1. You have a 4 year investment holding horizon, would like to earn a 4% annual compound return each year; you have a choice between two bonds. Whatever money you have to invest will be invested in one type of bond or another.

Find the Duration and Modified Duration for each bond (show your work and answer the questions below)

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

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

a. Price Bond 1 ___________ Price Bond 2 _ _______

b. Duration Bond 1 ________ Duration Bond 2 _________

c. Modified Duration Bond 1 _______ Modified Duration Bond 2 ____________

(Be sure to show your work for the bond price and duration calculations for credit).

d. Which of the two bonds should you choose for your 4-year investment horizon to duration match to ensure your desired 4% annual compound yield if you hold the bond to maturity? Explain why. (assume the same default risk for each bond).

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e. If interest rates go up by 2%, what will be the % Change in the market value for each Bonds Price? (Hint Change in Price % = - Modified Duration x Change in Rate (expressed as a fraction, i.e. .02).

f. Which of the 2 bonds has more price risk and which has more reinvestment risk?

Explain why.

2. a. For the Zero Coupon Bond 2 above, what will be your annual compound yield for your 4 year holding period if the bond is held until maturity.

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

In other words {[What you have at the end of 4 Years / Bonds Price] ^1/n } - 1

n = your 4-year holding period.

b. Suppose for the Coupon Bond 1 above, rates go down to 1% after you purchase the bond for the life of the bond. Thus, you have to invest each of your $40 coupon payments at a 1% rate, and hold the bond to maturity, receiving your $1,000 maturity value at the end of year 4.

What will be your annual compound yield?

Hint: Recall FV of Bond Coupons Reinvested for 4 years = Coupon Payment (FVIFA 1%, 4)

ACY = { [(FV of Coupons +Maturity Value) / (Price of Bond)] ^1/n } - 1, where n = 4 years

Annual Compound Yield for Bond 1 at the End of Year 4 _________

c. Explain why you received your desired annual compound return for the 4 year holding period for Bond 2 in a., but didnt receive your desired Annual Compound Return for Bond 1 for your 4 year holding period in b.?