Dr. P.V. Viswanath
1. (20 points) According to the June 30, 2004 balance sheet of Sun Microsystems, it has a net working capital of $2.19b, long-term assets of $7.2b, long-term liabilities (total liabilities less current liabilities) of $2.952b, and stockholders' equity of $6.438b.
2. (20 points) Altria (http://finance.yahoo.com/q/ks?s=MO) has an equity beta of 0.289. You estimate the market risk premium to be 6% per annum. If the yield on the 10-year T-bond is 4.22% (http://www.bloomberg.com), should Altria invest in a project that will have after-tax cashflows to equity of $20b. a year for the first 5 years, and then increasing at the rate of 2% per annum forever? This project will require an initial investment of $500b.
3. (20 points) You have been asked to value a 30-year, $1000 face value bond, issued by CVS with the following features. The coupon rate for the first 10 years will be 6%of the face value. The coupon rate for the second 10 years will be 7% of face value. Thereafter, the coupon payment will increase at the rate of 5% per annum (coupon growth will be based on the dollar coupon the previous year). Write out the time line of cashflows, and estimate the value of this bond, if CVS is rated AA. (AA-rated bonds are trading at a default spread of 0.25% over the 10-year treasury bond rate of 4.50%.)
4. (20 points) You have data for the returns on Time Warner for the years 1999, 2000, 2001 and 2002. They are 95%, -54%, -8% and -59%. For the same period, the returns on the S&P 500 were 20%, -10%, -13% and -23%.
5. (20 points) In the November 4, 2004 edition of The Economist, an article titled, "Family businesses: Passing on the crown" had the following paragraph:
Because family-owned businesses have a more restricted access to capital than publicly quoted firms, they tend to concentrate in businesses that require relatively few assets, such as trading, consumer goods and retailing. There are exceptions: Vittorio Merloni has built his company into one of Europe's biggest manufacturers of white goods. And family firms are often more diversified than quoted companies—they are, after all, by far the family's main asset, and so the firm's own diversification makes family owners feel more secure. Shareholders in quoted companies have more scope to diversify their own portfolios by buying shares in other firms.
If, indeed, family businesses are more diversified than quoted companies, should they sell for more or less than quoted companies, assuming all other things are comparable?
6. (10 points) A bank can either lend to a corporate customer at an APR of 12% p.a., where the coupon payment schedule is semi-annual, or it can lend to another party, which will make equal monthly payments over a period of 10 years. What is the minimum rate that the bank should quote to this second party, if it does not want to make any less money on the deal than if it lent to its corporate customer?
7. (30 points) Answer any five of the following questions:
According to our assumptions, the relevant debt/equity ratio is 2.952/6.438 = 0.4585
The formula is: Unlevered/firm beta = levered beta/[1+(1-tax rate(D/E))] = 2.772/[1+(1-0.4)(0.4585)] = 2.1739
b. If SUNW issued $1b of equity and bought back an equal amount of debt, its new D/E ratio would be 1.952/7.438 = 0.2624, and its equity beta would be 2.1739*[1+(1-0.4)(0.2624))] = 2.5162
2. The required rate of return on Altria is 4.22 + 0.289(6) = 5.954. Using this discount rate, the present value of the project can be computed as the sum of the present values of the annuity for the first five years plus the growing perpetuity, i.e. (20/0.0595)[1-(1.0595)-5] + 20(1.02)/[(0.0595-2)(1.0595)-5] = 84.36 + 386.84 = $471.20. Since the initial required investment is $500b, the project should not be undertaken.
3. 2. The PV of the cash flows for the first 10 years can be computed simply as . The cash flows for the following 10 years have a present value equal to . The final ten years have cashflows growing at the rate of 5% per annum; the present value of the cashflows during those ten years equals . To this, we need to add the present value of the repayment of the principal, which is . Adding all these values, together, we get 468.98 + 344 + 280.3636 + 248.53 = 1341.87
The covariance of returns can be computed as the sum of the product of deviations, i.e. (2689.75 + 166.25 + 9.75 + 866.25), divided by the number of observations less one. This gives us the covariance as 1244.
b. Time Warner's beta should be greater than one. This can be seen by the fact that its stock returns have a greater amplitude than that of the S&P 500, which can be thought of as the market. (In our case, we can compute the beta as 1244/343 or 3.63, which is greater than one, as we expected.
5. Saying that family businesses should sell for more is the same as saying that quoted companies should sell for less because they are not as diversified. But individual investors can diversify their own portfolios for very little money by buying mutual funds or by otherwise using intermediaries. Hence there is no reason to believe that quoted companies are penalized for not being diversified.
6. If the coupon payment schedule is semi-annual and the APR is 12%, then the effective rate per six months is 6%. The effective annual rate, therefore, is (1.06)2-1 = 12.36%. If this were to be used as the effective annual rate for a loan with monthly repayments, the effective monthly rate on that loan would have to be (1.1236)1/12-1 = 0.009759 or .9759% or an APR of 0.9759x12 = 11.71%
7.a. A 3-month T-bill is not riskless for somebody with a five-year horizon
because that investor would have to reinvest the money after 3 months,
and even though the initial 3-month return is known, the return for the
succeeding three month periods are uncertain; hence the investment itself
is effectively not riskless.