Question

1. What is the price of a $1000 face value zero-coupon bond with 4 years to maturity if the required return on these bonds is 3%?

2. Consider a bond with par value of $1000, 25 years left to maturity, and a coupon rate of 6.4% paid annually. If the yield to maturity on these bonds is 7.5%, what is the current bond price?

3. One year ago, your firm issued 14-year bonds with a coupon rate of 6.9%. The bonds make semiannual payments. If the yield to maturity on these bonds is currently 5.2% APR, what is the current bond price?

4. Suppose a zero-coupon bond with five years remaining to maturity is selling for 81.2% of face value. What is the yield to maturity of this bond?

5. Suppose your firm just issued a callable 10-year, 6% coupon bond with annual coupon payments. The bond can be called at par in one year or anytime thereafter on a coupon payment date. It is currently priced at 102% of par. What is the bond’s yield to maturity and yield to call?

Answer 1

price of coupon = Coupon payment per period * [1-(1+i)^-n]/i + par value/(1+i)^n

i = interest rate per period

n = number of periods

1)

Price = 1000/(1+0.03)^4

= 888.49

2)

Price = 64 * [1-(1+0.075)^-25]/0.075 + 1000/(1+0.075)^25

= 877.38

3)

Price = (69/2) * [1-(1+0.052/2)^-26]/(0.052/2) + 1000/(1+0.052/2)^26

= 1159.19

4)

812 = 1000/(1+YTM)^5

=>

Yield to maturity = (1000/812)^(1/5) - 1

= 4.25%

5)

using excel rate function

YTM = RATE(number_of_periods, payment_per_period, present_value, [future_value], [end_or_beginning], [rate_guess])

= RATE(10,60,-1020,1000)

= 5.73%

Yield to call = 6% , since call is price is equal to par value