Question

You’ve collected the following information from your favorite financial website.

52-Week Price		Stock (Cur div)	Div Yld %	PE Ratio	Close Price	Net Chg
Hi	Lo
77.40	10.43	Palm Coal .36	2.6	6	13.90	–.24
55.81	33.42	Lake Lead Grp 1.54	3.8	10	40.43	–.01
131.08	70.25	SIR 2.75	3.1	10	89.12	3.07
50.24	13.95	DR Dime .80	5.2	6	15.43	–.26
35.00	20.74	Candy Galore .32	1.5	28	??	.18

According to your research, the growth rate in dividends for SIR for the next five years is expected to be 21 percent. Suppose SIR meets this growth rate in dividends for the next five years and then the dividend growth rate falls to 5.75 percent indefinitely. Assume investors require a return of 15 percent on SIR stock.

According to the dividend growth model, what should the stock price be today? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
  
Current stock price            $

Answer 1

Step-1, Dividend for the 5 years

Dividend in Year 1 (D1) = $3.33 ($2.75 x 121%)

Dividend in Year 2 (D2) = $4.03 ($3.33 x 121%)

Dividend in Year 3 (D3) = $4.87 ($4.03 x 121%)

Dividend in Year 4 (D4) = $5.89 ($4.87 x 121%)

Dividend in Year 5 (D5) = $7.13 ($5.89 x 121%)

Step-2, Price of the stock at the end of Year 5

Stock Price in Year 5 (P5) = D5(1 + g) / (Ke – g)

= $7.13(1 + 0.575) / (0.15 – 0.0575)

= $7.54 / 0.0925

= $81.55

Step-3, Stock Price today

Stock Price today is the Present Value of the future dividend plus the present value of the share price in Year 5

Current Stock Price = D1/(1 + r)¹ + D2/(1 + r)² + D3/(1 + r)³ + D4/(1 + r)⁴ + D5/(1 + r)⁵ + P5/(1 + r)⁵

= [$3.33 / (1 + 0.15)¹] + [4.03 / (1 + 0.15)²] +[$4.87 / (1 + 0.15)³] +[$5.89 / (1 + 0.15)⁴] + [$7.13 / (1 + 0.15)⁵] + [$81.55 / (1 + 0.15)⁵]

= [$3.33 / 1.15] + [$4.03 / 1.32250] + [$4.87 / 1.52088] + [$5.89 / 1.74901] + [$7.13 / 2.01136] + [$81.55 / 2.01136]

= $2.89 + 3.04 + 3.20 + 3.37 + 3.55 + 40.54

= $56.60 per share

“Therefore, the Current Stock Price = $56.60”