Question

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

52-Week Price		Stock (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
130.98	69.75	SIR 2.25	2.5	10	89.02	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 20 percent. Suppose SIR meets this growth rate in dividends for the next five years and then the dividend growth rate falls to 5.25 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            $

Based on these assumptions, is the stock currently overvalued, undervalued, or correctly valued?

  

Answer 1

This is an application of dividend discount model, according to which current value of a stock is present value of all dividends expected in future. For this question, dividends for first five years is 20% and falls to 5.25% for the years after.

Based on this, the intrinsic value of stock could be calculated as:

where D1, D2, D3,... are dividends in years 1,2,3.... respectively, r is the required rate of return and V5 is the terminal value, which can be mathematically calculated as:

D0 = 2.25

D1 = 2.25 * (1 + 20%) = 2.700

D2 = 2.700 * (1 + 20%) = 3.240

D3 = 3.240 * (1 + 20%) = 3.888

D4 = 3.888 * (1 + 20%) = 4.666

D5 = 4.666 * (1 + 20%) = 5.599

D6 = 5.599 * (1 + 5.25%) = 5.893

Calculating terminal value V5,

V5 = 60.437

Now, using dividend discount model formula,

V0 = 2.348 + 2.450 + 2.556 + 2.668 + 2.783 + 30.048

V0 = $42.85. Answer

According to dividend discount model, the stocks seems to be overvalued, given the intrinsic value is greater than the trading price of stock ( $89.02).