Question

The Morgan corporation has two different bonds currently outstanding. Bond M has a face value of $20,000 and matures in 15 years. The bond makes no payments for the first 5 years, then pays $600 every six months over the subsequent six years, and finally pays $1,000 every six months over the last four years. Bond N also has a face value of $20,000 and a maturity of 15 years, it makes no coupon payments over the life of the bond. If the required return on both of these bonds is 10 percent compounded annually, what is the current price of bond M? Of Bond N?

Answer 1

For 6 months, the rate of interest will be (1.1^0.5) -1 = 4.88%

We can use excel excel to find present value of these cash flows in two parts

Use function =pv(.0488,12,600) to get the value of all these cash flows at the end of 5 years.

We will discount this value,i.e. divide by 1.1^5 to get its value today.

5364.13 comes as the value of excel function used. That is the value of all cashflows for 6 years at the end of fifth year. Their present value is

5364.13/1.1^5 = 3324.49

Again similarly, using =pv(.0488,8,1000) gives the value of all last 4 years' cashflows at the end of 11th year.

Value comes as 6494.68

Now we discount it by dividing it by 1.1^11

The value comes as 6494.68/1.1^11 = 2276.35

Finally we discount the face value we receive at the end of 15 years = 20000/1.1^15 = 4787.84

Therefore, the price of this bond should be 2276.35+3324.49+4787.84 = 10388.68

The price of bond M = 10388.68

Price of bond N is 4787.84 ( we have already calculated it above)