Question

A 20-year semi-annual bond has just been issued with its coupon rate set at the current market yield of 6 percent. How much would the price of the bond change (in percentage terms) if the market yield suddenly fell by 50 basis points? How much would the price change if the yield rose by 50 basis points?

Answer 1

(a)-Change (in percentage terms) if the market yield suddenly fell by 50 basis points = 6.02%

(b)-Change (in percentage terms) if the market yield rose by 50 basis points = -5.55% (Negative)

Workings

Change (in percentage terms) if the market yield suddenly fell by 50 basis points

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $30 [$1,000 x 6% x ½]

Semi-annual Yield to Maturity = 2.75% [(6% - 0.50%) x ½]

Maturity Period = 40 Years [20 Years x 2]

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

= $30[PVIFA 2.75%, 40 Years] + $1,000[PVIF 2.75%, 40 Years]

= [$30 x 24.07810] + [$1,000 x 0.33785]

= $722.35 + $337.85

= $1,060.20

Percentage change in the price of Bond = [(Current Price – Face Value) / Face Value] x 100

= [($1,060.20 - $1,000) / $1,000] x 100

= [$60.20 / $1,000] x 100

= 6.02%

Change (in percentage terms) if the market yield rose by 50 basis points

Face Value of the bond = $1,000

Semi-annual Coupon Amount = $30 [$1,000 x 6% x ½]

Semi-annual Yield to Maturity = 3.25% [(6% + 0.50%) x ½]

Maturity Period = 40 Years [20 Years x 2]

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

= $30[PVIFA 3.25%, 40 Years] + $1,000[PVIF 3.25%, 40 Years]

= [$30 x 22.20843] + [$1,000 x 0.27823]

= $666.25 + $278.23

= $944.48

Percentage change in the price of Bond = [(Current Price – Face Value) / Face Value] x 100

= [($944.48 - $1,000) / $1,000] x 100

= [-$55.52 / $1,000] x 100

= -5.55% (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.