Question

Q1) Two bonds with $1,000 par value were issued 2 years ago, with maturity 4 and 7 years. Their coupon rate was 9%. Today, interest rates are unstable. Calculate the current prices for both bonds in the following scenarios:

a. Similar risk bonds carry a 3 % interest rate

b. Similar risk bonds carry an 8 % interest rate

c. Similar risk bonds carry a 13 % interest rate

Explain your answer.

Note: this is not a multiple choice question

Answer 1

As two years have passed, we now have two bonds with maturity of 2 and 5 years. Coupon rate is 9%.

1.We need to discount the coming cashflows to get the price.

Price of first bond= 90/1.03+1090/1.03^2

Price of second bond = 90/1.03 + 90/1.03^2 + 90/1.03^3 + 90/1.03^ 4 + 1090/1.03^5

Hence, price of first bond = 1114.81

Price of second bond = 1274.78

We can use excel function =pv(.03,5,90,1000) for second bond's price calculation.

2. Similarly use excel function and replace .03 with 0.08 and get the price

Price of first bond = 1017.83

Price of second bond = 1039.93

3. Using 13%, we get price of

First bond = 933.28

Second bond= 859.31

Note in first two cases, interest rate in market is less than coupon rate, hence we are getting more money as coupon and that is the reason price is more than 1000. Price of second bond is higher in both cases as we are getting paid higher by coupon payments than current rate of interest. Hence we have to pay higher

In third case, we get coupon payments less than Market interest rate, hence we would want return in terms that we would pay less than 1000 face value today. For second bond for this compensation we would pay less than first bond as for 5 years we get paid in terms of coupon payments than prevalent market interest rate.

Note that had market interest been 9% both bonds' price today would have been 1000. In this case coupon = market interest rate.