Question

You buy an eight-year bond that has a 5.50% current yield and a 5.50% coupon (paid annually). In one year, promised yields to maturity have risen to 6.50%. What is your holding-period return?

Answer 1

Current Price of the Bond = $1,000 (Bond Price at 5.50% current yield and a 5.50% coupon rate)

Price of the Bond in One Year

Face Value = $1,000

Annual Coupon Amount = $55 [$1,000 x 5.50%]

Yield to Maturity (YTM) of the Bond = 6.50%

Maturity Years = 7 Years [8 Years – 1 Year]

The Price of the bond = Present Value of the Coupon payments + Present Value of Face Value

= $55[PVIFA 6.50%, 7 Years] + $1,000[PVIF 6.50%, 7 Years]

= [$55 x 5.48452] + [$1,000 x 0.64351]

= $301.64 + $643.51

= $945.15

Holding-period return on the Bond

Holding-period return on the Bond = [(Coupon Amount + Change in Bond Price) / Current Price of the Bond] x 100

= [{$55 + ($945.15 - $1,000)} / $1,000] x 100

= [($55 - $54.85) / $1,000] x 100

= [$0.15 / $1,000] x 100

= 0.02%

“Therefore, the Holding-period return on the Bond would be 0.02%”

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.