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Chapter 10 Questions

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Chapter 10 Questions

Question 1

Question 1
Price before dividend Price after dividend Dividend Tax on capital gains Tax on ordinary income
50 46.5 5 0.7 58.00%

To calculate the marginal tax rate on stockholders, we use the formula below:
(𝑃_π΅βˆ’π‘ƒ_𝐴)/𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑=(1βˆ’π‘‘_π‘œ)/(1βˆ’π‘‘_𝑐𝑔 )
Where:
𝑃_𝐡=π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘“π‘œπ‘Ÿπ‘’ 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑃_𝐴=π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘Žπ‘“π‘‘π‘’π‘Ÿ 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑑_π‘œ=π‘‡π‘Žπ‘₯ π‘œπ‘› π‘œπ‘Ÿπ‘‘π‘–π‘›π‘Žπ‘Ÿπ‘¦ π‘–π‘›π‘π‘œπ‘šπ‘’
𝑑_𝑐𝑔=π‘‡π‘Žπ‘₯ π‘œπ‘› π‘π‘Žπ‘π‘–π‘‘π‘Žπ‘™ π‘”π‘Žπ‘–π‘›π‘ 

Substituting the known values:
(50βˆ’46.5)/5=(1βˆ’π‘‘_π‘œ)/(1βˆ’0.4)
Re-arranging to make 𝑑_π‘œ the subject of the formula:
𝑑_π‘œ=1βˆ’((50βˆ’46.5)(1βˆ’0.4)/5)
𝑑_π‘œ=1βˆ’0.42
𝑑_π‘œ=0.58=58%

Question 3

Question 3 Capital Gains Rate 50%
Price Before Dividend Price After Dividend Dividend Tax on Capital Gains (1+R) (1+R)^n Number of years Ordinary Tax Rate 50%
10 9.2 1 37.50% 1.10 1.33 3 Discount Rate 10%

First, calculate the effective capital gain rate:

Effective capital gains rate=(Stated capital gains rate)/(1+R)^n

Where:

R=Discount rate=10%

n=Number of periods

Substituting the known values into the formula:

Effective capital gains rate=0.5/(1+0.1)^n =0.5/γ€–1.1γ€—^n

Next, relate the prices before and after the dividend to taxes using the following formula:

(P_B-P_A)/Dividend=(1-t_o)/(1-t_cg )

Where:

P_B=Price before dividend=10

P_A=Price after dividend=9.2

t_o=Tax on ordinary income=50%

t_cg=Tax on capital gains=0.5/γ€–1.1γ€—^n

Substituting the values into the formula:

(10-9.2)/1.0=(1-0.5)/(1-0.5/γ€–1.1γ€—^n )

0.8=0.5/(1-0.5/γ€–1.1γ€—^n )

Simplifying the expressions to solve for n gives:

γ€–1.1γ€—^n=1.33

Solving for n using logarithms gives:

n≅3

The capital gains taxes are being deferred by three years.

Question 4

Question 4 The ordinary income tax rate 40%
Effective Tax Rate on Dividends Price Before Dividend Dividend Price After Dividend Change in Share Price Capital gains tax rate 28%
6.00% 10 0.5 9.35 0.65 % of exempt dividend 85%

First, we evaluate the effective tax rate on dividends.
𝐸𝑓𝑓𝑒𝑐𝑑𝑖𝑣𝑒 π‘‘π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’ π‘œπ‘› 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠=(π‘‡π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’ π‘œπ‘› π‘œπ‘Ÿπ‘‘π‘–π‘›π‘Žπ‘Ÿπ‘¦ π‘–π‘›π‘π‘œπ‘šπ‘’)(1βˆ’% π‘œπ‘“ 𝑒π‘₯π‘’π‘šπ‘ 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠)

Where:

π‘‚π‘Ÿπ‘‘π‘–π‘›π‘Žπ‘Ÿπ‘¦ π‘–π‘›π‘π‘œπ‘šπ‘’ π‘‘π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’=40%
πΆπ‘Žπ‘π‘–π‘‘π‘Žπ‘™ π‘”π‘Žπ‘–π‘›π‘  π‘‘π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’=28%
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 π‘π‘’π‘Ÿ π‘ β„Žπ‘Žπ‘Ÿπ‘’=$0.50
% π‘œπ‘“ 𝑒π‘₯π‘’π‘šπ‘π‘‘ 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠=85%

Substituting the values into the equation.

𝐸𝑓𝑓𝑒𝑐𝑑𝑖𝑣𝑒 π‘‘π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’ π‘œπ‘› 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠=(0.4)(1βˆ’0.85)
𝐸𝑓𝑓𝑒𝑐𝑑𝑖𝑣𝑒 π‘‘π‘Žπ‘₯ π‘Ÿπ‘Žπ‘‘π‘’ π‘œπ‘› 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠=0.06=6%

Next, use the equation relating the prices before and after dividends to taxes to find the change in share price.

(𝑃_π΅βˆ’π‘ƒ_𝐴)/𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑=(1βˆ’π‘‘_π‘œ)/(1βˆ’π‘‘_𝑐𝑔 )

Where:

𝑃_𝐡=π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘π‘’π‘“π‘œπ‘Ÿπ‘’ 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑=$10
𝑃_𝐴=π‘ƒπ‘Ÿπ‘–π‘π‘’ π‘Žπ‘“π‘‘π‘’π‘Ÿ 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑑_π‘œ=π‘‡π‘Žπ‘₯ π‘œπ‘› π‘œπ‘Ÿπ‘‘π‘–π‘›π‘Žπ‘Ÿπ‘¦ π‘–π‘›π‘π‘œπ‘šπ‘’=6%(π΄π‘“π‘‘π‘’π‘Ÿ π‘Žπ‘‘π‘—π‘’π‘ π‘‘π‘šπ‘’π‘›π‘‘)
𝑑_𝑐𝑔=π‘‡π‘Žπ‘₯ π‘œπ‘› π‘π‘Žπ‘π‘–π‘‘π‘Žπ‘™ π‘”π‘Žπ‘–π‘›π‘ =28%

Substituting the given and calculated values into the equation.

($10βˆ’π‘ƒ_𝐴)/$0.50=(1βˆ’0.06)/(1βˆ’0.28)
Making 𝑃_𝐴 the subject of the equation.
𝑃_𝐴=$10βˆ’((1βˆ’0.06)($0.50)/((1βˆ’0.28) ))
𝑃_𝐴=$10βˆ’$0.653
𝑃_𝐴≅9.35

The share price drops from $10 to $9.35 after the dividend.

Similar Post: Adaptive Structures

Reference

Damodaran, A. (2010).Β Applied corporate finance. John Wiley & Sons.

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QuestionΒ 

Week 8 Chapter 10 Questions

Select three formula-driven problems from Chapter 10 that you wish to showcase and prepare a Microsoft Excel document showing the Excel formulas used to prepare the solution for those problems.

Chapter 10 Questions

REMINDER: Part of the grade you receive on your problems is the utilization of Formulas. Therefore, do not pick issues that only require a narrative!

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