Question

A 5-year bond, pays 8% coupon rate annually, If similar bonds are currently yielding 10% annually, what is the market value of the bond? Use the formula and semi-annual analysis.

Answer 1

Answer : Calculation of Market Value of Bond :

Market Value of Bond = (Coupon * PVAF @ 10% for 20 years) + (Face vaue * PVF@ 10% for 20th year)

Coupon = 1000 * 8% = 80

Face Value = 1000

Value of Bond = (80 * PVAF @ 10% for 5 years) + (1000 * PVF@ 10% for 5th year)

= (80 * 3.79078676939) + (1000 * 0.62092132305)

= 303.262941551 + 620.92132305

= 924.18

Now we will do Semi-annual Compounding :

Market Value of Bond = (Coupon * PVAF @ 10% for 20 years) + (Face vaue * PVF@ 10% for 20th year)

Coupon = 1000 * 8% / 4 = 40

Face Value = 1000

Yield rate is 10% / 2 = 5%

Number of years to maturity is 5 * 2 = 10

Value of Bond = (40 * PVAF @ 5% for 10 years) + (1000 * PVF@ 5% for 10th year)

= (40 * 7.72173492899) + (1000 * 0.61391325351)

= 308.869397159 + 613.91325351

= 922.78

We can see that semiannually coupon leads to lower share price as compared to annual Coupon.