Example Mills Company bond which currently sells for Sh.1080, has a 10% coupon rate and Sh.1000 par value, pays interest annually and has 10 years to maturity. Find YTM of the bond. 10 1 10 ) 1 ( ) 1 ( 1000 100 1080 t t k k d d or, PVIF PVIFA k k d d 10 , 10 , * 1000 * 100 1080 Trial and error We know that when K d = 10% (equal coupon rate), then B 0 = 1000. Thus the discount rate to result in 1080 must be less than 10%. (Try a lower rate if the PV of cash flows at a given rate is lower than the market price of the bond). Try 9% = 100 x 6.418 + 1000 x .422 = 1063.80 (The 9% rate is not low enough to get Sh.1080). Next try 8% = 100 x 6.710 + 1000 x .463 = 1134 Because 1080 lies between 1063.80 and 1134 the YTM must be between 8% and 9%. Because 1080 is closer to 1063.80, the YTM to the nearest whole per cent is 9%. By using interpolation, we find the more precise YTM value to be 8.77% as follows;
77 Interpolation 1134 1063.80 = 70.20 1080 1063.80 = 16.20 YTM = 9% - 16.20 = 9% - 0.2307692 70.20 = 8.77%) Using a financial calculator, we get 8.766%. PREFERENCE SHARES VALUATION This is a type of stock that promises a fixed dividend but at the discretion of the Board of directors. It has preference over ordinary shares in the payment of dividends and claims on the assets it has no maturity date (unless redeemable) and give the fixed nature of the dividend is similar to a perpetuity. Thus the PV of a preferred stock, V p , is k D V p p p (4.7) Where D p is the stated annual dividend, per share and k p is the appropriate discount rate. Example A company had issued a 9% Sh.100 par value preference shares and an investors require a rate of return of 14% on this investment. Find the value of a preference share to investors. D p = 9%*100 = Sh.9 k p = 14 The value of the preference share is, V p = 9/0.14 = Sh.64.29 Example A preferred stock paying a dividend of Sh. 5 and having a required return of 13% will have a value of Sh.38.46 (5÷0.13) VALUATION OF ORDINARY SHARES Common shareholders expect to be rewarded through periodic cash dividends and an increasing share value. It is the expectation of future to dividends and a future selling price (which itself is based on future dividends) that gives value to a share. Cash dividends are broadly defined to mean all cash distributions and are the foundation for valuation of shares. Dividend discount models are designed to compute the intrinsic value of a share under specific assumptions as to the expected growth patterns of future dividends and the appropriate discount rate to apply. Basic stock valuation equation The value of a share is equal to the PV of all future dividends it is expected to provide over an infinite time horizon (from a valuation viewpoint only dividends are relevant).
78 k D k D k D P s s s 1 ( ) 1 ( ) 1 ( ... 2 2 1 1 0 (4.7) Where P 0 = current value of ordinary share k s = required return on ordinary shares D t = per share dividend at end of year t. We illustrate the use of this formula to estimate the value of ordinary stock under three dividend growth assumptions i.e. zero growth in dividends, constant growth in dividends, and variable growth phases.
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- Fall '16