Question

1.) Find the APR, or stated rate, in each of the following cases:

a. EAR 11.5%, semi-annual compounding

b. EAR 12% with quarterly compounding

2.) Consider a 3-year bond with a face value of $1,000 that has a coupon rate of 7%, with semi-annual payments.

a. What is the dollar amount of each coupon from this bond?

b. How many times of coupon payments will be made to the maturity?

3. Assume that a bond will make coupon payments every six months as shown:

6 months= $20 dollars, 1 year= $20, 18 months= $20, 2 years= $20+$1000

a. What is the coupon rate (in percent)?

b. What is the face value?

4. What is the bond price of $1,000 bond with 6% coupon rate, annual coupons, and 2 years to maturity if the YTM is 8%?

5. What is the bond price of $1,000 bond with 6% coupon rate, semi-annual coupons, and 2 years to maturity if the YTM is 8%?

6. Suppose a 10-year, $1000 bond with an 8% coupon rate and annual coupons is sold for $1034.74.

a. What is the bond’s YTM?  

b. Is the YTM higher or lower than the coupon rate?

SHOW HOW YOU GOT ANSWERS PLEASE!

Answer 1

1) Stated rate is the annual interest rate.

     To calculate the same, we need to use the below formula:

     Stated rate = (1+r/n)^n-1

     r = interest rate

     n = number of compounding

    r = 11.5%

n = 2

So, stated rate = (1+0.115/2)^2-1 = 0.118306 or 11.8%

2. r = 12%

n = 4

So, stated rate = (1+0.12/4)^4-1 = 12.6%

2) Here, coupon is 7% with semi annual payment, so in a year coupon will be paid twice.

    a) The coupon payment will be $35 (1000*7%/2) each for each six months i.e $35 twice in a year.

    b) Each year, tow coupon payments will be made, so 6 in total (3*2).

3) The coupon payment is made twice in a year (semi-annual). The bond is of two years maturity as after two years coupon payment ($20) + face value ($1000) in paid.

    a) In a year, $40 is paid as coupon, so 40/1000 = 4% is the coupon rate.

    b) Face value is $1000

4) Now, the formula for calculating price. price is nothing but the present value of all the future cash flows of the bond

Price = Coupon payment * (1- (1+YTM)^-n)/YTM + Par value * (1+YTM)^-n

       = 60*(1-(1+0.08)^-2)/0.08+1000*(1+0.08)^-2

       = 964.33. Note that as coupon is lower than YTM, price is lesser than par value.

5) Now, the formula for calculating price. price is nothing but the present value of all the future cash flows of the bond. Here coupon is paid semi annually, so n will be 4 (2*2) while YTM and coupon wll be halved.

Price = Coupon payment * (1- (1+YTM)^-n)/YTM + Par value * (1+YTM)^-n

       = 30* (1-(1+0.04)^-4)/0.04+1000*(1+0.04)^-4

       = 963.7. Note that as coupon is lower than YTM, price is lesser than par     

          value.