Three coupon bonds with a 10% coupon rate all just sell for their face value of...

Three coupon bonds with a 10% coupon rate all just sell for their face value of $1,000. The three bonds will mature in one, two, and five years, respectively. Interest rates on all these bonds are 10% when they are bought, but decline to 5% after they are purchased. Calculate the one-year rates of return on these bonds. What are the initial current yields and the one-year rates of capital gain on these bonds? Which of the three bonds would be the best choice for an investor who has a one-year holding period? Why?

Solutions

Expert Solution

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 5% (YTM of bonds = market interest rate)

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

pmt = 1000 * 10% (annual coupon payment = face value * coupon rate)

fv = 1000 (face value receivable on maturity)

1-year rate of return = (price after 1 year - purchase price + annual coupon payment) / purchase price

purchase price = $1,000

annual coupon payment = face value * coupon rate = $1,000 * 10% = $100

current yield = annual coupon payment / bond price

1-year rate of capital gain = (price after 1 year - purchase price) / purchase price

The calculations are below :

For an investor who has a one-year holding period, Bond 3 (5-year bond) is the best choice because it has the highest 1-year return (both total return, and capital gain return).

jeff jeffy answered 1 year ago

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