Your company currently has a book equity per share of $100. Analyst forecasts st
ID: 2725526 • Letter: Y
Question
Your company currently has a book equity per share of $100. Analyst forecasts state that your return on equity (ROEE) will be 18 percent for the next 5 years (up until t=5), and 9 percent (ROEL) thereafter. Assume that the expected return on equity (the discount rate) for your stock is 8 percent and that these numbers are independent of your dividend policy.
a) Your plan is to plow back 90 percent of your earnings (bE=0.90) in the early period (up until t=5)and 20 percent of your earnings (bL=0.20) in the late period (after t=5). Given this dividend
policy, what is the price of your stock today? Show all work
Let’s try to understand how dividend policy affects firm value.
b) What happens to the stock price if you lower bE to 0.5? Increase bE to 1? Why?
c) What happens to the stock price if you increase bL to 0.7? Increase bL to 1? Why?
Suppose now that ROEL = 4%.
d) What is the stock price?
e) What happens to the stock price if you lower bE to 0.5? Increase bE to 1? Why?
f) What happens to the stock price if you increase bL to 0.7? Lower bL to 0? Why?
g) What is the optimal dividend policy? Hint: Use solver, allowing both bE and bL to vary.
Explanation / Answer
Since, there are multiple parts of the question, the first have been answered.
_______
Part A
Dividend Year 1 to 5 = (Book Value*ROEE)*(1-Plowback Ratio) = (100*18%)*(1-.90) = $1.80
Dividend from 5 Year> (Book Value*ROEL)*(1-Plowback Ratio) = (100*9%)*(1-.20) = $7.20
The stock price can be calculated with the use of following formula:
Stock Price = D1/(1+Discount Rate)^1 + D2/(1+Discount Rate)^2 + D3/(1+Discount Rate)^3 + D4/(1+Discount Rate)^4 + D5/(1+Discount Rate)^5 + D6/(Discount Rate - Growth Rate)*(1+Discount Rate)^5 (growth rate is assumed to be 0)
Stock Price Today = 1.80/(1+8%)^1 + 1.80/(1+8%)^2 + 1.80/(1+8%)^3 + 1.80/(1+8%)^4 + 1.80/(1+8%)^5 + 7.2/(8%)*(1+8%)^5 = $68.44
______
Part B
When bE is lowered to .5
Dividend Year 1 to 5 = (Book Value*ROEE)*(1-Plowback Ratio) = (100*18%)*(1-.50) = $9
Dividend from 5 Year Value*ROEL)*(1-Plowback Ratio) = (100*9%)*(1-.20) = $7.20
The stock price can be calculated with the use of following formula:
Stock Price = D1/(1+Discount Rate)^1 + D2/(1+Discount Rate)^2 + D3/(1+Discount Rate)^3 + D4/(1+Discount Rate)^4 + D5/(1+Discount Rate)^5 + D6/(Discount Rate - Growth Rate)*(1+Discount Rate)^5 (growth rate is assumed to be 0)
Stock Price Today = 9/(1+8%)^1 + 9/(1+8%)^2 + 9/(1+8%)^3 + 9/(1+8%)^4 + 9/(1+8%)^5 + 7.2/(8%)*(1+8%)^5 = $97.19
The stock price will increase because more amount of money (because of higher ROE) would get distributed to shareholders in early years.
______
When bE is Increased to .1
Dividend Year 1 to 5 = (Book Value*ROEE)*(1-Plowback Ratio) = (100*18%)*(1-1) = 0
Dividend from 5 Year Value*ROEL)*(1-Plowback Ratio) = (100*9%)*(1-.20) = $7.20
The stock price can be calculated with the use of following formula:
Stock Price = D1/(1+Discount Rate)^1 + D2/(1+Discount Rate)^2 + D3/(1+Discount Rate)^3 + D4/(1+Discount Rate)^4 + D5/(1+Discount Rate)^5 + D6/(Discount Rate - Growth Rate)*(1+Discount Rate)^5 (growth rate is assumed to be 0)
Stock Price Today = 0/(1+8%)^1 + 0/(1+8%)^2 + 0/(1+8%)^3 + 0/(1+8%)^4 + 0/(1+8%)^5 + 7.2/(8%)*(1+8%)^5 = $61.25
The stock price will decrease as no dividend will be paid in the early years when ROE is higher.
______
Part C
When bL is increased to .7
Dividend Year 1 to 5 = (Book Value*ROEE)*(1-Plowback Ratio) = (100*18%)*(1-.90) = $1.80
Dividend from 5 Year Value*ROEL)*(1-Plowback Ratio) = (100*9%)*(1-.70) = $2,70
The stock price can be calculated with the use of following formula:
Stock Price = D1/(1+Discount Rate)^1 + D2/(1+Discount Rate)^2 + D3/(1+Discount Rate)^3 + D4/(1+Discount Rate)^4 + D5/(1+Discount Rate)^5 + D6/(Discount Rate - Growth Rate)*(1+Discount Rate)^5 (growth rate is assumed to be 0)
Stock Price Today = 1.8/(1+8%)^1 + 1.8/(1+8%)^2 + 1.8/(1+8%)^3 + 1.8/(1+8%)^4 + 1.8/(1+8%)^5 + 2.7/(8%)*(1+8%)^5 = $30.16
The stock price will decrease because of higher proportion of earnings would be plowed back in the firm in later years with lower ROE.
______
When bL is lowered to 0
Dividend Year 1 to 5 = (Book Value*ROEE)*(1-Plowback Ratio) = (100*18%)*(1-.90) = $1.80
Dividend from 5 Year Value*ROEL)*(1-Plowback Ratio) = (100*9%)*(1-0) = $9
The stock price can be calculated with the use of following formula:
Stock Price = D1/(1+Discount Rate)^1 + D2/(1+Discount Rate)^2 + D3/(1+Discount Rate)^3 + D4/(1+Discount Rate)^4 + D5/(1+Discount Rate)^5 + D6/(Discount Rate - Growth Rate)*(1+Discount Rate)^5 (growth rate is assumed to be 0)
Stock Price Today = 1.8/(1+8%)^1 + 1.8/(1+8%)^2 + 1.8/(1+8%)^3 + 1.8/(1+8%)^4 + 1.8/(1+8%)^5 + 9/(8%)*(1+8%)^5 = $83.75
The stock price will Increase as higher dividend will be paid in the later years when ROE is lower.
_______
Part D
Dividend Year 1 to 5 = (Book Value*ROEE)*(1-Plowback Ratio) = (100*18%)*(1-.90) = $1.80
Dividend from 5 Year Value*ROEL)*(1-Plowback Ratio) = (100*4%)*(1-.20) = $3.20
The stock price can be calculated with the use of following formula:
Stock Price = D1/(1+Discount Rate)^1 + D2/(1+Discount Rate)^2 + D3/(1+Discount Rate)^3 + D4/(1+Discount Rate)^4 + D5/(1+Discount Rate)^5 + D6/(Discount Rate - Growth Rate)*(1+Discount Rate)^5 (growth rate is assumed to be 0)
Stock Price Today = 1.80/(1+8%)^1 + 1.80/(1+8%)^2 + 1.80/(1+8%)^3 + 1.80/(1+8%)^4 + 1.80/(1+8%)^5 + 3.2/(8%)*(1+8%)^5 = $34.41
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.