Question

Assume that Treasury bonds with a par value of $1,000,000 have 3 years to maturity and a coupon rate of 6%. The yield to maturity is 11% and coupon is paid semi-annually. What is the value of the bonds?

Answer 1

Yield to maturity of a bond is nothing but the current yield of a bond except that the total return is calculated by holding the bond till maturity. It assumes that each coupon payment made would be reinvested and recieved at the end of the maturity period.

Given,
Par value = $1000,000
N = number of payments = 3*2 = 6 . (semi-annually)
Coupon rate = 6% p.a.
Coupon paid semi annually, therefore coupon payment or cash flow CF = (6%÷ 2)*1000000 = $30000
YTM = 11%p.a.
YTM semiannual or reinvestment rate "r"= 5.5%, (11/2)
We also get the par value at the end of the maturity period,hence that needs to be discounted at the end of 6th payment.

Bond Price = CF₁/(1+r)¹+CF₂/(1+r)²+CF₃/(1+r)³+CF₄/(1+r)⁴+CF₅/(1+r)⁵+CF₆/(1+r)⁶+Par value/(1+r)⁶
   = 30000/(1+0.055)¹+30000/(1+0.055)²+30000/(1+0.055)³+30000/(1+0.055)⁴+30000/(1+0.055)⁵+ 30000/(1+0.055)⁶+1000000/(1+0.055)6
   = $875111.74

Refer to the table beow :

Payment	Cash Flows	Calculation	Discounted cash flow value
Period 1	30000	30000/(1+0.055)^1	28436.02
Period 2	30000	30000/(1+0.055)^2	26953.57
Period 3	30000	30000/(1+0.055)^3	25548.41
Period 4	30000	30000/(1+0.055)^4	24216.50
Period 5	30000	30000/(1+0.055)^5	22954.03
Period 6	30000	30000/(1+0.055)^6	21757.37
Period 6	1000000	1000000/(1+0.055)^6	725245.83
			875111.74

The bond is trading at a discount with a bond price of $875111.74