Question

Nonconstant growth

Carnes Cosmetics Co.'s stock price is $63.11, and it recently paid a $2.00 dividend. This dividend is expected to grow by 19% for the next 3 years, then grow forever at a constant rate, g; and r_s = 12%. At what constant rate is the stock expected to grow after Year 3? Round your answer to two decimal places. Do not round your intermediate calculations.

%

Answer 1

Current price of stock, PO - S63.11 Recently paid dividend. DO$2.00 Growth rate, g-19% for next 3 years and thereafter g per year forever RR 12% DI-D0 * ( 1 + g )-S2.0 * ( 1 + 19% )-$2.38 D2 = $2.38 * ( 1 + 1996) = $2.8322 D3 $2.8322(119% S3.370318 D4- $3.370318 (1+g) Terminal value ofstock at the end ofyear 3,P3-D4/(RR-g) P3 = $3.370318 * ( 1 g ) / ( 1296-g )

Current price of stock, PO - Present value of dividends and terminal value of stock $63.11 = $2.38 * PVIE(12%, 1) + $2.8322 * PVIF(12%. 2) + [S3.370318 +53.3703 18 * ( 1 + g) /( 12%-g ) ] * PVIE(12%. 3) $63.11-$2.38 * 0.8920+ $2.8322 * 0.7972+ [$3.3703 18 + $3.3703 18 * ( 1 + g) / ( 12%-g) ] * 071 18 $63.11-$2.125 102 + $2.2578298 + $2.3989924 + $2.3989924 * ( 1 g) / ( 1 290-g) $63. 11-S6.78 19242 +52.3989924 * ( 1 + g) / ( 1290-g) $63. 11-S6.78 19242-$2.3989924 * ( 1 + g) / ( 1290-g) $56.328076/ $2.3989924-( 1 g) / ( 1290-g) 23.47989-( 1 + g) / ( 12%-g) 23.47989 * ( 12%-g) ( 1 + g) 2.8175868- 23.47989g(1+g) 2.8175868-1- g+ 23.47989 * g 2.8175868 - 1 - 24.47989 *g g = 2.8175868/2447989 - 0.115098 11.5098 % -11.51% (Rounded) A ns : Constant growth rate expected to grow after Year3, g - 11.51 %