Question

INTEREST RATE SENSITIVITY An investor purchased the following 5 bonds. Each bond had a par value of $1,000 and an 10% yield to maturity on the purchase day. Immediately after the investor purchased them, interest rates fell, and each then had a new YTM of 5%. What is the percentage change in price for each bond after the decline in interest rates? Fill in the following table. Round your answers to the nearest cent or to two decimal places. Enter all amounts as positive numbers. Price @ 10% Price @ 5% Percentage Change 4 10-year, 10% annual coupon 10-year zero 5-year zero 30-year zero $100 perpetuity

Answer 1

a]

YTM is calculated using RATE function in Excel with these inputs :

nper = 28 (28 years to maturity with 1 annual coupon payment each year)

pmt = 1000 * 9.5% (annual coupon payment = face value * annual coupon rate. This is a positive figure as it is an inflow to the bondholder)

pv = -1165.75 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1000 (face value of the bond receivable on maturity. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 8.00%. This is the YTM.

Al X f =RATE(28,1000*9.5%,-1165.75, 1000) B C D I F A 8.00%!

YTC is calculated using RATE function in Excel with these inputs :

nper = 3 (3 years to call date with 1 annual coupon payment each year)

pmt = 1000 * 9.5% (annual coupon payment = face value * annual coupon rate. This is a positive figure as it is an inflow to the bondholder)

pv = -1165.75 (current bond price. This is a negative figure as it is an outflow to the buyer of the bond)

fv = 1090 (call price of the bond receivable on call date. This is a positive figure as it is an inflow to the bondholder)

The RATE is calculated to be 6.11%. This is the YTC.

X foc =RATE(3,1000*9.5%,-1165.75,1090) 6.11%

b]

As the interest rates have declined, the bond is likely to be called because the issuer can refinance their debt by calling the bonds and reissuing new bonds at the lower interest rates.

Investors can expect to earn the YTC because YTC is less than YTM. The YTC is less because the bond is likely to be called.

The correct option is III
c]

If the bond was selling at a discount, it means that interest rates have increased since the bond was issued (as a bond sells at a discount if YTM > coupon rate).

The bond is not likely to be called, and investors can expect to earn the YTM as the bond will not likely be called.

The correct option is II