The expected pretax return on three stocks is divided between dividends and capi
ID: 2802537 • Letter: T
Question
The expected pretax return on three stocks is divided between dividends and capital gains in the following way:
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.)
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.)
A)
B)
C)
Explanation / Answer
Answer a)
This solution basically needs us to calculate holding period return of every stock in each case
that is holding period return on stock A,B,C if they were in pension fund and so on
Now first we will understand the formula of Holding period return
Which is HPR = (selling price – purchase price )(1-Tax) + dividend (1-Tax)
Purchase price
Explanation of this formula
take first term ie. (sale price – purchase price)(1-Tax), it is basically capital gain which an investor earns by sell stock at higher price the purchase price. Such return will be taken after deduction tax that is why such term is multiplied by (1 – tax rate).
Similarly for dividend as it is also our income (it is also taken after tax as we get net of tax amount only in our hand
so basically Holding period return is % of total profit or loss that occur on purchase price of the stock.
Now practical Solution
Stock
Pension Fund
Corporation
Individual
A
= 0 + 5
100
= 5%
= 0 + 5(1-.45)
100
= 0 + 2.75
100
= 2.75%
= 0 + 5(1- .05)
100
= 0 + 4.75
100
= 4.75%
B
= 5+5
100
= 10%
= 5(1- .105) + 5(1-.45)
100
= 4.475 + 2.75
100
= 7.225%
= 5 (1-.10) + 5(1-.05)
100
= 4.5 + 4.75
100
= 9.25%
C
= 25 + 0
100
= 25%
= 25(1-.105) + 0
100
= 22.375 + 0
100
= 22.375 %
= 25(1-.10) + 0
100
= 22.5 + 0
100
= 22.5%
Answer B
Now using similar formula i.e. Holding period return we have to calculate the purchase price of each stock
So just put the values in the formula
Stock A
.10 = 0 + 5(1-.10)
Purchase Price
Purchase price = 4.5
.10
= 45
Stock B
.10 = 5(1-.40) + 5(1-.10)
Purchase price
Purchase price = 3 + 4.5
.10
= 75
Stock C
.10 = 25(1-.40) + 0
Purchase price
Purchase price = 15 + 0
.10
= 150
Stock
Pension Fund
Corporation
Individual
A
= 0 + 5
100
= 5%
= 0 + 5(1-.45)
100
= 0 + 2.75
100
= 2.75%
= 0 + 5(1- .05)
100
= 0 + 4.75
100
= 4.75%
B
= 5+5
100
= 10%
= 5(1- .105) + 5(1-.45)
100
= 4.475 + 2.75
100
= 7.225%
= 5 (1-.10) + 5(1-.05)
100
= 4.5 + 4.75
100
= 9.25%
C
= 25 + 0
100
= 25%
= 25(1-.105) + 0
100
= 22.375 + 0
100
= 22.375 %
= 25(1-.10) + 0
100
= 22.5 + 0
100
= 22.5%
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