Amanda Monaco has just inherited her father's company. Prior to his death, Mr$.$ Monaco was thesole stockholder, and he left the entire company tohis only daughter. Although Amanda has worked for the firm for many years as a commercial artist, she does not feel qualified to manage the operation. She has considered selling the firm while operation.

She has considered selling the firm while it is still a viable operation and before her father.$\text{'}$

rate. Amanda realizes that selling the firm will result in losing control, but her father granted her a long$-$term contract that guarantees employment or a generous severance package. Furthermore, if Amanda were to sell for cash, she should receive a

substantial amount of money, so her financial position would be secure$.$

Even though Amanda would like to sell out, she has enough business sense to realize that she does not know how to place an asking price $($a value$)$ on the firm. The Internal Revenue Service $($IRS$)$ had established a value on her father's stock of $$100$ established a value on her father's stock of $$100$ a share, and since he owned $100,000$ shares, the value of the company for estate tax purposes was $$10,000,000.$ Amanda thought that was a reasonable amount but decided to consult with Sophie Ryer, the CPA who completed the estate tax return.

Ryer suggested that the firm could be valued using a discounted cash flow method in which the using a discounted cash flow method in which the current and future dividends are discounted back to the present to determine the value of the firm. She explained to Amanda that this technique, the dividend$-$growth model, is an important theoretical model used for the valuation of companies. In addition, she suggested that the price$/$earnings

ratio of similar firms may be used as a guide to the ratio of similar firms may be used as a guide to the value of the firm. Amanda asked Ryer to prepare a valuation of the stock based on P$/$E ratios and the dividend$-$growth model. While Amanda realized that she could get only one price, she requested a range of values from an optimistic price to a minimum, rock bottom value. To aid in the valuation process, Ryer assembled the following information. The firm earned $$8\mathrm{.}50$ a share and distributed $60$ percent in cash dividends during its last fiscal year. This payout ratio had been maintained for several years, with $40$ percent of the earnings being retained to finance future growth. The per$-$share five years were as follows: future growth. The per$-$share five years were as follows:

Year

$20$x$1$

$20$x$2$

$20$x$3$

$20$x$4$

$20$x$5$

EPS

$$6\mathrm{.}70$

$7\mathrm{.}40$

$7\mathrm{.}85$

$8\mathrm{.}20$

$8\mathrm{.}50$

Publicly held firms in the industry have an average P$/$E ratio of $12,$ with the highest being $17$

and the lowest $9.$ The betas of these firms tend to be less than $1\mathrm{.}0,$ with $0\mathrm{.}85$ being typical. While the firm is not publicly held, it is similar in structure to other firms in the industry. It is$,$ however, perceptibly smaller than the publicly held firms. The Treasury bill rate is currently $5\mathrm{.}2$ percent, and most financial analysts anticipate that the market as a whole will average a return of $6$ to $6\mathrm{.}5$ percent greater than the Treasury bill rate.

Amanda has come to you to help devise a financial plan after the company is sold. Such a plan would encompass the construction of a well$-$diversified portfolio with sufficient resources to meet temporary needs for cash. You do not want to blindly accept the

IRS estate value of $$10,000,000.$ Obviously, if the firm could be sold for more, that would be beneficial to your client. In addition, you want an indication of the value Ryer may place on the firm, so you resolve to answer the following questions:

$1.$ Based on the background information, what are the highest$/$lowest values of the stock based on P$/$E ratios?

$2.$ What has been the firm$$s earnings growth rate $($the rate of growth from $$6\mathrm{.}70$ to $$8\mathrm{.}50)$ for the prior five years?

$3.$ What are the highest and lowest values of the stock based on the dividend growth model?

$4.$ What assumptions must be made to determine these values using these two techniques?

$5.$ Explain the impact each of the following would have on valuation of the stock:

a$)$ The anticipated return on the market rises.

b$)$ The rate of growth declines

c$)$ The average P$/$E is $15$ instead of $12.$

$6.$ If the estate tax rate is $35$ percent, what is the implication of a valuation if less than $$100$ per share?