Question

Komiko Tanaka invests $21,000 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 willkomiko retain after-taxes 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

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=$21000(1+10%)5

FV5=$33820.71

Capital gains on above is $33820.71*15%=$5073.1065

so, the cash as on the end of year 5 would be $33820.71-$5073.1065=$26748(rounded off)

(b)

Future value5=Present value(1+r)n

Here n= period=5years;Future Value5=$28748

$28748=$21000(1+r)5

r = 6.48%p.a

So, the after tax rate of return is 6.48%p.a

(c)

Future value5=Present value(1+r)n

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

FV5=$21000(1+10%)5

FV5=$33820.71

Capital gains on above is $33820.71*25%=$8455.1775

so, the cash as on the end of year 5 would be $33820.71-$8455.1775=$25365(rounded off)

(d)

Future value5=Present value(1+r)n

Here n= period=5years;Future Value5=$25365

$25365=$21000(1+r)5

r = 3.85%p.a

So, the after tax rate of return is 3.85%p.a

(e)

Future value15=Present value(1+r)n

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

FV15=$21000(1+10%)15

FV15=$87722

Capital gains on above is $87722*15%=$13158.3

so, the cash as on the end of year 5 would be $87722-$13158.3=$74564(rounded off)

(f)

Future value15=Present value(1+r)n

Here n= period=15years;Future Value15=$74564

$74564=$21000(1+r)15

r = 8.82%p.a

So, the after tax rate of return is 8.82%p.a