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- 1. Valuation of Long Term Securities Presented by: Ashra Rehmat
- 2. Bond valuation – Important Terms – Types of Bonds – Valuation of Bonds – Handling Semiannual Compounding
- 3. Important Terms • A bond is a long-term debt instrument issued by a corporation or government. • The maturity value (MV) [or face value] of a bond is the stated value. In the case of a US bond, the face value is usually $1,000. • The bond’s coupon rate is the stated rate of interest; the annual interest payment divided by the bond face value. • The discount rate (capitalization rate) is dependent on the risk of the bond and is composed of the risk- free rate plus a premium for risk. Bonds:
- 4. Different types of bonds A perpetual bond is a bond that never matures. It has infinite life. V = I / kd Example: Bond P has a $1,000 face value and provides an 8% annual coupon. The appropriate discount rate is 10%. What is the value of the perpetual bond?
- 5. Types of bonds: • A non-zero coupon-paying bond is a coupon paying bond with a finite life. V = I (PVIFA kd, n) + MV (PVIF kd, n) Bond C has a $1,000 face value and provides an 8% annual coupon for 30 years. The appropriate discount rate is 10%. What is the value of the coupon bond? Coupon Bond Example
- 6. TYPES: • A zero coupon bond is a bond that pays no interest but sells at a deep discount from its face value; it provides compensation to investors in the form of price appreciation (1 + kd)n V= MV = MV(PVIFkd, n) Bond Z has a $1,000 face value and a 30 year life. The appropriate discount rate is 10%. What is the value of the zero-coupon bond?
- 7. Semiannual compounding A non-zero coupon bond adjusted for semi-annual compounding.. (1) Divide kd by 2 (2) (2) Multiply n by 2 (3) Divide I by 2 = I/2 (PVIFAkd /2 ,2*n) + MV (PVIFkd /2 ,2*n) EXAMPLE:- Bond C has a $1,000 face value and provides an 8% semi-annual coupon for 15 years. The appropriate discount rate is 10% (annual rate). What is the value of the coupon bond?
- 8. Preferred Stock Valuation Common Stock Valuation
- 9. Preferred Stock is a type of stock that promises a (usually) fixed dividend, but at the discretion of the board of directors. V = DivP / kP (1 + kP)1 (1 + kP)2 (1 + kP)V = + + ... + DivP DivPDivP Stock PS has an 8%, $100 par value issue outstanding. The appropriate discount rate is 10%. What is the value of the preferred stock? Example:
- 10. Common stock • Common stock represents a residual ownership position in the corporation. • Dividend Valuation Model Basic dividend valuation model accounts for the PV of all future dividends. = S t=1 (1 + ke)t Divt V Divt: Cash Dividend at time t ke: Equity investor’s required return
- 11. Dividend Growth Pattern Assumptions The dividend valuation model requires the forecast of all future dividends. The following dividend growth rate assumptions simplify the valuation process. Constant Growth No Growth Growth Phases
- 12. The constant growth model assumes that dividends will grow forever at the rate g. The growth phases model assumes that dividends for each share will grow at two or more different growth rates. The zero growth model assumes that dividends will grow forever at the rate g = 0. Zero Growth Model Growth Phases Model Constant Growth Model
- 13. Example James Consol Company currently pays a dividend of $1.60 per share on its common stock. The company expects to increase the dividend at a 20 % annual rate for the first four years and at a 13 % rate for the next four years, and then grow the dividend at a 7 percent rate thereafter. This phased-growth pattern is in keeping with the expected life cycle of earnings. You require a 16 % return to invest in this stock. What value should you place on a share of this stock?
- 14. Solution PHASES 1 and 2: PRESENT VALUE OF DIVIDENDS TO BE RECEIVED OVER FIRST 8 YEARS END OF PRESENT VALUE CALCULATION PRESENT VALUE YEAR (Dividend × PVIF16%,t ) OF DIVIDEND Phase 1 1 $1.60(1.20)1 = $1.92 × 0.862 = $ 1.66 2 1.60(1.20)2 = 2.30 × 0.743 = 1.71 3 1.60(1.20)3 = 2.76 × 0.641 = 1.77 4 1.60(1.20)4 = 3.32 × 0.552 = 1.83 Phase 2 5 3.32(1.13)1 = 3.75 × 0.476 = 1.79 6 3.32(1.13)2 = 4.24 × 0.410 = 1.74 7 3.32(1.13)3 = 4.79 × 0.354 = 1.70 8 3.32(1.13)4 = 5.41 × 0.305 = 1.65 = $13.85
- 15. PHASE 3: PRESENT VALUE OF CONSTANT GROWTH COMPONENT Dividend at the end of year 9 = D8 ( 1 + g ) $5.41(1.07) = $5.79 Value of stock at the end of year 8 D9 $ 5.79 $64.33 ke – g (0.16 – 0.07) Present value of $64.33 at end of year 8 = V8 = FV (PVIF16%,8) =($64.33)(PVIF16%,8) = ($64.33)(0.305) = $19.62 PRESENT VALUE OF STOCK V = $13.85 + $19.62 = $33.47
- 16. YIELD TO MATURITY (YTM)
- 17. DEFINITION:- The expected rate of return on a bond if bought at its current market price and held to maturity. Internal rate of return (IRR) It is also known as the bonds internal rate of return.
- 18. Calculating Rates of Return (or Yields) 1. Determine the expected cash flows. 2. Replace the intrinsic value (V) with market price (P0). 3. Solve for the market required rate of return That equates the discount cash flows to the market price. Steps to calculate the rate of return (or Yield).
- 19. Determining Bond YTM Determine the Yield-to-Maturity (YTM) for the annual coupon paying bond with a finite life. P0 = S n t=1 (1 + kd )t I = I (PVIFA kd , n) + MV (PVIF kd , n) (1 + kd )n + MV kd = YTM
- 20. Bond Price - Yield Relationship Discount Bond – The market required rate of return exceeds the coupon rate (Par > P0 ). Premium Bond – The coupon rate exceeds the market required rate of return (P0 > Par). Par Bond – The coupon rate equals the market required rate of return (P0 = Par).
- 21. Yield to maturity Interest rate (or yield) risk Interpolation:- Estimate an unknown number that lies somewhere between to unknown numbers. For example:- The variation in market price of a security caused by changes in interest rates.
- 22. Determining the YTM Julie Miller want to determine the YTM for an issue of outstanding bonds at Basket Wonders (BW). BW has an issue of 10% annual coupon bonds with 15 years left to maturity. The bonds have a current market value of $1,250. What is the YTM?

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