1. Review
Bond Yields and Prices

2. Learning Objectives Calculate the price of a bond.
Calculate major bond yield measures, including yield to maturity, current yield, coupon rate
Account for changes in bond prices.
Explain and apply the concept of duration. 2

3. Bond Valuation Principle
Intrinsic value
Is an estimated value
Present value of the expected future cash flows
Required to compute intrinsic value
Expected future cash flows
Timing of expected cash flows
Discount rate, or required rate of return by investors 10

4. Bond Valuation
Value of a coupon bond with semi-annual payments:
Biggest problem is determining the discount rate or required yield
Required yield is the current market rate earned on comparable bonds with same maturity and credit risk 11

5. Yield to Maturity Yield to maturity (YTM)
Rate of return on bonds most often quoted for investors
Promised compound rate of return received from a bond purchased at the current market price and held to maturity
Equates the present value of the expected future cash flows to the initial investment
Similar to internal rate of return 6

6. Yield to Maturity
Solve for YTM (semi-annual coupons):
Investors earn the YTM if the bond is held to maturity and all coupons are reinvested at YTM 7

7. Reinvestment Risk For: (1) longer-term bonds
(2) bonds with higher coupon rates
(i.e., have more money to reinvest)
NO reinvestment risk for “Zeroes”

8. Bond Price Changes
Over time, bond prices that differ from face value must change
Bond prices move inversely to market yields
The change in bond prices due to a yield change is directly related to time to maturity and inversely related to coupon rate 12

9. Measuring Bond Price Volatility: Duration
Important considerations
Different effects of yield changes on the prices and rates of return for different bonds
Maturity inadequate measure of a bond’s economic lifetime
A measure is needed that accounts for both size and timing of cash flows 14

10. Duration
A measure of a bond’s lifetime, stated in years, that accounts for the entire pattern (both size and timing) of the cash flows over the life of the bond
The weighted average maturity of a bond’s cash flows
Weights determined by present value of cash flows 15

11. Calculating Duration Duration depends on three factors
Need to time-weight present value of cash flows from bond
Duration depends on three factors
Maturity of the bond
Coupon payments
Yield to maturity 16

12. Duration Relationships
Duration increases with time to maturity, but at a decreasing rate
For coupon paying bonds, duration is always less than maturity
For zero coupon-bonds, duration equals time to maturity
Duration increases with lower coupons
Duration increases with lower yield to maturity 17

13. Why is Duration Important?
Allows comparison of effective lives of bonds that differ in maturity, coupon
Used in bond management strategies, particularly immunization
Measures bond price sensitivity to interest rate movements, which is very important in any bond analysis 18

14. Convexity
Refers to the degree to which duration changes as the yield to maturity changes
Price-yield relationship is convex
Duration equation assumes a linear relationship between price and yield
Convexity largest for low coupon, long-maturity bonds, and low yield to maturity 20

15. Duration Conclusions
To obtain maximum price volatility, investors should choose bonds with the longest duration
Duration is additive
Portfolio duration is just a weighted average
Duration measures volatility, which is not the only aspect of risk in bonds 21

16. Common Stock Valuation
Review part 2
Common Stock Valuation
Company Analysis

17. Learning Objectives
The dividend discount model to estimate stock prices
Explain the P/E ratio approach.
Fundamental Analysis : estimate share’s intrinsic value

18. Present Value Approach DDM
Intrinsic value of a security is
Estimated intrinsic value compared to the current market price
What if market price is different than estimated intrinsic value? 3

19. Required Inputs Expected cash flows Dividends paid out of earnings
Earnings important in valuing stocks
Retained earnings enhance future earnings and ultimately dividends
Retained earnings imply growth and future dividends
Produces similar results as current dividends in valuation of common shares 5

20. Dividend Discount Model
Current value of a share of stock is the discounted value of all future dividends 6

21. Dividend Discount Model
Problems:
Need infinite stream of dividends
Dividend stream is uncertain
Must estimate future dividends
Dividends may be expected to grow over time
Must model expected growth rate of dividends and need not be constant 7

22. Dividend Discount Model
Assume constant growth rate in dividends
Dividends expected to grow at a constant rate, g, over time
D1 is the expected dividend at end of the first period
D1 = D0 x (1+g) 9

23. Dividend Discount Model
Multiple growth rates: two or more expected growth rates in dividends
Ultimately, growth rate must equal that of the economy as a whole
Assume growth at a rapid rate for n periods, followed by steady growth 11

24. P/E Ratio Approach P/E ratio can be derived from
To estimate share value
P/E ratio can be derived from
Indicates the factors that affect the estimated P/E ratio 17

25. Other Valuation Techniques
Market-to-book ratio (M/B)
Ratio of share price to per share shareholder’s equity as measured on the balance sheet
Price paid for each $1 of equity
Price-to-sales ratio (P/S)
Ratio of company’s market value (price times number of shares) divided by sales
Market valuation of a firm’s revenues 23

26. Company Analysis

27. P0 = estimated EPS  justified P/E ratio
Fundamental Analysis
Earnings multiple could also be used
P0 = estimated EPS  justified P/E ratio
Stock is under- (over-) valued if intrinsic value is larger (smaller) than current market price
Focus on earnings and P/E ratio
Dividends paid from earnings
Close correlation between earnings and stock price changes 3

28. Required Rate of Return
A function of the riskless rate of return and a risk premium
k = RF + RP
Constant growth version of dividend discount model can be rearranged so that
k = (D1/P0) + g
Growth forecasts are readily available 20

29. Required Rate of Return
Risk premium for a stock regarded as a composite of business, financial, and other risks
If the risk premium rises (falls), then k will rise (fall) and P0 will fall (rise)
If RF rises (falls), then k will rise (fall) and P0 will fall (rise)
Discount rates and P/E ratios move inversely to each other 21

30. Appendix 17-A Financial Ratio Analysis
Five types of ratios used to analyze a firm:
Liquidity: ability to generate cash and meet short-term debt
Asset Management: ability to effectively manage its assets to generate sales and profits
Debt Management: ability to effectively handle its debt
Profitability: ability to generate profits
Value: market value versus accounting values

31. DuPont Analysis XYZ (2004) Industry averages (2004)
ROE = (NI/Sales) (Sales/TA) ((TA/Equity)
= (.0299)(1.042)(4.339) = 13.51%
Industry averages (2004)
= (.0568)(1.23)(1.74) = 12.16%
This analysis suggests that XYZ displays an above average ROE due to its higher leverage factor, and despite the fact it has below average profitability and asset turnover