The expected pretax return on three stocks is divided between dividends and capi
ID: 2750557 • Letter: T
Question
The expected pretax return on three stocks is divided between dividends and capital gains in the following way:
Stock Expected Dividend Expected Capital Gain
A $ 0 $ 9
B 4 4
C 21 0
a. If each stock is priced at $100, what are the expected net percentage returns on each stock to (i) a pension fund that does not pay taxes, (ii) a corporation paying tax at 45% (The effective tax rate on dividends received by corporations is 10.5%), and (iii) an individual with an effective tax rate of 10% on dividends and 5% on capital gains? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)
Stock Pension Investor Corporation Individual
A % % %
B % % %
C % % %
b. Suppose that investors pay 40% tax on dividends and 10% tax on capital gains. If stocks are priced to yield an after-tax return of 10%, what would A, B, and C each sell for? Assume the expected dividend is a level perpetuity. (Do not round intermediate calculations. Round your answers to 2 decimal places.)
Stock Price
A $
B $
C $
Explanation / Answer
Answer (a)
Pension Fund
Corporate
Individual
Stock A
9.00%
4.95%
8.55%
Stock B
8.00%
5.78%
7.40%
Stock C
21.00%
18.80%
18.90%
Answer (b)
A $ 81
B $ 60
C $ 126
Pension Fund - No Taxes
Corporate - Tax Dividends received – 10.5%
Tax on Capitalgains - 45%
Individual – Effective tax rate on dividends = 10%
Effective tax rate on capital gains = 5%
Stock A
Stock Price = 100
Expected Dividend = 0
Expected Capitalgain = 9
Total return for pension fund = (Capital gains + Dividend)/Share Price
= (0+9)/100 = 9/100 = 0.09 or 9.00%
Total return for Corporate = [(Capital gains *(1-tax) + Dividend * (1-tax)]/Share Price
= [(0*(1-0.105) + 9 * (1-0.45)]/100
= [0+4.95]/100 = 0.0495 or 4.95%
Total return for individual = [(Capital gains *(1-tax) + Dividend * (1-tax)]/Share Price
= [0*(1-0.10) + 9 * (1-0.05)]/100
= [0+ 8.55]/100 = 0.0855 or 8.55%
If investors pay 40% tax on dividends and 10% on capital gains, stocks are priced to yield an after tax return of 10%.
Price of Stock A = [(Dividend * (1-tax) + Capital gain * (1-tax) / after tax return on stock
= [0*(1-0.40) + 9 * (1-0.10)]/0.10 = (0 + 8.10) / 0.10 = $ 81
Stock B
Stock Price = 100
Expected Dividend = 4
Expected Capitalgain = 4
Total return for pension fund = (Capital gains + Dividend)/Share Price
= (4+4)/100 = 8/100 = 0.08 or 8.00%
Total return for Corporate = [(Capital gains *(1-tax) + Dividend * (1-tax)]/Share Price
= [(4*(1-0.105) + 4 * (1-0.45)]/100
= [3.58+2.2]/100 = 5.78/100 = 0.0578 or 5.78%
Total return for individual = [(Capital gains *(1-tax) + Dividend * (1-tax)]/Share Price
= [4*(1-0.10) + 4 * (1-0.05)]/100
= [3.6+ 3.8]/100 = 7.4/100 = 0.074 or 7.40%
If investors pay 40% tax on dividends and 10% on capital gains, stocks are priced to yield an after tax return of 10%.
Price of Stock B = [(Dividend * (1-tax) + Capital gain * (1-tax) / after tax return on stock
= [4*(1-0.40) + 4 * (1-0.10)]/0.10 = (2.40 + 3.60) / 0.10 = 6/0.10 = $60
Stock C
Stock Price = 100
Expected Dividend = 21
Expected Capitalgain = 0
Total return for pension fund = (Capital gains + Dividend)/Share Price
= (0+21)/100 = 21/100 = 0.21 or 21.00%
Total return for Corporate = [(Capital gains *(1-tax) + Dividend * (1-tax)]/Share Price
= [(21*(1-0.105) + 0 * (1-0.45)]/100
= [18.795+0]/100 = 18.795/100 = 0.18795 or 18.80%
Total return for individual = [(Capital gains *(1-tax) + Dividend * (1-tax)]/Share Price
= [21*(1-0.10) + 0 * (1-0.05)]/100
= [18.9+ 0]/100 = 18.9/100 = 0.189 or 18.90%
If investors pay 40% tax on dividends and 10% on capital gains, stocks are priced to yield an after tax return of 10%.
Price of Stock C = [(Dividend * (1-tax) + Capital gain * (1-tax) / after tax return on stock
= [21*(1-0.40) + 0* (1-0.10)]/0.10 = (12.6 + 0) / 0.10 = 12.6/0.10 = $126
Pension Fund
Corporate
Individual
Stock A
9.00%
4.95%
8.55%
Stock B
8.00%
5.78%
7.40%
Stock C
21.00%
18.80%
18.90%
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