Question

Please by detials !

2. Assume a bond matures for $1000 six years from today and has a 7% coupon rate with semiannual coupons. What is the value of the bond today if the yield to maturity on the bond equals 8.5%?

Answer 1

Calculation of Value of Bond

Formula:

Value of Bond = (Coupon X PVAF @ YTM for n years) + (Face Value X PVF @ YTM for n^th year)

It is given that the bond is a semiannual coupon.

Coupon = (1000 * 7%)/2

= 35

Yield To Maturity (YTM) = 8.5%/2

= 4.25%

n is the number of years to maturity which is 6 * 2 = 12

Calculation of PVF by this formula

PVF   = 1 / (1+r)ⁿ

= 1 / (1 + 0.0425)¹²

= 0.60686

Calculation of PVAF by this formula

PVAF = {[1 - (1 + 0.07)^-12] / 0.0425}

= 9.25

Value of Bond = (Coupon X PVAF @ YTM for n years) + (Face Value X PVF @ YTM for n^th year)

Value of Bond = (35 X PVAF @ 4.25% for 12 years) + (1000 X PVF @ 4.25% for 12th year)

= (35 X 9.25) + (1000 X 0.60686)

= 323.75 + 606.86

= 930.61

Value of Bond = $930.61

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