A stock pays a dividend that grows at rate g each year. The first dividend, which...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
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?
Expert Answer:
Answer rating: 100% (QA)
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:
Students also viewed these accounting questions
-
Tori can be paid in one of two ways for selling insurance policies: Plan A: A salary of $750 per month, plus a commission of 10% of sales; Plan B: A salary of $1000 per month, plus a commission of 8%...
-
Achal can be paid in one of two ways for the furniture he sells: Plan A: A salary of $900 per month, plus a commission of 10% of sales; Plan B: A salary of $1200 per month, plus a commission of 15%...
-
A stock pays a dividend of $134, $262 and $306 in the next 3 years . The value of the stock at the end of year 3 is expected to be $4194 Assume that the return on this stock is 8, what is the value...
-
Middleton Spas provides the following data for the year just ended on December 31. Requirement Prepare the operating activities section of Middleton Spas' statement of cash flows for the year just...
-
Why are small companies more susceptible to business crime than large companies?
-
Given: Suppose you are given the following market supply and demand curves for energy drinks. Table: Demand Curve Price Quantity Demanded (in 1,000s of cans per day) 90 $0 20 Point LL F $5 15 E $7.50...
-
Describe triggers. Discuss their advantages and disadvantages.
-
Giant acquired all of Small's common stock on January 1, 2011. Over the next few years, Giant applied the equity method to the recording of this investment. At the date of the original acquisition,...
-
Walton Company measured its quality costs for the past two years and summarized those costs using the four categories shown below: Last Year Appraisal costs Prevention costs Internal failure costs $...
-
What is activity-based costing, and what are its potential benefits?
-
Read the case study Relationship between quality management practices and innovation and Review for article: the link between innovation and quality management practices and also write about the...
-
An automobile dealer reports the 1994 and 2011 sales for three models in the following table. Compute quantity relatives and use them to develop a weighted aggregate quantity index for 2011 using the...
-
Data on quantities of three items sold in 1997 and 2011 are given here along with the sales prices of the items in 1997. Compute a weighted aggregate quantity index for 2011. Quantity Sold Item 1997...
-
Why do accountants have to make these allowances?
-
At the beginning of the financial year on 1 April 2017, a company had a balance on plant account of 372,000 and on provision for depreciation of plant account of 205,400. The company's policy is to...
-
(a) Distinguish between capital and revenue expenditure. (b) Drake Ltd took delivery of a computer network on 1 July 2016, the beginning of its financial year. The list price of the equipment was...
-
You want to plan to provide for 4 year college expenses for two children. Assume that the first child will be college going in 16 years and the other in 12 years. College tuition is 30,000 per year...
-
For the following exercises, write the polynomial function that models the given situation. Consider the same rectangle of the preceding problem. Squares of 2x by 2x units are cut out of each corner....
-
Discuss a corporate repurchase announcement on the basis of market efficiency.
-
On a Saturday afternoon in May 2015, Robert Boyle and his wife Janet were sitting on the porch of their house on Saltspring Island, British Columbia, watching the fog roll in. The couple frequently...
-
Using the expectations hypothesis theory for the term structure of interest rates, determine the expected return for securities with maturities of two, three, and four years based on the following...
-
2019. Peabody Energy Company and Arch Resources, Inc., are two titans in a now-dwindling industry. Peabody operates three mines in the Southern Powder River Basin (SPRB) in Wyoming, one of which is...
-
Beginning around 1915, Natural Products Refining Corporation (NPRC) operated a chemical plant in Jersey City, New Jersey, at which it turned chromite ore into chromium chemicals (primarily sodium...
-
When GTE Sylvania discovered it was losing market share to other television manufacturers, it developed a franchise plan that limited the number of retailers selling its product in each area....
Study smarter with the SolutionInn App