CFP Topic 29: Bond and Stock Valuation Concepts

Key Summary for Duration

1. For zero-coupon bonds, time to maturity equals the duration. 2. For coupon bonds, the duration is always less than the time to maturity. 3. The longer the maturity of a bond, the greater the duration and the greater the price volatility. 4. The smaller the coupon for a bond, the greater the duration and the greater the price volatility. 5. The greater the duration for a bond, the greater the interest rate risk. If interest rates are expected to rise, the manager will try to seek to shorten duration by trying to buy bonds with larger coupons and shorter maturities. If interest rates are expected to fall, the manager will seek to lengthen duration by trying to buy bonds with small coupons and longer maturities.

Convexity

Convexity is a measure of the curvature in the relationship between bond prices and bond yields that demonstrates how the duration of a bond changes as the interest rate changes. Convexity is used as a risk-management tool, and helps to measure and manage the amount of market risk to which a portfolio of bonds is exposed. While duration appears adequate for measuring interest rate sensitivity for small changes in bond yields, convexity measurement is necessary to obtain price-yield relationships that are larger. Prices of bonds with high convexity increase more when yields decrease and decline less when yields increase.

Modified Duration

The concept of modified duration is used to measure the effect of interest rate changes on a bond's price. Given the duration, one can use the formula for modified duration to estimate the effect on the bond's price for shall change in interest rates.

Zero-Growth Rate Model (Preferred Stock)

The security with a zero-dividend growth rate is treated as a perpetuity, like preferred stock. Simply divided the present dividend, which presumably is the same as all future dividends, by the appropriate discount or capitalization rate to produce the intrinsic value. Example: a stock pays a dividend of .50 per share, with no growth expected. If a cap rate of 15% is selected, based on riskiness involved, the intrinsic value is: .50 / .15 = $3.33

Multiple Growth Rates

With multiple growth rates of dividends (dividends are expected to grow at one rate for an initial period, followed by a different growth rate thereafter), the procedure is to separately discount each set of dividends at its expected growth rate and total the results to determine the stock's intrinsic value. Question #32 on page 29.21 is this kind of problem.

Modified Duration Formula & example

An investor has purchased bonds that have a yield to maturity of 6.5%; the duration for the is bonds is 11.6 years. The investor wants to invest $40,000 in the bonds. If the interest rates rise by one-half percent of a percent, the change in price of the bonds is estimated by the formula as follows: Change in the bond price = -(11.6) x [(.005) / (1 + .065)] = -(11.6) x (.0047) = -0.0545, or -5.45% The change will mean a drop in the bonds' price of 5.45%, or a loss of (0.0545)($40,000) = $2,180

Book Value

Book value is the value of each stock share per the books and based on historical cost. BV = total stockholder equity - liquidation value of the preferred stock / outstanding common shares If market price exceeds book value it may mean that the market looks favorably on the stock. If the price is below book value, the expectation by value investors is that buying now will lead to substantial gains over the long term.

Price/Free Cash Flow

Companies that generate more cash can reinvest in their businesses, reduce debt, buy back stock or pay dividends. Free cash flow is a company's cash earnings from operations (net income plus depreciation and amortization, adjusted for working capital changes) and subtracting plant, property and equipment purchases and dividend payouts for the previous 12 months. The more cash left over, the better. The more free cash flow, the lower the price/free cash flow (P/FCF) ratio would be. Therefore, low price to free cash flow ratios are favorable. A company's price/free cash flow ratio can be measured against a market index average or an industry index average. It can also be measured against the company's historic data to identify trends. Reasons that free cash flow is such a valuable number is that it is free from accounting assumptions. Unlike earnings, which is net of non-cash charges such as depreciation and amortization, free cash flow gives us a clear idea of how much cash the company has after capital spending. Companies with a lot of assets that are being depreciated may have lower P/E ratios but higher P/FCF ratios. Since no cash is actually spent on depreciation, it may be deceiving to rely on P/E alone to judge the company's earning power. What a company does with its free cash flow has a big effect on how valuable that cash flow is to an investor. For example, a company that used its free cash flow on low-returning projects is probably a less attractive investment than one that reinvests cash flow at a higher rate of return.

