A stock pays a dividend that grows at rate g each year. The first dividend, which...
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A stock pays a dividend that grows at rate g each year. The first dividend, which will be paid in one year, will be D, the next dividend, which will be paid in two years, will be (1+g)D, the third dividend will be (1+g)2D, etc. The interest rate is r, g<r. What is the price of the stock today? Σογί, Hint: Recall that = 1 (1-y) A firm sells a consol that promises to pay C each year forever. You are certain the firm will pay next year, but after that, there is a probability p each year that the firm will fail and not make any of the subsequent payments. The interest rate is r. In any given year, there is, of course, a probability (1-p) that the firm will not fail and make the payment, but the following year there will again be a probability p the firm will fail. What is the expected value today of the consol payment in 3 years? In j years? (Remember that you are certain the firm will make its payment in one year, the chance of failure only starts after that.) What is the value of the consol? A "risk premium" is an additional amount added to the risk-free interest rate to discount a risky asset. So if risk-free interest rate is r, and the risk premium is x, the value of a risky stream of income Ž is Σ( ₁₁ +7 + x)) Ži i=1 In this simple example, what is the relationship between the risk premium and the probability of failure? In the Treasury futures market, you can buy a 1-year Treasury bill futures for delivery four years from now. When it is delivered, you will pay x. One year later, when the bill matures, you will get $1000. The four-year zero-coupon Treasury term rate is r² = *√(1 + r) (1 + r + ¹₂) (1 + r£ + tỷ )(1 + r£ + r) -1 The five-year zero-coupon Treasury term rate is r = (1 + r)(1 + r₂ + 1₂ )(1 + rf + tỷ)(1 + r£ + {)(1 + rf + ) - 1 A. You can get $1000 in five years by buying y = $1000 B. As noted, you can get $1000 in five years by buying a futures contract that will require me to pay x in four years. I can get x in four years by buying z = (1+r)* in four-year zero-coupon Treasury notes today. The two strategies both get me $1000 in five years with a only a cash outlay today, y for strategy A and z for strategy B. The absence of arbitrage hypothesis requires that y=z. Assuming there is no arbitrage, what is x? What does your result show about the relationship between futures prices and forward rates? A stock pays a dividend that grows at rate g each year. The first dividend, which will be paid in one year, will be D, the next dividend, which will be paid in two years, will be (1+g)D, the third dividend will be (1+g)2D, etc. The interest rate is r, g<r. What is the price of the stock today? Σογί, Hint: Recall that = 1 (1-y) A firm sells a consol that promises to pay C each year forever. You are certain the firm will pay next year, but after that, there is a probability p each year that the firm will fail and not make any of the subsequent payments. The interest rate is r. In any given year, there is, of course, a probability (1-p) that the firm will not fail and make the payment, but the following year there will again be a probability p the firm will fail. What is the expected value today of the consol payment in 3 years? In j years? (Remember that you are certain the firm will make its payment in one year, the chance of failure only starts after that.) What is the value of the consol? A "risk premium" is an additional amount added to the risk-free interest rate to discount a risky asset. So if risk-free interest rate is r, and the risk premium is x, the value of a risky stream of income Ž is Σ( ₁₁ +7 + x)) Ži i=1 In this simple example, what is the relationship between the risk premium and the probability of failure? In the Treasury futures market, you can buy a 1-year Treasury bill futures for delivery four years from now. When it is delivered, you will pay x. One year later, when the bill matures, you will get $1000. The four-year zero-coupon Treasury term rate is r² = *√(1 + r) (1 + r + ¹₂) (1 + r£ + tỷ )(1 + r£ + r) -1 The five-year zero-coupon Treasury term rate is r = (1 + r)(1 + r₂ + 1₂ )(1 + rf + tỷ)(1 + r£ + {)(1 + rf + ) - 1 A. You can get $1000 in five years by buying y = $1000 B. As noted, you can get $1000 in five years by buying a futures contract that will require me to pay x in four years. I can get x in four years by buying z = (1+r)* in four-year zero-coupon Treasury notes today. The two strategies both get me $1000 in five years with a only a cash outlay today, y for strategy A and z for strategy B. The absence of arbitrage hypothesis requires that y=z. Assuming there is no arbitrage, what is x? What does your result show about the relationship between futures prices and forward rates?
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Stock Price with Growing Dividends The formula for the price P of a stock that pays a constant dividend D that grows at a rate g each year with an interest rate r and g r is P D r g This formula uses ... View the full answer
Related Book For
Foundations of Financial Management
ISBN: 978-1259024979
10th Canadian edition
Authors: Stanley Block, Geoffrey Hirt, Bartley Danielsen, Doug Short, Michael Perretta
Posted Date:
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