. You own 1000 shares of stock in Avondale Corp. You will receive dividend of $1
ID: 2752090 • Letter: #
Question
. You own 1000 shares of stock in Avondale Corp. You will receive dividend of $1 per share in one year. In two years, Avondale will pay a liquidating dividend of $56 per share. The required rate of return on Avondale stock is 14%. Ignore taxes. (25 pt) (i) What is Avondale's current stock price? (2 pt) (ii) What is Avondale's stock price in 1 year after the $1 dividend payment? (2 pt) (iii) If you would rather receive dividend of $4 per share in 1 year, (a) show you can accomplish this by creating homemade dividends. (3 pt) (b) As a result, what is your total income in year 1 and year 2 respectively? (3 pt) (c) What is the present value of your cash flows (income) in years 1 and 2? (2 pt) Divide it by 1000 (number of shares you own). Is it same as (or very close to) Avondale's current stock price? (1 pt) (iv) If you prefer to receive an income of $400 only in year 1 and you plan to reinvest excess cash in the stock (by buying more shares) after you receive the $1 dividend per share from the company, (a) what is your total income in year 2? (3 pt) (b) What is the present value of your cash flows (income) in years 1 and 2? Divide it by 1000 (number of shares you own). Is it same as (or very close to) Avondale's current stock price? (3 pt) (v) If you would prefer to receive equal dividends in each of the next two years, show you can accomplish this by creating homemade dividends. (6 pt) Hint: from (iii) and (iv) above, we know homemade dividend does not change stock price, i.e. the present value of homemade dividends (X in each period) = current stock price.
Explanation / Answer
Answer (i)
Current Share price = $ 43.97
Answer (ii)
Stock price after 1 year and payment of $1 dividend = $ 49.12
Answer (iii) (a)
Required homemade dividend on total investment = $ 3000
Number of shares to be sold for home dividend = 61
Answer (iii) (b)
Total Income in Year 1 = $ 4,000
Total Income in Year 2 = $ 52,584
Answer (iii) (c)
Total present value /1000 = $ 43.97 which is same as current stock price
Answer (iv)(a)
Total Income in year 2 = $ 56,672
Answer (iv)(b)
Total Present Value / 1000 = $ 43.96 which is close to current stock price
Answer (v)
Equal dividends are required in both the years
Dividend in year 1 = $ 1 * 1000 = $ 1000
Dividend in year 2 = $ 56 * 1000 = $ 56000
Total Dividend in 2 years = $ 1000 + $ 56000 = $ 57000
Amount to be received in each year if dividend required is equal = $ 57000/2 = $ 28,500
Homemade dividend to be created in year 1 = $ 28500 - $ 1000 = $ 27500
Number of shares to be sold in year 1 = $ 27500 / $ 49.12 = 559.8534 or 560 shares
working
Expected Dividend in 1 year = $ 1
Expected liquidating dividend in 2 years = $ 56
Required rate of return = 14%
Current stock price = Expected Dividend in 1 year /(1+0.14) + Liquidating Dividend / (1+0.14)^2
= $ 1 / 1.14 + $ 56/1.14^2
= 0.8771929 + $ 56/1.2996
= 0.8771929 + 43.09018159
= $ 43.9673745 or $ 43.97 (rounded off)
Stock price after 1 year = Liquidating dividend / 1.14
= $ 56 / 1.14 = $ 49.1228 or $ 49.12
Required dividend in year 1 = $ 4 per share
Dividend expected in year 1 = $ 1
Homemade Dividend required = $ 4 - $ 1 = $ 3
Total dividend amount on investment = $ 3 * 1000 = $ 3000
Number of shares to be sold after 1 year = Home Dividend amount / Expected share price after 1 yr
= $ 3000 / $ 49.12 = 61.07 or 61 shares
Total Income in year 1 = $ 1 *1000 + $ 3000 (Home made dividend) = $ 4000
Total income in year 2 = $ 56 * (1000-61) = $ 56 * 939 = $ 52,584
Present Value of Cash flow in year 1 = $ 4000/1.14 = 3508.7719 or 3508.77 (rounded off)
Present Value of Cash flow in year 2 = $ 52,584/1.14^2 = $ 52584/1.2996 = $ 46461.6805
Total Present Value = $ 3508.7719 + $ 46461.6805 = $ 43970.4524
Total Present Value / 1000 = $ 43970.4524/1000 = $ 43.9704524 or $ 43.97 (rounded off)
Total Dividend received in year 1 = $1 * 1000 = $ 1000
Amount of dividend income reinvested = $ 1000 - $ 400 = $ 600
Number of additional shares bought = $ 600 / $ 49.12 = 12.21 or 12 shares
Total income in year 2 = $ 56 * (1000+12) = $ 56 * 1012 = $ 56,672
Total Present Value = $400/1.14 + $ 56672/1.14^2 = $400/1.14+$56672/1.2996
= $ 350.8772 + $ 43607.2638
= $43958.141
Total Present Value / 1000 = $ 43958.141/1000 = $ 43.958141 or $ 43.96 (rounded off)
Equal dividends are required in both the years
Dividend in year 1 = $ 1 * 1000 = $ 1000
Dividend in year 2 = $ 56 * 1000 = $ 56000
Total Dividend in 2 years = $ 1000 + $ 56000 = $ 57000
Amount to be received in each year if dividend required is equal = $ 57000/2 = $ 28,500
Homemade dividend to be created in year 1 = $ 28500 - $ 1000 = $ 27500
Number of shares to be sold in year 1 = $ 27500 / $ 49.12 = 559.8534 or 560 shares
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