Question

 

1. Jack and Jill Jones are considering the purchase of a one-thousand-dollar par value bond that pays a five percent coupon. The bond that they are considering has no default             (credit) risk. Coupon interest payments are made semi-annually. There are exactly six-years remaining until maturity. This bond’s market price is equal to $983.25. What is the yield-to-maturity for this bond?

1. 4.33 percent
2. 5.33 percent
3. 6.33 percent
4. 7.33 percent

2.  Jack and Jill Jones are considering the purchase of a one-thousand-dollar par value bond that pays a three percent coupon. The bond that they are considering has no default (credit) risk. Coupon interest payments are made semi-annually. There are exactly ten-years remaining until maturity. This bond’s yield-to-maturity is equal to four percent. What is the market price for this bond?

1. $1,018.20
2. $   718.20
3. $   818.20
4. $   918.20

Answer 1

1). Semi-annual coupon (C) = annual coupon*par value/2 = 5%*1,000/2 = 25

PV (current bond price) = 983.25; FV (par value) = 1,000; N (number of payments) = 6*2 = 12; semi-annual yield = r

The price of the bond has to equal the total of all discounted future cash flows.

Using PV of annuity formula, we can write this as:

Current price = C*[1 - (1+r)^-N]/r + FV/(1+r)^N

983.25 = 25*[1 - (1+r)^-12]/r + 1,000/(1+r)^12

As can be seen, this is a polynomial equation and can be solved by hand, only through trial and error. Since price is a little less than par value, we know that the the YTM has to be slightly greater than the coupon rate of 5%. Keeping that in mind and looking at the options, only option 5.33% seems close enough so we test the equation for it.

r = 5.33%/2 = 2.665%

983.25 = 25*[1 - (1+2.665%)^-12]/2.665% + 1,000/(1+2.665%)^12

983.25 = 983.25 So, answer has to be 5.33% (Option B)

2). Using the same equation as shown above, we have:

Semi-annual coupon (C) = 3%*1,000/2 = 15

FV = 1,000; N = 10*2 = 20; r = 4%/2 = 2%

Bond price = 15*[1 - (1+2%)^-20]/2% + 1,000/(1+2%)^20 = 918.24 (Option D)