Question

You have a $22,000 semi-annual 1.000% bond maturing in exactly 18 years. If it is priced to yield 8.250% then the bond has a market value of

$ XXX

and the income yield is XXX%

Answer 1

No of periods = 18 years * 2 = 36 semi-annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (1% / 2) * $22,000

Coupon per period = $110

Bond Price = Coupon / (1 + YTM)^period + Face value / (1 + YTM)^period

Bond Price = $110 / (1 + 8.25% / 2)¹ + $110 / (1 + 8.25% / 2)² +...+$110 / (1 + 8.25% / 2)³⁶ + $22,000 / (1 + 8.25% / 2)³⁶

Using PVIFA = ((1 - (1 + Interest rate)^{- no of periods}) / interest rate) to value coupons

Bond Price = $110 * ((1 - (1 + 8.25% / 2)^-36) / 8.25%) + $22,000 / (1 + 8.25% / 2)³

Bond Price = $2044.38 + $5133.84

Bond Price = $7178.22

Bond Market value = $7178.22

Income Yield = Annual Coupon Payment / Bond price

Income Yield = ($110 * 2) / $7178.22

Income Yield = 3.0648%