2% 4% 7% 10%
The prices of its products average $30 per unit, and variable costs average $25 per unit. If the company has a before-tax opportunity cost of 20%, which credit policy should be pursued?

(20)4. ABC Construction must replace a number of its concrete mixer trucks with new trucks. It has received two bids and has evaluated closely the performance characteristics of the various trucks. The truck A, which costs $69,000, is top-of-the-line equipment. The truck has a life of eight years, assuming that the engine is rebuilt in the fifth year. Maintenance costs of $3,000 a year are expected in the first four years, followed by total maintenance and rebuilding costs of $12,000 in the fifth year. During the last three years, maintenance costs are expected to be $4,000 a year. At the end of eight years the truck will have an estimated scrap value of $10,000.
The trucks B cost $52,000 a truck. Maintenance costs for the truck will be higher. In the first year they are expected to be $4,000, and this amount is expected to increase by $1,500 a year through the eighth year. In the fourth year the engine will need to be rebuilt, and this will cost the company $18,000 in addition to maintenance costs in that year. At the end of eight years the truck will have an estimated scrap value of $7,000.
a) Using MACRS (5-year property), estimate theafter-tax cash flows related to the trucks? (Use Tax rate of 35%)
b) If ABC Construction’s opportunity cost of funds is 10%, which truck should it accept?
c) If its opportunity cost were 15%, would your answer change?

(20)5. Proposals A, B, C, D, E and F are being considered with money flows over 10 years.
A B C D E F
Investment $35,000 $10,000 $60,000 $45,000 $15,000 $55,000
Net Annual Benefit $7,000 $2,200 $10,000 $12,000 $2,400 $14,000
Salvage Value $3,000 $0 $5,000 $2,000 $500 0
Proposal (A and D) are mutually exclusive, (C and F) are also mutually exclusive, and proposal B depends on C or F. The MARR is set at 8%. a) Which proposal(s) should be selected if the amount of money available for investment is $110,000? b) Formulate the problem with Integer Programming.