Question

Komiko Tanaka invests $24,500 in LymaBean, Inc. LymaBean does not pay any dividends. Komiko projects that her investment will generate a 10 percent before-tax rate of return. She plans to invest for the long term.

a. How much cash will Komiko retain, after-taxes, if she holds the investment for 5 years and then she sells it when the long-term capital gains rate is 15 percent? (Do not round intermediate calculations. Round your final answer to the nearest whole dollar amount.)

Cash retained ( )

b. What is Komiko’s after-tax rate of return on her investment in part (a)?

(Do not round intermediate calculations. Round your percentage answer to 2 decimal places.)

After-tax rate of return ( )

c. How much cash will Komiko retain, after-taxes, if she holds the investment for 5 years and then sells when the long-term capital gains rate is 25 percent? (Do not round intermediate calculations. Round your final answer to the nearest whole dollar amount.)

Cash retained ( )

d. What is Komiko’s after-tax rate of return on her investment in part (c)? (Do not round intermediate calculations. Round your percentage answer to 2 decimal places.)

After-tax rate of return ( )

e. How much cash will Komiko retain, after taxes, if she holds the investment for 15 years and then she sells when the long-term capital gains rate is 15 percent? (Do not round intermediate calculations. Round your final answer to the nearest whole dollar amount.)

Cash retained ( )

f. What is Komiko’s after-tax rate of return on her investment in part (e)? (Do not round intermediate calculations. Round your percentage answer to 2 decimal places.)

After-tax rate of return ( )

Answer 1

In the books of Komiko Tanaka

(a)

Future value5=Present value(1+r)n

Here n= period=5years;r=required rate of return=10%

FV5=$24500(1+10%)5

FV5=$39457.495

Capital gains on above is $39457.495*15%=$5918.62425

so, the cash as on the end of year 5 would be $39457.495-$5918.62425=$33539(rounded off)

(b)

Future value5=Present value(1+r)n

Here n= period=5years;Future Value5=$33539

$33539=$21000(1+r)5

r = 9.82%p.a

So, the after tax rate of return is 9.82%p.a

(c)

Future value5=Present value(1+r)n

Here n= period=5years;r=required rate of return=10%

FV5=$24500(1+10%)5

FV5=$39457.495

Capital gains on above is $39457.495*25%=$9864.37375

so, the cash as on the end of year 5 would be $39457.495-$9864.37375=$29593(rounded off)

(d)

Future value5=Present value(1+r)n

Here n= period=5years;Future Value5=$29593

$29593=$21000(1+r)5

r = 7.10%p.a

So, the after tax rate of return is 7.10%p.a

(e)

Future value15=Present value(1+r)n

Here n= period=15years;r=required rate of return=10%

FV15=$24500(1+10%)15

FV15=$102342.58015

Capital gains on above is $102342.58015*15%=$15351.3870225

so, the cash as on the end of year 15 would be $102342.58015-$15351.3870225=$86991(rounded off)

(f)

Future value15=Present value(1+r)n

Here n= period=15years;Future Value15=$86991

$86991=$24500(1+r)15

r = 4.31%p.a

So, the after tax rate of return is 4.31%p.a