Private Corp. is a privately held firm that builds and sells widgets globally. The business has prospered in the last few years, but the owners are afraid the growth may be slowing down. To that end, the Finance division started looking at competitors and came up with the following table:

EPS

Dividends$/$Share

Stock Price

ROE

R

Debt Rating

Yield

ABC Corp.

$$1\mathrm{.}30$

$$0\mathrm{.}16$

$$25\mathrm{.}34$

$8\mathrm{.}50\%$

$8\mathrm{.}00\%$

AA

$3\mathrm{.}15\%$

XYZ Inc.

$$1\mathrm{.}95$

$$0\mathrm{.}23$

$$29\mathrm{.}85$

$10\mathrm{.}50\%$

$13\mathrm{.}00\%$

A

$3\mathrm{.}56\%$

Widgets Inc.

$-$$$0\mathrm{.}37$

$$0\mathrm{.}14$

$$22\mathrm{.}13$

$9\mathrm{.}78\%$

$12\mathrm{.}00\%$

BBB$+$

$4\mathrm{.}04\%$

JKL Corp.

$$0\mathrm{.}50$

$$0\mathrm{.}05$

$$28\mathrm{.}56$

$9\mathrm{.}00\%$

$11\mathrm{.}50\%$

BB$+$

$6\mathrm{.}12\%$

RTS Systems

$$1$:$00$

$$0\mathrm{.}17$

$$25\mathrm{.}12$

$11\mathrm{.}00\%$

$14\mathrm{.}00\%$

BB

$8\mathrm{.}02\%$

OAZ Technologies

$$1\mathrm{.}10$

$$0\mathrm{.}18$

$$23\mathrm{.}54$

$9\mathrm{.}20\%$

$10\mathrm{.}50\%$

BB

$7\mathrm{.}14\%$

Industry Average

$$0\mathrm{.}91$

$$0\mathrm{.}16$

$$25\mathrm{.}76$

$9\mathrm{.}66\%$

$11\mathrm{.}50\%$

$-$

$5\mathrm{.}34\%$

While gathering the data above, the Finance division noted that Widgets Inc. took an accounting write$-$off last year that caused the negative earnings. According to the same note, the impact of that write$-$off was $$1\mathrm{.}20$ per share.

In the past year, Private Corp. had Earnings per Share of $$3\mathrm{.}25$ and paid a total dividend of $$40,000.$ The company is supported only by equity with no debt. There are a total of $50,000$ shares outstanding. Last year the Return on Equity was $18\%$ and the owners believe the required rate for the whole company is $15\%.$ Private Corp's debt rating is regarded by investors as BB$.$

Suppose the company keeps growing at the same rate. What is the value per share of the stock of Private Corp?

Since the owners are skeptical the growth can remain so high going forward, they hired an external firm to perform a detailed market research concerning Private Corp's business. The conclusion from this study was that Private Corp will probably be able to grow at the current rate for about $5$ years, but after that will most likely slow down to the industry average. The market research firm also concluded that the company is not as risky as the owners assume and believe the required return should be in line with the industry average required return. If the market research firm is correct, what should the stock price of Private Corp be$?$

What is the industry average price$-$earnings ratio? What about Private Corp's price$-$earnings ratio? Explain the relationship between those two numbers.

Assume the market research firm is correct and the growth rate does indeed slow down to the industry average in $5$ years. Assuming a constant payout ratio, what is the new Return on Equity?

After looking at all the numbers, the owners of Private Corp. decided that they should pursue a more aggressive growth plan. To that end, they decided to issue debt to fund new projects. After discussing with their banker, the Finance division concluded that they should be able to issue a debt offering at a cost of $2\%$ of the notional value. Management is comfortable issuing $$1\mathrm{.}25$MM in new debt maturing in $5$ years, but the Finance division imposed a $5\%$ coupon a year. Management believes they will be able to raise $$1\mathrm{.}25$MM in capital minus the initial cost of issuance. Are they correct? If so$,$ explain why, if not compute how far off they are from the target $$1\mathrm{.}25$MM$.$

It may be useful to use the identity:

g $=$ ROE x b

which states that the growth rate in dividends depends on the ROE and the retention rate.