Suppose you buy a 8.2 percent coupon bond today for $1,100. The bond has 7 years

Question

Suppose you buy a 8.2 percent coupon bond today for $1,100. The bond has 7 years to maturity.

What rate of return do you expect to earn on your investment? (Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Two years from now, the YTM on your bond has increased by 2 percent, and you decide to sell. What price will your bond sell for? (Round your answer to 2 decimal places. Omit the "$" sign in your response.)

What is the annual realized yield on your investment? (Negative amounts should be indicated by a minus sign. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Suppose you buy a 8.2 percent coupon bond today for $1,100. The bond has 7 years to maturity.

Explanation / Answer

Part a)

The rate of return indicates the YTM that can be earned on the bonds. Rate of return can be easily calculated with the use EXCEL/Financial Calculator. The formula/function for calculation YTM is Rate(Nper,PMT,PV, FV) where Nper is the period, PMT is the amount of interest payment, PV is the current selling price and FV is the face value.

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Solution:

Here, Nper = 7 Years, PMT = 1000*8.2% = 82, PV = -$1,100 and FV = $1,000

Using the above mentioned formula/function we get,

Rate of Return = Rate(7,82,-1100,1000) = 6.38%

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Part b1)

To calculate Selling Price with the use of EXCEL/Financial Calculator, we will use the following formula/function.

Selling Price = PV(Rate,Nper,PMT,FV) where Rate is YTM, Nper is the period, PMT is the amount of interest payment and FV is the face value.

Solution:

Here, Rate = 6.38%+2% = 8.38%, Nper = 5 (7-2) Years, PMT = $1,000*8.2% = 82 and FV = $1,000

Using the above mentioned formula/function we get,

Selling Price = PV(8.38%,5,82,1000) = $992.88

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Part b)

Annual realized rate of return is similar to Holding Period Return. Since, the bond will be sold in the Year 2, the annual realized return will get calculated for the 2 years. Here the face value will change to the redemeption/sales value as calculated in part b1).

The formula/function for calculating realized return would be Rate(Nper,PMT,PV,FV) where Nper is the period till the time of sale, PMT is the Annual Interest Payment, PV is the Selling Price Today and FV is the Face Value.

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Solution:

Here, Nper = 2 Years, PMT = $1,000*8.2% = 82, PV = -$1,100 and FV = $992.88 (as calculated in part b1)

Annual Realized Return = Rate(2,82,-1100,992.88) = 2.65%

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