Question

What are the YTM of these two bonds?

Bond 1. 100,000 bonds with a coupon rate of 8% (paid semi-annually), a price quote of 120.0 and have 30 years to maturity. The semi-annual YTM is 3.24%.
Bond 2. 100,000 zero coupon bonds (semi-annual compounding) with a price quote of 30.0 and 20 years until maturity.

Answer 1

1)

No of periods = 30 years * 2 = 60 semi annual periods

Coupon per period = (Coupon rate / No of coupon payments per year) * Face value

Coupon per period = (8% / 2) * $100

Coupon per period = $4

Let us compute Yield to Maturity(YTM)

Bond Price = Coupon / (1 + YTM / 2)^period + Face value / (1 + YTM / 2)^period

$120 = $4 / (1 + YTM / 2)¹ + $4 / (1 + YTM / 2)² + ...+ $4 / (1 + YTM / 2)⁶⁰ + $100 / (1 + YTM / 2)⁶⁰

Using Texas Internements BA 2 plus calculator

SET N = 60, PV = -120, FV = 100, PMT = 4

CPT --> I/Y = 3.2398

Yield to Maturity(YTM) = 2 * I/Y

Yield to Maturity(YTM) = 2 * 3.2398%

Yield to Maturity(YTM) = 6.4796%

2)

No of periods = 20 years * 2 = 40 semi annual periods

Bond Price = Face value / (1 + YTM / 2)^period

$30 = $100 / (1 + YTM / 2)⁴⁰

(1 + YTM / 2)⁴⁰ = $100 / $30

(1 + YTM / 2)⁴⁰ = 3.3333

(1 + YTM / 2) = (3.3333)^{(1 / 40)}

(1 + YTM / 2) = 1.030557

YTM / 2 = 0.030557

YTM = 2 * 0.030557

Yield to Maturity(YTM) = 6.1114%

We can also calculate the YTM through the financial calculator

Using Texas Internements BA 2 plus calculator

SET N = 40, PV = -30, FV = 100, PMT = 0

CPT --> I/Y = 3.0557

Yield to Maturity(YTM) = 2 * I/Y

Yield to Maturity(YTM) = 2 * 3.0557%

Yield to Maturity(YTM) = 6.1114%