How to calculate the new price of a bond if its YTM increases?

Question

I'm trying to calculate the current price of a corporate bond one year after its YTM has changed.

A corporate bond was issued at 01/01/2010, has the following caracteristics:

• A face value of 5000$.
• A duration of 6 years.
• A coupon rate of 7%.
• A YTM of 7.53%.

Questions:

1. What is the price of the bond?
2. If at 01/01/2011 the YTM increases to 9%, what will the new price be?

My answer:

1. Bond Price = 350/(1+0.0753) +...+ 350/(1+0.0753)^6 + 5000/(1+0.0753)^6 = 4875.727183

where: 350 = 5000*0.07

2. One of the formulas used to calculate the current market price of the bond is:

Current Market Price of Bond = Annual Interest Payment/Current Yield.

But this formula doesn't take the remaining years of the corporate bond into account. How should I go about calculating the bond's current market price in this situation?

Thanks in advance.

Answer 1

this formula doesn't take into account the remaining years of the corporate bond into account

You're right - but you also need the current yield, which you do not have (it is different than yield to maturity). The current yield is just the coupon divided by the market price, so the formula you have is just a rearrangement of that.

However, you can use the same formula you used in step 1. In Step 1, you are discounting 6 years' worth of coupons and the final face value. So after one year, there are now five years of coupons and the final value that are discounted:

350/(1+0.09) +...+ 350/(1+0.09)^5 + 5000/(1+0.09)^5 

I'll leave the actual arithmetic to you...