Analyzing P/E

Divide both sides of P = D1/(k-g) by the stock's expected earnings per share (E1). This will create an equation where P/E = payout ratio divided by the quantity of the discount rate minus the growth rate. See image Consider the Battel Corporation. This year's cash dividends are DIV0 = $2.00; the firm's growth rate is g = 2%. The corporation's cost of equity capital is k = 10%, and its initial value is $25.50 per share. Assume Battel's expected earnings per share are E1 = $3.00. Under these circumstances, Battel's price/earnings ratio is 8.5: P/E = (D1/E1)/(k-g) = ($2.04/$3.00)/(0.10-0.02) = 8.5 Therefore, the price of Battel Corporation per share should be around 8.5 times that of its earnings per share. In equilibrium, a stock's price/earnings ratio has three primary determinants: 1. A risk-adjusted discount rate that exceeds the stock's average growth rate, k 2. A growth rate, g 3. A cash dividend payout ratio, D1/E1

Price/Earning Ratio (P/E)

Fundamental common stock analysts utilize a well-known procedure to estimate the value of a share of common stock. They prepare an estimate of a stock's earnings per share and an estimate of the stock's price/earnings ratio, and then multiply these two quantities to obtain their estimate of the share's value: P/E = Price/Earnings per share The P/E ratio will be higher for: greater expected payout ratios greater expected growth rates in EPS, and smaller required rate of return.

Bond Duration

How can an investor decide which has a higher interest rate risk - a high-coupon, long-maturity bond or a low-coupon, short-maturity bond? Duration analysis gives the answer by combining both interest rate risks: 1) its impact on the price of the security, and 2) its impact on the reinvestment rate opportunity. A bond's duration is the weighted-average number of years it takes for the investor to receive the present value of all the bond's future cash flows. A bond's duration will always be less than its years to maturity, except for zero-coupon bonds, where duration and maturity are equal. A bond's duration is a function of its current price, time to maturity, yield to maturity and coupon rate.

Intrinsic Value of a Stock Definition

Investment value of the stock based on estimated future cash flows, generated by an investment in the stock.

Keystrokes for Calculating Duration

Investor buys a bond for $906.93 because comparable bonds are yielding 11%. The bond has a $1,000 face, or par, value; an 8% coupon payable annually; and 4 years to run before maturity. 0, blue g, CFo 80, blue g, CFj 160, blue g, CFj 240, blue g, CFj 4320, blue g, CFj 11, i yellow f, NPV The number before the blue g key is determined by the # of the year x the cash inflow that for that year. In other words 80 = year 1 x the $80 coupon payment for that year. Note: be sure to include the first entry which is the initial year and it = 0. Make sure to know how to do Questions 38 - 41 on page 29.22.

Justified P/E Multiplier

JP/EM = Est. div. payout ratio / (r - g) Where: r = Investor's required rate of return g = Investor's estimate of the growth rate in dividends

Price/Earnings/Growth (PEG)

PEG is calculated by dividing the P/E ratio by the sum of the estimated earnings growth rate and dividend yield. It indicates what price the market has placed on earnings expectations.

Price/Earnings Ratio

Price per share / Earnings per share

Required Rate of Return using Constant Dividend Growth Model

The constant dividend growth model formula can be rearranged as follows to solve to for the client's required rate of return. Where: r = Investor's required rate of return, based on risk D1 = Next (not the present) annual dividend P = Price of the stock g = Expected annual growth rate in the dividends. Example: The most recent dividend on a stock was $2 and it is expected to grow by 5% per year for the foreseeable future. If the intrinsic value of the stock is $25, the client's rate of return is what? = [($2 x 1.05)/$25] + .05 = .084 + .05 = .134 or 13.4%

Price/Sales

This is can be used for new companies working to grow fast while in the beginning stages of development. The explosion in Internet stocks forced investors to look for ways to value companies with lots of potential, but no earnings. Moreover, many investors do not trust net earnings anymore, since they are often manipulated through write-offs and other creative accounting practices. Sales are much harder to disguise. The price/sales ratio is the company's price divided by its sales (or revenue). This value is arrived by dividing revenue by the number of shares outstanding, and then dividing the revenue per share into the price per share. But because the sales number is rarely expressed as a per-share figure, it's easier to divide a company's total market value by its total sales for the last 12 months. Price/Sales works well in analyzing large-cap companies, whose sales are so great, that it is closer to their market capitalization. The ratio is less appropriate for service companies like banks or insurers that don't really have sales. Most value investors set their P/S hurdle at 2 and below when looking for undervalued situations. Again, with ratios, it is better to compare a company's P/S value to its competitors and its own history.

Price/Free Cash Flow

This uses operating cash flow which is net of any new investment or cash remaining after satisfying capital expenditures.

Constant Dividend Growth Model formula

Where: D1 = Next (not the present) annual dividend r = Investor's required rate of return, based on risk g = Expected annual growth rate in the dividends. Note: Make sure to remember how to calculate the investor's required rate of return based on risk (from section 27). The problem may require that I calculate this first and then solve for the valuation based on the constant dividend growth model.