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Price of a Stock, Buy on Margin, Sell Short, Rate of Return

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1. Underwood Industries just paid a dividend of $1.45 per share. The dividends are expected to grow at 25% rate for the next eight years and then level off to a 7% growth rate indefinitely. If the required return is 12%, what would be the price of the stock today?

2. You have ordered your broker to purchase 100 shares each of 2 stocks, TLC and OET. The price of TLC is $49 and OET is $83. You have decided to take advantage of the ability to buy these stocks on margin, using all 50% of the allowed initial margin. (You will put up half the money for these purchases and borrow the rest). The rate on your margin loan is 6%.

a. What is your net worth if TLC changes to $51 and OET changes to $82?
b. What is your rate of return if TLC changes to $50 and OET changes to $80 after exactly one year?
c. If the maintenance margin is 30%, and the price of TLC falls to $42, how low can OETâ??s price change before you get a margin call?

3. You are bearish on IMM stock and KIT stock. Thus decide to sell 250 shares of the IMM short for $28 per share and 200 shares of KIT short for $34 share.

a. If the initial margin is 50%, how much cash will your broker require you deposit?
b. At what price for IMM will you receive a margin call from your broker if the maintenance margin is 25% and the price of LIT rises to $39?
c. If after six months, you purchase 250 shares of IMM at $25 per share and 200 shares of KIT at $33, (in order to return the borrowed shares) what was your rate of return?

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The solution provides the price of stock, buy on margin, sell short, and rate of return.

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1. Underwood Industries just paid a dividend of $1.45 per share. The dividends are expected to grow at 25% rate for the next eight years and then level off to a 7% growth rate indefinitely. If the required return is 12%, what would be the price of the stock today?

The price of the stock is the present value of all dividends. The dividends are
Year Growth rate Dividends
0 1.45
1 25% 1.81
2 25% 2.27
3 25% 2.83
4 25% 3.54
5 25% 4.43
6 25% 5.53
7 25% 6.91
8 25% 8.64
9 7% 9.25

From year 9 the dividends grow at a constant rate. The PV of all dividends from year 9 in year 8, we can calculate using the constant growth model
PV in year 8 P8 = D9/(Required return - growth rate)
= 9.25/(12%-7%) = 184.95
We then discount all these dividends at 12% to get the price today
Price now = 1.81/1.12 + 2.27/1.12^2 + ...

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