Question

Question 7

You bought a 10-year, 5% coupon bond for $1,000 and sold it 1 year later for $1,050.

What is the rate of return on your investment if the bond pays interest annually?

If your marginal tax rate is 35%, and 50% of capital gains are taxable, what is the after-tax rate of return on your bond investment?

Answer 1

ROI = [Int Income + Capital gain] / Investment

Int Income = face Value * Coupon rate

= $ 1000 * 5% = $ 50

capital gain = Sale value - Purchase value

a.

ROI = [Int Income + Capital gain] / Investment

$ 1050 - $ 1000 = $ 50

= [($1000*5%)+ ($1050 - $1000)]/ $ 1000

= [ $50 + $ 50 ] / $ 1000

= $ 100 / $ 1000

= 0.10 i.e 10%

ROI after tax = [Int Income after tax + Capital gain after tax] / Investment

Int Income after Tax = Int Income * (1 - Tax rate )

= $ 50 * (1 - 0.35)

= $ 50 *0.65

= $ 32.5

capital gain after tax = capital Gain (1 - Capital Gain tax rate)

= $ 50*(1-0.50)

=$50*0.50

= $ 25

ROI after tax = [Int Income after tax + Capital gain after tax] / Investment

= [$ 32.5 + $ 25 ] / $ 1000

= $ 57.5 / $ 1000

= 0.0575 i.e 5.75%

After tax rate of return is 5.75%

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