Findamentals of Finance

Finance Fundamentals

Fundamentals of Finance

Assuming a par value of $1,000 for each of the following bonds, proper prices would be:

(1 / (1.02500^14))) / .025) + (1 000 / (1.02500^14)) = $1,175.36

(1 / (1.02500^15))) / .025) + (1 000 / (1.02500^15)) = $1,185.72

(1 / (1.03500^7))) / .035)) + (1 000 / (1.03500^7)) = $1,275.15

Assuming zero-coupon bonds with a par value of $1,000, the yield curve for these bonds would look something like this:

This graph is somewhat distorted due to the changes in interval along the horizontal axis, but the general upward curve is still visible (and would taper off more reasonably with an accurate spread represented in the graph; something Microsoft's basic graphing programs are apparently incapable of handling). The liquidity premium theory explains this curve by suggesting that investors essentially demand a premium for the lack of liquidity in bonds that take longer to reach maturity -- having money tied up longer carries increased risks as well as a longer lack of liquidity, so higher returns on these investments are sought. Market segmentation theory, on the other hand, asserts that the prices of short- and long-term bonds are set independently, as the two are not exchangeable types of securities (i.e. different segments of the market determine a need for one or the other type of bond based on specific needs and situations). A higher general demand for short-term bonds, according to this theory, gives them higher prices and lower yields, and lower demand for long-term bonds gives higher yields and lower prices. Finally, preferred habitat theory can be seen as sort of a combination of these two other theories, asserting that consumers have specific maturity targets they seek in their investments (generally shorter-term), and that they require premiums to invest outside of these maturity "habitats."

3) a. If $1.25 represents a 40% dividend payout ratio, earnings per share are $3.13. A six percent return (the required return) would put future earnings at $3.32. ((3.32-3.13)*100)/3.13 = 6.07%

b. 40% (the dividend payout ratio) of $3.32 (future estimated earnings) is $1.33

c. The price of the stock cannot be calculated accurately with the information given, however if its is assumed that the earnings per share (currently $3.13 with dividends of $1.25 and a dividend payout ratio of 40%) represent the 20% return on equity, then the price is simply five times the earnings per share, or $15.65.

d. assuming the dividend payout ratio and return on equity remain constant at 40% and 20% throughout this period, a and the same relationship for the ROE and stock price, in the first year, a dividend of $2 means EPS increases to $5, translating to a stock price of $25; four percent dividend growth the following year becomes $2.08, EPS of $5.20, and a stock price of $26. The stock price essentially grows at the same percentage as the dividend if these relationships remain constant.

e. A stock price of $30 would still be relatively cheap (a P/E of just under 10) given an industry average of a P/E of 15. This also means that the valuation of the stock using the ROE as the P/E is probably inaccurate, as it suggests a price for the stock that is far cheaper than the industry average.