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Dvinal [7]
3 years ago
14

Consider a stock with current year dividend equal to $2.00 per share. You believe the dividend will grow 15% per year for 10 yea

rs and 4% per year thereafter.The required equity rate of return (and your hurdle rate) is 10%. What is the fair price of the stock? Assuming the market price of the stock is $70, what is the expected return?
Business
1 answer:
goblinko [34]3 years ago
4 0

Answer:

a. Fair price of the stock = $79.82

b. The expected return is 7.29%

Explanation:

a. What is the fair price of the stock?

Note: See the attached file for the calculation of present values (PV) of dividends for year 1 to 10.

From the attached excel file, we have:

Previous year dividend in year 1 = Current year dividend = $2

Total of dividends from year 1 to year 10 = $25.74793130208810

Year 10 dividend = $8.09111547141582

Therefore, we have:

Year 11 dividend = Year 10 dividend * (100% + Dividend growth rate in year 11) = $8.09111547141582 * (100% + 4%) = $8.41476009027245

Share price at year 10 = Year 11 dividend / (Required equity rate of return - Perpetual dividend growth rate) = $8.41476009027245 / (10% - 4%) = $140.246001504541

PV of share price at year 10 = Price at year 10 / (100% + required equity rate of return)^Number of years = $140.246001504541 / (100% + 10%)^10 = $54.0709047493998

Therefore, we have:

Fair price of the stock = Total of dividends from year 1 to year 10 + PV of share price at year 10 = $25.74793130208810 + $54.0709047493998 = $79.82

b. Assuming the market price of the stock is $70, what is the expected return?

This can be calculated using the dividend discount model formula as follows:

P = D1 / (r - g) ............................ (1)

Where,

P = Market price of the stock = $70

D1 = Next dividend = Current dividend * (100% + Dividend growth rate in perpetuity) = $2 * (100% + 4%) = $2.30

r = Expected return = ?

g = Dividend growth rate in perpetuity = 4%, or 0.04

Substituting the values into equation (1) and solve for r, we have:

70 = 2.30 / (r - 0.04)

70(r - 0.04) = 2.30

70r - 2.80 = 2.30

70r = 2.30 + 2.80

70r = 5.10

r = 5.10 / 70

r = 0.0729, or 7.29%

Therefore, the expected return is 7.29%.

Download xlsx
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Suppose that the duopolists Carl and Simon face an inverse demand function for pumpkins of P = 400 - Q, where Q = Qs + Qc is the
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the Cournot-Nash equilibrium, Simon's production is 82 units

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TR_c = 400Q_c -Q_sQ_c -Q_c^2

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Set HR_c = HC_c

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Reaction function of Simon

Since Simon maximize profit  at HR_s = HC_s

TR_s = PQ_s \\ \\ TR_s = (400-Q_c -Q_s)Q_s \\ \\ TR_s = 400 Q_s - Q_cQ_s - Q_s^2

HR_s = \delta TR_s/ \delta Q_s

HR_s =400 - Q_c -2Q_s

C_s = Q_s^2

HC_s= \delta C_s/ \delta Q_s

HC_s=2Q_s

Set HR_s = HC_s

400- Q_c - 2Q_s = 2Q_s \\ \\ 400 - Q_c = 2Q_s+2Q_s \\ \\ 4Q_s = 400 - Q_c \\ \\ Q_s = (4000- Q_c)/4 \\ \\ Q_s = 100 -0.25 Q_c  ---  Reaction \ function \ of \ Simon \ -- equation (2)

Substituting equation (1) into equation (2)

Q_s =100 -0.25Q_c \\ \\ Q_s = 100 - 0.25(92.5-0.25 Q_s) \\ \\ Q_s = 100 -23.125 +0.0625Q_s  \\ \\ (Q_s-0.0625Q_s) = 76.375 \\ \\ 0.9375 Q_s = 76.875 \\ \\ Q_s = 76.375/0.9375 \\ \\ Q_s = 82

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3 years ago
The Carry-on Luggage Company must set up an assembly line for a wheeled carry-on bag. Forecasts show that 60 units per hour shou
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Answer:

a. See attachment below

b. 60 seconds per unit

c. 4 workstations

d. See attachment below

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Explanation:

b.

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Task time = Time required to for production per units

Since 1 hour is required for 60 units and there are 3600 seconds in one hour (60 * 60)

This is calculated by.

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d. See Attachment Below

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= 195/(4 * 60)

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