# Tax Liability, CAPM, Capital Investment Decisions, etc.

1. (2-16) The Hermann Company has made $150,000 before taxes each of the last 15 years, and it expects to make $150,000 a year before taxes in the future. However, in 2001 the firm incurred a loss of $650,000. The firm will claim a tax

credit at the time it files its 2001 income tax return, and it will receive a check from the U.S. Treasury. Show how it calculates this credit, and then indicate the firm's tax liability for each of the next 5 years. Assume a 40% tax rate on all income to ease the calculations.

2 (7-2) You are given the following set of data:

Historical Rates of Return

Year NYSE Stock Y

1 4.0% 3.0%

2 14.3 18.2

3 19.0 9.1

4 (14.7) (6.0)

5 (26.5) (15.3)

6 37.2 33.1

7 23.8 6.1

8 (7.2) 3.2

9 6.6 14.8

10 20.5 24.1

11 30.6 18.0

Mean = 9.8% 9.8%

Standard Deviation = 19.6% 13.8%

a. Construct a scatter diagram showing the relationship between returns on Stock Y and the market, and then draw a freehand approximation of the regression line. What is the approximate value of the beta coefficient? If you have a calculator with a linear regression function or a spreadsheet, check the approximate value of beta obtained from the graph.

b. Give a verbal interpretation of what the regression line and the beta coefficient show about Stock Y's volatility and relative riskiness as compared with those of other stocks.

c. Suppose the scatter of points had been more spread out, but the regression line was exactly where your present graph shows it. How would this effect (1) the firm's risk if the stock is held in a one-asset portfolio and (2) the actual risk premium on the stock if the CAPM holds exactly?

d. Suppose the regression line had been downward sloping and the beta coefficient had been negative. What would this imply about (1) Stock Y's relative riskiness, (2) its correlation with the market, and (3) its probable risk premium?

e. Construct an illustrative probability distribution graph of returns on portfolios consisting of (1) only Stock Y, (2) 1% each of 100 stocks with beta coefficients similar to that of Stock Y, and (3) all stocks (i.e. the distribution of returns on the market). Use as the expected rate of return the arithmetic mean as given previously for both Stock Y and the market and assume that the distributions are normal. Are the expected returns "reasonable"; that is, is it reasonable that ^ = ^ = 9.8% Y M k k ?

3 (13-27) Filkins Fabric Company is considering the replacement of its old, fully depreciated knitting machine. Two new models are available: Machine 190-3, which has a cost of $190,000, a 3-year expected life, and after-tax cash flows (labor savings and depreciation) of $87,000 per year; and Machine 360-6, which has a cost of $360,000, a 6-year life, and after-tax cash flows of $98,300 per year. Knitting machine prices are not expected to rise, because inflation will be offset by cheaper components (microprocessors) used in the machines. Assume that Filkins' cost of capital is 14%. Should the firm replace its old knitting machine and if so, which new machine should it use. Give supporting evidence.

4 (20-5) A. Sadik Industries must install $1 million of new machinery in its Texas plant. It can obtain a bank loan for 100% of the required amount. Alternately, a Texas investment banking firm which represents a group of investors believes that it can arrange for a lease financing plan. Assume that these facts apply:

1) The equipment falls in the MACRS 3-year class.

2) Estimated maintenance expenses are $50,000 per year.

3) The firm's tax rate is 34%.

4) If the money is borrowed, the bank loan will be at a rate of 14%, amortized in 3 equal installments at the end of each year.

5) The tentative lease terms call for payments of $320,000 at the end of each year for 3 years. The lease is a guideline lease.

6) Under the proposed lease terms, the lessee must pay for insurance, property taxes, and maintenance.

7) Sadik must use the equipment if it is to continue in business, so it will almost certainly want to acquire the property at the end of the lease. If it does, then under the lease terms it can purchase the machinery at its fair market value at that time. The best estimate of this market value is $200,000, but it could be much higher or lower under certain circumstances.

To assist management in making the proper lease-versus-buy decision, you are asked to answer the following questions:

a. Assuming that the lease can be arranged, should the firm lease or borrow and buy the equipment? (Hint: In this situation, the firm plans to use the asset beyond the term of the lease. Thus, the residual value becomes a cost to leasing in Year 3. Also, there is no Year 3 residual value tax consequence, as the firm cannot immediately deduct the Tear 3 purchase price from taxable income).

b. Consider the $200,000 estimated residual value. Is it appropriate to discount it at the same rate as the other cash flows? What about the other cash flows - are they all equally risky? (Hint: Riskier cash flows are normally discounted at higher rates, but when the cash flows are costs rather than inflows, the normal procedure must be reversed).

#### Solution Preview

Please see the attached file. The text here may not be printed correctly due to formatting issues with tables / charts/ symbols.

1.

The firm can carry back credit for the tax paid for the last two years.

So prior years

Year 1999 2000

Profit earned 150000 150000

Carry back Credit 150000 150000

Adjusted Profit 0 0

Tax payable 0 0

Tax previously Paid @40% 60000 60000

tax refund 60000 60000

Total check to be received from US treasury 120000

Future years

Year 2002 2003 2004 2005 2006

Estimated profit 150000 150000 150000 150000 150000

carry Forward Credit 150000 150000 50000 0 0 The amount of loss of $650000 will exhaust in year 2004

Adjusted profit 0 0 100000 150000 150000

tax parable @40% 0 0 40000 60000 60000

2.

Historical Rates of Return

Year NYSE Stock ...

#### Solution Summary

This post answers five different question on corporate finance. The problems are solved in Excel for easy understanding.