Question

What is the price of a four-year zero-coupon (or pure discount) bond with a $100 face value and yield to maturity (YTM) of 5.95%?

The Japanese government issued a zero-coupon bond with maturity of 2054 and face value of ?50,000. The current price of this bond is ?42,690. Find its YTM in percentage

Suppose we have a seven-year bond with face value of $1000, a coupon rate of 7%, quarterly coupon payments, and a yield to maturity of 5% APR. Find its price.

Answer 1

We can calculate the price of the zero coupon bond by bringing its future cash flows in present terms, using its yield-to-maturity.

The zero-coupon bond will have only one payment which is its face value $100, at the end of four years.

The formula for calculating its price is (face value of bond)/ (1 + YTM)ⁿ. where n is the time to maturity in years.

Hence the price of the first bond = $100. (1.0595)⁴ = $79.36

We will have to use a financial calculator to calculate the YTM  on the Japanese bond. The maturity is in 2054, which means there are 2054-2019 = 35 years to maturity

Input, n = 35, PV = - Y 42,690, PMT = 0 (as there are no coupons), FV = Y 50,000, into the calculator. I/Y or YTM = 0.45%

Now, let's calculate the price on the last bond. We can calculate the bond price using financial calculator,

coupons are paid quarterly

coupon payment per quarter = (7%/4 )*$1000 = $17.5

Enter into the calculator,

n = 7 * 4 = 28

YTM or I/Y = 5%/4 = 1.25%

PMT = $17.5

FV = par value = $1,000

PV, which is the current price of the bond will be $1,117.51