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4.ABC Corp. has just paid an annual dividend of $0.50 per share. Dividends are expected to grow at 15% for each of the next 8 years, at 10% for the 2 years after that, and at 3% thereafter. If the appropriate discount rate is 10%, what is the intrinsic value of the stock? Clue start with a stream of discounted dividends and price the stock.

The timeline for the dividends looks like this (split to fit on the page):
0 1 2 3 4 5 6 7
| | | | | | | |
| | | | | | | |

8 9 10 11 12
| | | | |
| | | | |
0.5(1+g)8 ..


5. You are a research analyst for a major investment bank and have been asked to evaluate three candidates for a takeover and recommend one. You estimate the risk-free rate to be 5% and the market risk premium to be 8%. You also have the following data

MTT Corp. NOR Corp. TECH Corp.
current price $20 $25 $200
number shares 100,000 80,000 10,000
current EPS $4 $2.50 $5
payout ratio 50% 20% 10%
(first 5 yrs)
beta 1.0 1.25 1.5
growth rate:
first 5 yrs. 5% 20% 50%
beyond 5 yrs. 5% 10% 10%
D/E ratio 0 0 0
first 5 yrs. 10% 25% 55.56%
beyond 5 yrs. 10% 20% 25%
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Which firm is the best candidate for a takeover?Clue calculate intrinsic value and overvaluation/undervaluation using relevant metrics like Gordon Shapiro model, constant dividend growth model etc.

6. It is now time 0. You are a bond portfolio manager using a barbell strategy to immunize. Your portfolio will consist of two bonds: bond A, which is a $100 par zero coupon bond maturing in five years; bond B, which is a $100 par zero-coupon bond maturing in ten years. You are trying to immunize a $1 million liability that is due in six years. The yield curve is flat at 10%, so you need a present value of $1 million/(1.10)6 = $564,474.

a. Of the $564,474, how much will you put in bond A and how much will you put in bond B? How many of the A and B bonds will you buy?
b. One minute after you set up the portfolio, the yield curve shifts up to 15% (staying flat). How much is your portfolio worth?
c. After the shift in part b, is your liability immunized? If not, what should you do to immunize it? Be specific, and give numbers if you can.
d. Now assume that the shift in part b never happened. You leave the firm and nobody bothers to look at the portfolio again until the end of year 4. Interest rates are still at 10%; there have been no further changes. At the end of year 4, a new bond portfolio manager takes over, goes through the files, and finds the records of the portfolio. What, if anything, will she have to do to keep the liability immunized? Be specific, and give numbers if you can.

7.Consider the following data for a stock and a call option on that stock: S0 = $50, S1 = $75 or $100, E = $50, and r = 1.10. Derive the hedge ratio (α) and the price of the call option
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