Question

use Excel : The Mann company belongs to a risk class for which the appropriate discount rate is 10%. The company currently has 260,000 outstanding shares selling at $107 each. The firm is contemplating the declaration of a $4 dividend at the end of the fiscal year that just began. Assume there are no taxes on dividends. Answer the following questions based on the Miller and Modigliani model, which is discussed in the text.

A. What will be the price of the stock on the ex-dividend date if the dividend is declared?

B. What will be the price of the stock at the end of the year if the dividend is not declared?

C. If the company makes $3.8 million of new investments at the beginning of the period, earns net income of $1.75 million, and pays the dividend at the end of the year, how many shares of new stock must the firm issue to meet its funding needs?

D. Is it realistic to use the MM model in the real world to value stock? Why or why not?

Answer 1

A. What will be the price of the stock on the ex-dividend date if the dividend is declared?

According to the MM approach, the dividend policy of a firm has not effect on the share price but rather the investment policy decides the firm value. The firm could retain the earnings or distribute them in the form on dividends. The investors are satisfied with the firm’s retained earnings, as long as the return on equity capital is more than the equity capitalization rate or the required rate of return on equity. If the returns are less than this discount rate, then the investors would rather have dividends than retained earnings.

Having this in mind, we can say that the total value of the share is simple addition of the dividend value and the intrinsic value. When the dividend is paid out (ex-dividend), the share price of the firm will decrease by an amount equal to the dividend. The ex-dividend share price= 107-4= $103

B. What will be the price of the stock at the end of the year if the dividend is not declared?

If the dividend is not declared and paid out, the share price will remain stable at $107 per share. The MM approach, the dividend policy of a firm has not effect on the share price.

C. If the company makes $3.8 million of new investments at the beginning of the period, earns net income of $1.75 million, and pays the dividend at the end of the year, how many shares of new stock must the firm issue to meet its funding needs?

The required return to the investors is 10%. The return could be in form of capital (value) appreciation or dividend payout, the investors, are neutral, according to the MM model. The calculation for additional funding is as follows-

net income	1,750,000.00
less dividend payout	1,040,000.00	=260000*4
after dividend capital	710,000.00	=1750000-1040000
Equity capital	26,780,000.00	=260000*103	(ex-dividend price)
Current return on capital	2.65%	=(1750000-1040000)/(260000*103)

Additional capital raised through equity will increase the funds available (numerator) as well the invested capital (denominator). Assume the additional number of shares to be raised after dividend is declared is x. We have a required rate of return 10% which can be achieved as follows-

91750000+x*103)/ ((260000+x)*103)= 10%
Solving for x, we get
x= 10,000
total available funds	2,785,150.00	=1750000+10000*103
total available capital	27,815,150.00	=(260000+10000)*103
Return on capital	10.01%	=2780000/27810000

Hence, 10,000 new shares need to be raised at the ex-dividend price of $103 per share.

D. Is it realistic to use the MM model in the real world to value stock? Why or why not?

MM approach ha assumptions, which are unrealistic. Hence, we do not recommend using this model in the real life. Some of the criticism for this model is as follows-

It assumes that a perfect capital market exists, which implies no taxes, no flotation cost, and the transaction cost. These are not observed in the real life situations. Flotation cost, brokerage, commissions etc. need to be considered while using this model in real life.

The tax rates on dividends (income portion) is different from that on value appreciation (capital gains) for most of the investors. Mostly, the income is taxed at a higher rate than the capital gains. Also, dividend is sometimes taxed at two levels- company level and individual investor level. Hence, in real life, most of the investors prefer value appreciations than dividend payout.

MM model assumes that futures profits can be reliably estimated. This is unrealistic assumption. Since the future cash flows and profits are uncertain, the investors prefer current income (dividends) than future growth (capital appreciation).

The MM model can be adjusted to accommodate the implication of quantitative factors (taxes, costs etc.). However, the individual investor preferences for current vs. future income are diverse and cannot be reliably quantified in a simplistic model such as the one proposed MM model. Hence, we cannot use this model in real life as effectively.