1.if a stock is expected to pay a dividend of $ 25 for the current year, what is
ID: 1201291 • Letter: 1
Question
1.if a stock is expected to pay a dividend of $ 25 for the current year, what is the approximate present value of this stock, given at discount rate of 10 % and a dividend growth rate 2 %.
2. suppose the price of beans rises from $1.00 a pound, to $2.00 a pound quantity demanded falls from 10 units to 6 units, compute the coefficient of elasticity of demand for beans using the arc elasticity approach.
3. if a price of corn is $ 3.00 a bushel, 5000 bushels would be demanded. if the price rises to $ 4.00 a bushel , 4000 bushel would be demanded.
A. what is the arc price elasticity of demand ?
B. based on this answer, if the price of corn rose to $ 5.00 a bushel , what would be the demand for corn ?
C if the price of corn decreased from 4.00 to $ 3.00 a bushel , what would be the change in total revenue for sellers of corn ?
D. if the price of corn increased from 4.00 to $ 5.00 a bushel, what would be the change in total revenue for sellers of corn ?
Explanation / Answer
1. Present value of the stock (Po) = Div1 / r – g
(Where Div1 is dividend for next period, r is the required rate of return (or discount rate), g is the growth rate)
PV of stock = $25 / (0.10 – 0.02) = $25 / 0.08
PV of stock = $312.50.
2. To calculate arc elasticity of demand we take the midpoint in between.
Price increases from $1 to $2
The % change in price = 1 / (average of 1 and 2) = 1 / 1.5 = 0.66
Quantity decreases from 10 units to 6 units
The % change in quantity = - 4/ (average of 10 and 6) = -4 / 8 = - 0.5.
Coefficient of elasticity of demand using arc elasticity = - 0.5 / 0.66 = - 0.75.
3. A. Price of corn increases from $3 a bushel to $4 a bushel
The % change in price = $1 / 3.5 (average of 3 and 4) = 0.28
The quantity of corn decrease from 5000 bushels to 4000 bushels (-)
The % change in quantity of corn = - 1000 / 4500 (average of 4000 and 5000) = - 0.22
The arc elasticity of demand = -0.22.
3 B. If the price of corn rose from $3 to $5 a bushel:
The % change in price = @2 / 4 (average of 3 and 5) = 0.5.
% change in quantity / 0.5 (% change in price) = -0.22
The % change in quantity = -0.22 x 0.5 = -11.
The quantity demanded will fall by 11 percent.
3. C if the price of corn decreased from 4.00 to $ 3.00 a bushel:
At price $3 per bushel, quantity demanded = 5,000 units
Revenue = $3 x 5000 = $15.000
At price $4 per bushel, quantity demanded = 4,000
Revenue = $4 x 4,000 = $16,000
The change in the revenue = $16,000 - $15,000 = $1,000.
3. D. if the price of corn increased from $4 to $5 a bushel
The % change in quantity demanded when price rose from $3 to $5 = 11% decrease
The quantity decreased from 5,000 to 4,500 ( 5000 / 111 x 1000 = 4504)
Revenue at price $5 = 4,500 x 5 = $22,500
Revenue at price $4 = 4,000 x 4 = 16,000
The change in revenue if price increases from $ to $5 per bushel = $22,500 - $16,000 = $6,500.
The change in revenue = $6,500
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