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Citrus2011 [14]
3 years ago
8

Consider the following three stocks. (a) Stock A is expected to provide a dividend of $10 a share forever. (b) Stock B is expect

ed to pay a dividend of $5 next year. The dividend growth is expected to be 4% per year forever. (c) Stock C is expected to pay a dividend of $5 next year. The dividend is expected to grow by 20% annually for 5 years (i.e., until year 6) and then become zero forever. If the discount rate for each stock is 10 %, which stock is the most valuable?
Business
1 answer:
Archy [21]3 years ago
3 0

Answer:

The stock A is most valuable as the fair value of Stock A is $100 which is more than the fair value of Stock B ( $83.33) and Stock C ($34.28).

Explanation:

to calculate the fair price of the stocks, we will use the DDM or dividend discount model. The DDM bases the value of a stock on the present value of the expected future dividends from the stock.

Let r be the discount rate which is 10%.

a.

The stock is like a perpetuity as it pays a constant dividend after equal intervals of time and for an indefinite period.

The price of this stock can be calculated as,

Price or P0 =  Dividend / r

P0 = 10 / 0.1  = $100

b.

The constant growth model of DDM can be used to calculate the price of this stock as its dividends are growing at a constant rate forever.

P0 = D1 / r - g

Where,

  • D1 is the dividend for the next period
  • r is the cost of equity or discount rate
  • g is the growth rate in dividends

P0 = 5 / (0.1 - 0.04)

P0 = $83.33

c.

The price of this stock can be calculated using the present of dividends.

P0 = 5 / (1+0.1)  +  5 * (1+0.2) / (1+0.1)^2  +  5 * (1+0.2)^2 / (1+0.1)^3  +  

5 * (1+0.2)^3 / (1+0.1)^4  +  5 * (1+0.2)^4 / (1+0.1)^5  +  5 * (1+0.2)^5 / (1+0.1)^6

P0 = $34.28

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3 0
1 year ago
Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 9.1% and 12.
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Answer:

A.) ALPHA

Portfolio A = 8.5%

Portflio B = 13.5%

B.) Sharpe measure

Portfolio A = 0.1519

Portflio B = 0.1479

Explanation:

T- bill rate (Rf) =5%

S&P 500 index ( Rm) = 10%

Portfolio A;

Expected rate of return = 9.1%

Beta (B) = 0.7

Standard deviation (s) = 27%

Portfolio B;

Expected rate of return = 12.1%

Beta (B) = 1.7

Standard deviation = 48%

Required rate of return for both portfolios;

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5% + 3.5% = 8.5%

Portfolio B :

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5% + 8.5% = 13.5%

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A = Expected return - Required return

Alpha of portfolio A :

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Alpha of Portfolio B:

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Sharpe ratio = (Expected rate of return - Rf) / s

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Portfolio B = (12.1% - 5%)/48% = 0.1479

I will choose Portfolio A

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