Question

Bond 1 has a 4%annual coupon rate, $1000 maturity value, n = 5 years, YTM = 4% (pays a $40 annual coupon at the end of each year for each of the 5 years and $1,000 maturity payment at the end of year 5).

Bond 2 is a zero couponbond with a $1000 maturity value, and n = 5 years; YTM= 4%. (pays no coupons; only a $1,000 maturity payment at the end of year 5)

a. For the Zero Coupon Bond 2 above,what will be your annual compound yield for your 5 year holding period if the bond is held until maturity. (Hint: PV is the price you calculated for Bond 2and FV is the bond’s maturity value of $1,000 and n is the 5 year holding period; solving for i) (see formulas below).

Hint Recall: Annual Compound Yield = {[FV / PV] ^ 1/n} - 1 or

In other words {[What you have at the end of 5 Years / What You Paid] ^1/n } - 1

n = your 5-year holding period.  

Annual Compound Yield for Bond 2 at End of Year 5 __________________

b. Suppose for the Coupon Bond 1 above, rates go down to 2% after you purchase the bond for the life of the bond. Thus, you have to invest each of your $40 coupon payments at a 2% rate, and hold the bond to maturity, receiving your $1,000 maturity value at the end of year 5.

            What will be your annual compound yield?

Hint: Recall FV of Bond Coupons Reinvested for 5 years = Coupon Payment (FVIFA 2%, 5)

ACY = { [(FV of Coupons +Maturity Value) / (Price of Bond)] ^1/n } - 1, where n = 5 years

Annual Compound Yield for Bond 1 at the End of Year 5____________

c. Explain why you received your desired annual compound return for the 5 year holding period for Bond 2 in a., but didn’t receive your desired Annual Compound Return for Bond 1 for your 5 year holding period in b.?

Answer 1

a.Annual Compound Yield = (FV/PV)^(1/n)-1

ie.(What you have at the end of 5 Years / What You Paid] ^1/n ) - 1

n = the 5-year holding period.

FV= $ 1000

PV=1000/1.04^5=821.9271

So,the

Annual Compound Yield for Bond 2 at End of Year 5 =

(1000/821.9271)^(1/5)-1=

4.00%

b.FV of Bond Coupons Reinvested for 5 years = Coupon Payment (FVIFA 2%, 5)

ACY =( (FV of Coupons +Maturity Value) / (Price of Bond)) ^1/n - 1, where n = 5 years

ie.FV=(40*(1.02^5-1)/0.02)+1000=

1208.161606

PV=1000( coupon rate=YTM on purchase)

ACY=(1208.162/1000)^(1/5)-1=

3.85%

Annual Compound Yield for Bond 1 at the End of Year 5 is 3.85%

c.From the above, we can see that

Annual return on a coupon-interest bond will equal its yield to maturity only if the coupons are reinvested at its yield to maturity

In b. above, the annual yield is less than the YTM ,as the coupons are reinvested at a lower market interest rate of 2%

whereas,

annual compound yield on a zero-coupon bond , is not subject to market fluctuations with respect to its coupons , as there are no coupons , to be reinvested.