Question

Mary buys a 10-year, 1,000 par value bond with 8% semiannual coupons. The price
of the bond to earn a yield of 6% convertible semiannually is 1,204.15. The redemption value is more
than the par value. Calculate the price Mary would have to pay for the same bond to yield 10%
convertible semiannually. Show all work.

Answer 1

We will first calculate the Redemption Value of this bond, as below:

Tenure = 10 years or 20 semi annual periods

Coupon = 8% p.a. or 4% per semi annual period

Par Value = 1000 and at 6% YTM (or 3% per semi annual period), the current price of the bond is 1204.15

Now, we will first calculate all the cash flows for this bond till maturity i.e 40 per semi annual period for 19 periods and the 20 semi annual period Mary shall receive 40 plus the Redemption Value (RV). When we discount these cash flows at 3% per semi annual period (6% annual YTM) the present value should be equal to 1204.15

Hence, 1204.15 = 40/(1.03) + 40/(1.03)² + 40/(1.03)³ ..... + 40/(1.03)^​19 + 40/(1.03)²⁰ + RV/(1.03)^​20 ​

We can solve this equation, using excel sheet, as below

​Now solving this, we get 1204.15 = 595.10 + RV/(1.03)^​20 which will give us (1204.15 - 595.10) = RV / (1.81)

i.e RV = 609.05 * 1.81 = 1100.01 1100.

Thus, we get the RV to be 1100.

Now we calculate the current price which Mary should pay to earn an yeild of 10% by simply discounting the 20 semi annual period bond cash flows by 5% (semi annual period rate). The sum of these discounted cash flows shall be the current price which will result in 10% annual yeild.

Current Price_{10% yeild}​ = 40/(1.05) + 40/(1.05)² + 40/(1.05)³​ ...... + 40/(1.05)¹⁹​ + 40/(1.05)²⁰​ + 1100/(1.05)²⁰

This will give us Current Price_{​10% yield}​ = 913.07. The excel sheet is also enclosed below