Question

In: Finance

Suppose a firm’s common stock has just paid a dividend of $3 (hint: t = 0)....

Suppose a firm’s common stock has just paid a dividend of $3 (hint: t = 0). You expect the dividend to grow at the rate of g1 = 0.2 per year for the next 3 years (t = 1, 2, 3); if you buy the stock, you plan to hold it for 3 years and then sell it. Assume that the appropriate discount rate is 0.13.

Question 2.1 Answer the following question

What is the expected dividend to be received in 3 years?

Given that the first of these dividend payments will occur 1 year from now, what is the present value of the sum of expected dividends to be received in the next three years?

Assume that you expect the price of the stock to be 34.2 in 3 years from now. What is the present value (t = 0) of this expected future stock price?

If you plan to buy the stock, hold it for 3 years, and then sell it for 34.2, what is the most you should pay for it today (t = 0)?

Assume that after the three years, the growth rate drops to 0.05 and stays there for ever. What is the most you should pay for the stock under these conditions today?

Solutions

Expert Solution

Answer : 2.1 ) Calculation of Expected Dividend to be received in three years

Year Dividend
1 3.6 (3 * 1.2)
2 4.32 (3.6 * 1.2)
3 5.184 (4.32 * 1.2)

2.2 ) Present Value of Dividend :

Year Dividend PVF @13% Present Value of Dividend
1 3.6 0.884955752 3.185840708
2 4.32 0.783146683 3.383193672
3 5.184 0.693050162 3.592772041
Present Value of Dividend 10.16180642

3.3) Present Value of Expected Stock Price = 34.2 * [1 / (1 + 0.13)^3]

= 34.2 * 0.693050162

= 23.70231555

3.4) Price to be paid today :

Price = Present Value of Dividend and Stock Price

= 10.16180642 + 23.70231555

= 33.86412197 or 33.86

Year Dividend / Price PVF @13% Present Value of Dividend/Price
1 3.6 0.884955752 3.185840708
2 4.32 0.783146683 3.383193672
3 5.184 0.693050162 3.592772041
3 34.2 oo 0.693050162 23.70231555
Current Stock Price 33.86412197

If growth rate drops to 0.05 per year Calculation of Expected Price :

Year Dividend / Price PVF @13% Present Value of Dividend
1 3.6 0.884955752 3.185840708
2 4.32 0.783146683 3.383193672
3 5.184 0.693050162 3.592772041
3 68.04 (Working Note) 0.693050162 47.15513304
Current Stock Price 57.31693946

Working Note :

Calculation of Expected Price in year 3 = (5.184 * 1.05) / (0.13 - 0.05)

= 68.04

The most you should pay for the stock under these conditions today is 57.32

jeff jeffy answered 1 year ago
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