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_𝐵−𝑃_𝐴)/𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑=(1−𝑡_𝑜)/(1−𝑡_𝑐𝑔 )
Where:
𝑃_𝐵=𝑃𝑟𝑖𝑐𝑒 𝑏𝑒𝑓𝑜𝑟𝑒 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑃_𝐴=𝑃𝑟𝑖𝑐𝑒 𝑎𝑓𝑡𝑒𝑟 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑡_𝑜=𝑇𝑎𝑥 𝑜𝑛 𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑖𝑛𝑐𝑜𝑚𝑒
𝑡_𝑐𝑔=𝑇𝑎𝑥 𝑜𝑛 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛𝑠

Substituting the known values:
(50−46.5)/5=(1−𝑡_𝑜)/(1−0.4)
Re-arranging to make 𝑡_𝑜 the subject of the formula:
𝑡_𝑜=1−((50−46.5)(1−0.4)/5)
𝑡_𝑜=1−0.42
𝑡_𝑜=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/〖1.1〗^n

Next, relate the prices before and after 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/〖1.1〗^n

Substituting the values into the formula:

(10-9.2)/1.0=(1-0.5)/(1-0.5/〖1.1〗^n )

0.8=0.5/(1-0.5/〖1.1〗^n )

Simplifying the expressions to solve for n gives:

〖1.1〗^n=1.33

Solving for n using logarithms gives:

n≅3

The capital gains taxes are being deferred by 3 years.

Question 4

Question 4					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.
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑜𝑛 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠=(𝑇𝑎𝑥 𝑟𝑎𝑡𝑒 𝑜𝑛 𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑖𝑛𝑐𝑜𝑚𝑒)(1−% 𝑜𝑓 𝑒𝑥𝑒𝑚𝑝 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠)

Where:

𝑂𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑖𝑛𝑐𝑜𝑚𝑒 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒=40%
𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛𝑠 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒=28%
𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑝𝑒𝑟 𝑠ℎ𝑎𝑟𝑒=$0.50
% 𝑜𝑓 𝑒𝑥𝑒𝑚𝑝𝑡 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠=85%

Substituting the values into the equation.

𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑜𝑛 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑𝑠=(0.4)(1−0.85)
𝐸𝑓𝑓𝑒𝑐𝑡𝑖𝑣𝑒 𝑡𝑎𝑥 𝑟𝑎𝑡𝑒 𝑜𝑛 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_𝐵−𝑃_𝐴)/𝐷𝑖𝑣𝑖𝑑𝑒𝑛𝑑=(1−𝑡_𝑜)/(1−𝑡_𝑐𝑔 )

Where:

𝑃_𝐵=𝑃𝑟𝑖𝑐𝑒 𝑏𝑒𝑓𝑜𝑟𝑒 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑=$10
𝑃_𝐴=𝑃𝑟𝑖𝑐𝑒 𝑎𝑓𝑡𝑒𝑟 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑
𝑡_𝑜=𝑇𝑎𝑥 𝑜𝑛 𝑜𝑟𝑑𝑖𝑛𝑎𝑟𝑦 𝑖𝑛𝑐𝑜𝑚𝑒=6%(𝐴𝑓𝑡𝑒𝑟 𝑎𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡)
𝑡_𝑐𝑔=𝑇𝑎𝑥 𝑜𝑛 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑔𝑎𝑖𝑛𝑠=28%

Substituting the given and calculated values into the equation.

($10−𝑃_𝐴)/$0.50=(1−0.06)/(1−0.28)
Making 𝑃_𝐴 the subject of the equation.
𝑃_𝐴=$10−((1−0.06)($0.50)/((1−0.28) ))
𝑃_𝐴=$10−$0.653
𝑃_𝐴≅9.35

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

Reference

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

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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.

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