Question

A 7.00 percent coupon bond with 25 years left to maturity is priced to offer a 5.6 percent yield to maturity. You believe that in one year, the yield to maturity will be 6.1 percent.

What would be the total return of the bond in dollars? (Assume interest payments are semiannual.)

What would be the total return of the bond in percent? (Assume interest payments are semiannual.)

Answer 1

Current Price of the Bond

The Price of the is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 2.80% [5.60% c ½]

Maturity Period = 50 Year [25 Years x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $35[PVIFA 2.80%, 50 Year] + $1,000[PVIF 2.80%, 50 Years]

= [$35 x 26.73615] + [$1,000 x 0.25139]

= $935.76 + $251.39

= $1,187.15

Price of the Bond in 1 year

The Price of the is the Present Value of the Coupon Payments plus the Present Value of the face Value

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $35 [$1,000 x 7% x ½]

Semi-annual Yield to Maturity = 3.05% [6.10% c ½]

Maturity Period = 48 Year [24 Years x 2]

Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value

= $35[PVIFA 3.05%, 48 Year] + $1,000[PVIF 3.05%, 48 Years]

= [$35 x 25.03520] + [$1,000 x 0.23643]

= $876.23 + $236.43

= $1,112.66

The total return of the bond in dollars

The total return of the bond in dollars = Annual Coupon amount + Change in the bond’s price in dollars

= [$35 x 2] + [$1,112.66 - $1,187.15]

= $70 - $74.49

= -$4.49 (Negative)

“The total return of the bond in dollars = -$4.49 (Negative)”

The total return of the bond in percentage

The total return of the bond in percentage = [The total return of the bond in dollars / Current Bond Price] x 100

= [-$4.49 / $1,187.15] x 100

= -0.38% (Negative)

“The total return of the bond in percentage = -0.38% (Negative)”

NOTE

-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)ⁿ} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.  

--The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)ⁿ], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.