1. On June 2011, you buy a corporate bond with FV of 1000 and annual coupon of 8
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Question
1. On June 2011, you buy a corporate bond with FV of 1000 and annual coupon of 8%. At the time of purchase, the bond had a maturity of 10 years and a yield to maturity of 12%.
On June 2012, the yield to maturity of this bond was 11.5% and you sell it at its market value. You pay 40% tax on your coupon income and 25% tax on your capital gain income.
Calculate after tax rate of return on this investment.
2. A 9%, 16-year bond has a yield to maturity of 11% and a duration of 9.25 years. If the market yield changes by 32 basis points, how much change will there be in the bond price in percentage? And in dollar price?
Explanation / Answer
1. On June 2011, you buy a corporate bond with FV of 1000 and annual coupon of 8%. At the time of purchase, the bond had a maturity of 10 years and a yield to maturity of 12%.
On June 2012, the yield to maturity of this bond was 11.5% and you sell it at its market value. You pay 40% tax on your coupon income and 25% tax on your capital gain income.
Calculate after tax rate of return on this investment.
Purchase Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the period) = 10
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*8% = 80
FV (indicates the face value) = 1000
Rate (indicates YTM) = 12%
Purchase Bond Value = pv( 12%,10,80,1000)
Purchase Bond Value = $ 773.99
Sale Bond Value = pv(rate, nper,pmt,fv)
Nper (indicates the period) = 9
PV (indicates the price) = ?
PMT (indicate the annual payment) = 1000*8% = 80
FV (indicates the face value) = 1000
Rate (indicates YTM) = 11.5%
Sale Bond Value = pv( 11.5%,9,80,1000)
Sale Bond Value = $ 809.91
Capital Gain = Sale Bond Value - Purchase Bond Value
Capital Gain = 809.91 - 773.99
Capital Gain = $ 35.92
Coupon Income = 1000*8% = $ 80
Tax on Coupon Income = 40%*80 = $ 32
Tax on Capital Gain Income = 25%*35.92 = $ 8.98
After Tax Income = Capital Gain + Coupon Income - Tax on Coupon Income - Tax on Capital Gain Income
After Tax Income = 35.92 + 80 - 32 - 8.98
After Tax Income = $ 74.94
After tax rate of return on this investment = After Tax Income/ Purchase Bond Value
After tax rate of return on this investment = 74.94/773.99
After tax rate of return on this investment = 9.68%
Answer
After tax rate of return on this investment = 9.68%
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