Question

need help w tables

1. Since 2014, Abercrombie & Fitch (NYSE: ANF) has been paying annual dividends of $0.80 per share. Assume ANF has a cost of equity capital of 9%. The stock has recently traded around $12 per share. Required: a. Assuming the dividend will continue to stay at $0.80 per share on a continuing basis, what is the estimated value per share for ANF? b. Given the difference between the estimated value and the trading price, what inferences can be made? c. What conclusions might we make about the appropriateness of the constant dividend model for ANF? 3 a. Estimated value per share for ANF 4 Dividend 5 Growth in dividends 6 Cost of equity capital re 7 Current stock price 8 $0.80 0.0% 9.0% $12.00

Answer 1

Both the situations below are two variants of Dividend Discount model of stock valuation : Constant growth model and Two-stage DDM model.

The Dividend discount model basically assumes that a stock’s current value is the sum of present values of all the dividends that the stock will yield in the future.

Under constant growth model, it is assumed that the dividend on the stock will grow at a constant rate.

The formula for stock valuation under this model is,

Stock value at time 0 (V0) = D1 / (r-g)

Where, D1 = Dividend at time period 1 (derived as D0 (1+g)

R = Cost of equity

G = Growth rate in dividend

Under two-stage DDM, dividend growth rate will be a certain percentage for some period, then will settle down at another rate until perpetuity. Here, the terminal value of all second-growth rate dividends is first calculated until perpetuity at a constant rate as at the last year expected for the first growth stage of dividend. Then this is discounted back alongwith first growth stage dividends.

Cost of equity capital (r	9%
Growth in dividend (g)	0%
Current price of share (P)	$12
Current dividend (D0)	$0.80

Ans. 1

	End of 2017	End of 2018	End of 2019	Terminal Period
Anticipated dividends	$0.80	$0.80	$0.80	$0.80
Present value factor at 9%	1	0.91743119	0.84167999
Present value as of start of 2017	$0.80	$0.73	$0.67	$8.89
Cumulative present value	$8.89
PV of dividend in perpetuity	$8.89

Here, dividend is expected to remain constant at $0.80

Present value factors are calculated as :( 1/ (1+9%)^0) for end of 2017, since it is t=0, (1/(1+9%)^1) for end of 2018 and (1/(1+9%)^2) for end of 2019

Present value as of start of 2017 for each year is anticipated dividend * Present value factor

For eg. for 2018 it is $0.80 * 0.91743119 = $0.73

  Terminal Value is calculated using Gordon Growth formula mentioned above = D1 / (R – G)

Here, dividends are constant at $0.80, so D1 = $0.80

R = 9% , G= 0%

So, terminal value = $ 0.80 / (9% - 0%) = $8.89

Same is the present value of dividends in perpetuity, since perpetuity means infinite time, applying the formula as at end of 2017, since dividends are constant at $0.80, yields us same value ( $0.80/9%) = $8.89

b. The estimated share value is $8.89 while the current share price is $ 12. So, we can infer that the share is being traded for more than what it is worth. It may be an over-valued share, since its intrinsic value is less than its market value. Thus, it is an expensive buy at the current prices.

c. The constant dividend model is quite unrealistic as the dividends in reality increase or decrease as per Co. performance. Further, constant dividend is lowering the intrinsic value of share for ANF, considering which, it is not quite appropriate.

Ans. 2

	End of 2017	End of 2018	End of 2019	Terminal Period
Anticipated dividends	$0.80	$0.80	$0.80	$12.62
Present value factor at 9%	1	0.91743119	0.84167999
Present value as of start of 2017	$0.80	$0.73	$0.67	$10.62
Cumulative present value	$12.83

Now, here dividend remains constant at $0.80 for 2 years after which increases @ 2.5% until perpetuity. So, dividend for current year 2017 and next two years, 2018 and 2019 will be $0.80.

Terminal Value as at the end of 2019 is calculated as = D1 / (R-G) = D0(1+G)/(R-G)

                                                                                                = ($0.80*(1+2.5%))/(9%-2.5%)

                                                                                                 = $12.62

Further, discounting the terminal value as at the end of 2019 at 9% for 2 years to get present value at the end of 2017 = ($12.62 / (1+9%)^2) = $10.62

Present value of dividends at the end of 2017, 2018 and 2019 is calculated by multiplying dividend by present value factors.

Cumulative present value = $0.80 + $0.73 + $0.67 + $10.62 = $12.83

b. Comparing the value of $12.83 with the stock price of $12, we can say that the stock is under-valued in the market. Its intrinsic value is more than its market price, thus, it is a cheap buy at the current prices.

c. The increasing perpetuity dividend model seems more realistic (since dividends grow will time) and appropriate for ANF since it reflects a better picture of the Company and yields good intrinsic value.