Question

7. Bond 1 and Bond 2 both have a face value of $1,000. Bond 1 pays a 5% coupon (annual payments) while Bond 2 is a zero coupon bond. On November 30, 2014 (immediately after the annual coupon payment), Bond 1 had exactly 20 years to maturity, while Bond 2 had 15 years to maturity. The yield to maturity for each bond was 10% on November 30, 2014, and was 8% on November 30, 2015.

A. What was the price of each bond on November 30, 2014?

B. What was the duration of each bond on November 30, 2014?

C. What was the price of each bond on November 30, 2015?

D. What was the one-year return on each bond if the bond was purchased on November 31, 2014 (immediately after the coupon was paid) and was sold on November 31, 2015 (immediately after the coupon was received)?

E. Which bond was more “sensitive” to this interest rate change, and why? In your answer to this question, address the following items:

• Based upon “time to maturity,” which bond should be more sensitive to the interest rate change? • Based upon the relative size of the coupon payments, which bond should be more sensitive to the interest rate change?

Answer 1

A]

Price of Bond 1 is calculated using PV function in Excel :

rate = 10% (YTM of bond)

nper = 20 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 5% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $574.32

Price of Bond 1 is $574.32

Price of zero-coupon bond = face value / (1 + YTM)^{years to maturity}

Price of Bond 2 = $1,000 / (1 + 10%)¹⁵ = $239.39

Price of Bond 2 is $239.39

B]

Duration of Bond 1 is calculated using DURATION function in Excel :

settlement = November 30, 2014

maturity = 15 years from November 30, 2014, which is November 30, 2029

coupon = coupon rate of bond, which is 5%

yld = YTM of bond, which is 10%

frequency = number of coupon payments per year, which is 1

DURATION is calculated to be 9.65

Duration of a zero-coupon bond is equal to the years until maturity.

Duration of Bond 2 is 15.00

C]

Price of Bond 1 is calculated using PV function in Excel :

rate = 8% (YTM of bond)

nper = 19 (Years remaining until maturity with 1 coupon payment each year)

pmt = 1000 * 5% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

PV is calculated to be $711.89

Price of Bond 1 is $711.89

Price of zero-coupon bond = face value / (1 + YTM)^{years to maturity}

Price of Bond 2 = $1,000 / (1 + 8%)¹⁴ = $340.46

Price of Bond 2 is $340.46

D]

Return on Bond 1 = (sale price - purchase price + annual coupon payment) / purchase price

Return on Bond 1 = ($711.89 - $574.32 + ($1,000 * 5%)) / $574.32

Return on Bond 1 = 32.66%

Return on Bond 2 = (sale price - purchase price ) / purchase price

Return on Bond 2 = ($340.46 - $239.39) / $239.39

Return on Bond 2 = 42.22%