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Homework answers / question archive / A newly issued 10-year maturity, 9% coupon bond making annual coupon payments is sold to the public at a price of $958
A newly issued 10-year maturity, 9% coupon bond making annual coupon payments is sold to the public at a price of $958. What will be an investor’s taxable income from the bond over the coming year? The bond will not be sold at the end of the year. The bond is treated as an original issue discount bond.
taxable income ?
NPER = 10 years [Number of periods signified by Time to maturity]
PMT = 9% * 1,000 = $90 [Coupon Payment = Coupon rate * Face Value]
PV = -958 [Price of bond paid at the time of purchase. As it is a cash outflow, hence, with a negative sign]
FV = 1,000 [Face value received at maturity of the bond]
Putting the above paramteres either in Excel's RATE function or a financial calculator and solving for Rate. The calculated Rate will be the Yield To Maturity of the bond.
YTM of the bond = RATE(NPER, PMT, PV, FV) = RATE(10,90,-958,1000) = 9.67%
Using the YTM, we can find the Price of bond one year later.
Time to maturity after 1 year = 9 years
Price of the bond after 1 year = Coupon * (1 - (1+YTM)-T) / YTM + Face Value / (1 + YTM)T
Price of the bond after 1 year = 90 * (1 - (1 + 9.67%)-9) / 9.67% + 1000 / (1 + 9.67%)9
Price of the bond after 1 year = 90 * 5.8344 + 435.58 = 525.10 + 435.58
Price of the bond after 1 year = $960.68
Capital Gains over the year = Price of the bond after 1 year - Price of the bond at the time of purchase
Capital Gains over the year = 960.68 - 958 = $2.68
Interest Earnings over the year = $90
Total Taxable Income = Capital Gains + Interest earning = 90 + 2.68
Hence, Taxable Income from the bond over the year = $92.68
