Question

A 6.70 percent coupon bond with 24 years left to maturity is priced to offer a 5.8 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.3 percent.

What would be the total return of the bond in dollars? (assume interest payments are semiannual) (negative amount should be indicated by a minus sign. do not round intermediate calculations. Round your final answer to 2 decimal places)

What would be the total return of the bond in percent? (assume interest payments are semiannual) (negative amount should be indicated by a minus sign. do not round intermediate calculations. Round your final answer to 2 decimal places)

Answer 1

a). Current Bond Price = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{(6.70%/2)*$1,000} * {(1 - (1 + 0.058/2)^-(24*2)) / (0.058/2)}] + [$1,000 / {1 + (0.058/2)}^(24*2)]

= [$33.5 * {0.7465 / 0.029}] + [$1,000 / 3.9440]

= [$33.5 * 25.7397] + $253.55

= $862.28 + $253.55 = $1,115.828594

Bond Price in 1 year = PV of Coupon Payment + PV of Maturity Value

= [Periodic Coupon Payment * {(1 - (1 + r)^-n) / r}] + [Face Value / (1 + r)^n]

= [{(6.70%/2)*$1,000} * {(1 - (1 + 0.063/2)^-(23*2)) / (0.063/2)}] + [$1,000 / {1 + (0.063/2)}^(23*2)]

= [$33.5 * {0.7599 / 0.0315}] + [$1,000 / 4.1647]

= [$33.5 * 24.1234] + $240.11

= $808.13 + $240.11 = $1,048.25

Dollar Profit = Price in 1 year - Current Bond Price

= $1,048.25 - $1,115.83 = -$67.58

b). Rate of Return = Dollar Profit / Current Bond Price

= -$67.58 / $1,115.83 = -0.0606, or 6.06%