Consider ABC company which does not plan to sell stock, or buy back stock. ABC has 10 million shares of common stock outstanding. The actual price of the stock is $62.00 per share. The book value of the common equity is $40.00 per share. The current fair value of the stock (via a dividend discount model) is $77.04 per share.

The current dividend policy is to payout 80% of earnings as dividends and this is expected to continue forever. The firms ROE is 13% per year and this is also expected to continue forever. Given the risk of the stock, the appropriate discount rate is E[r] = 8% per year.

Part A

WHY is the fair price of the stock different than the book value of the equity?

NOTE: The answer here requires that you understand a very fundamental concept in stock pricing.

Given Answer: The fair price is higher than the book value because ROE > E[r].

Part B

Youve just been hired to advise ABC regarding their dividend policy going forward. ABC currently pays out 80% of their PAT in the form of dividends. They have hired you to advise them regarding whether or not they should: (1) leave the payout ratio unchanged at 80% forever, (2) immediately reduce the payout ratio to 60% - forever, or (3) immediately increase the payout ratio to 100% - forever.

Part C

If ABC takes your advice, what will be the current fair price of the stock? (on a per share basis).

NOTE: Be careful here. Notice that IF the payout ratio stays at 80% then the dividend in one year will be $4.16 per share (you learned how to compute this dividend on the Day 13 problems), BUT if the payout ratio changes, then so too will the dividend paid at time 1. Of course, a change in the payout ratio will likely impact the growth rate of dividends as well.

Part D:

If your advice was good, the fair price computed in Part C will be greater than the current fair price of $77.04. (using a Payout Ratio of 80%)

Compute the percentage change in the fair value of the stock, if ABC takes your advice.

NOTE: There are 4 ways to compute the percentage change in the fair value of the stock. Three of the four are wrong, only one is correct. The correct form is:

Pct. Change = (P^Post P^Pre) / P^Pre

Where P^Pre is the fair stock price before you offered the advice, and P^Post is the fair stock price after they take your advice.

NOTE: The 3 incorrect versions of the percentage change, either (i) swap the order of the prices in the numerator, and/or (ii) divide by the wrong price).

Answer as a decimal, not as a percent, with at least 4 digits of precision.

Part E

If your consulting fee is equal to 10% of the overall increase in fair value, (i.e. the fair value, as computed in Part C (using your advice) versus the fair value of $77.04 - corresponding to an 80% payout ratio), then how big will your consulting fee be? Remember that ABC has 10 million shares outstanding. (Hint: Financial consulting pays pretty darn well!).

Remember to answer in dollars, not millions of dollars without commas or dollar signs.

Hint: your answer should start with 34 million: