View Question
 Question
 Subject: Finance Category: Reference, Education and News > Homework Help Asked by: jaemarie-ga List Price: \$5.00 Posted: 19 Sep 2005 15:23 PDT Expires: 19 Oct 2005 15:23 PDT Question ID: 569844
 ```Company Z-prime is like Z in all respects save one : Its growth will stop after 4 year. In year 5 and afterward, it will pay ot all earnings as dividends. What is Z-prime's stock price? Assume next year's EPS is \$15.``` Request for Question Clarification by omnivorous-ga on 19 Sep 2005 17:06 PDT ```Jaemarie -- We can't tell from the information provided: you have no idea what the market rate-of-return is. We also have no idea how it grows in years 1-4. Best regards, Omnivorous-GA``` Clarification of Question by jaemarie-ga on 19 Sep 2005 20:16 PDT ```Company Z,s earnings and dividends per share are expected to grow indefinitely by 5% per year. If next year's dividend is \$10 and the market capitalization rate is 8 percent, what is the current stock price? Company Z-prime is like Z in all aspects save one: Its growth will stop after year 4. In year 5 and afterward, it will pay out all earnings as dividends. What is Z-prime's stock price? Assume next year's EPS is \$15. Hope this clarifies the question.```
 Subject: Re: Finance Answered By: omnivorous-ga on 19 Sep 2005 21:53 PDT Rated:
 ```Jaemarie ? Here are the important assumptions about Z-Prime: ? Year 1 dividend = \$10 ? Year 2 dividend = \$10.50 ? Year 3 dividend = \$11.025 ? Year 4 dividend = \$11.576 ? Year 5 and onwards: \$17.36 Ks or discount rate = 8% This provides the following discount factors for NPV: Year1: 1/1.08 = .9259 Year2: 1/(1.08)^2 = .8573 Year3: 1/(1.08)^3 = .7938 Year4 1/(1.08)^4 = .7350 Year5: 1/(1.08)^5 = .6806 So it become easy to track NPV of the cash flows for years 1-4 by multiplying each by their NPV factor: Year1: \$9.26 Year2: \$9.00 Year3: \$8.75 Year4: \$8.51 But what?s the value of the never-ending series of dividend payments from year 5 to eternity? CONSTANT GROWTH MODEL ========================== Also called the Dividend Valuation Model, this allows an investor to calculate a value based on returns to the investor. Here, the dividends represent cash flows ? something that?s not always true in the real world. The general model for stock pricing is below. We?ll use period 5 (year 5) but you can use i as year one or any other starting point if you?re an analyst trying to figure out how to value a company -- Pi = Di / (Ks - g) Pi = price in period i Di = dividends in period i Ks = required rate of return (in decimals) g = dividend growth rate (in decimals) i = period, usually expressed in years So the value at the end of year 5 is: P = \$17.36 / (0.08 ? 0.05) = \$17.36 / 0.03 = \$578.67 However, that?s the value in year 5 ? not today. We have to discount it back to year 0 (that?s how ?today? is often described in financial problems ? so it?s: \$578.67 * Year5 NPV factor = \$393.84 TOTAL VALUE OF Z-PRIME = \$9.26 + \$9.00 + \$8.75 + \$8.51 + \$393.84 = \$429.36 Google search strategy: ?constant growth model? dividends Best regards, Omnivorous-GA``` Clarification of Answer by omnivorous-ga on 19 Sep 2005 22:04 PDT ```Jaemarie -- I no sooner than finished the calculations when I realized that I'd over-estimated the Year5 onwards. There's no growth in the firm, which substantially reduces the value of the now-constant dividends. Here's how the Constant Growth Model should evaluate it: The value at the end of year 5 is: P = \$17.36 / (0.08 ? 0.00) = \$17.36 / 0.08 = \$217.00 However, that?s the value in year 5 ? not today. We have to discount it back to year 0 (that?s how ?today? is often described in financial problems ? so it?s: \$217 * Year5 NPV factor = \$147.69 TOTAL VALUE OF Z-PRIME = \$9.26 + \$9.00 + \$8.75 + \$8.51 + \$147.69 = \$183.21 My apologies for the confusion. Best regards, Omnivorous-GA```
 ```As I was looking at the answers, how did you calculated Z-Prime's 5 year onward dividend to be at \$17.36?```
 `I also could not figure out the \$17.36`
 ```How could you use the EPS of \$15 to find this answer? Or is there somehow a simpler way to calculate the NPV of yrs 1-4 as a growth stock and then add that to the NPV of Yr 5 as a dividend/nongrowth stock for the price?```