Consider a bond paying a coupon rate of 7.75% per year semiannually when the mar

Question

Consider a bond paying a coupon rate of 7.75% per year semiannually when the market interest rate is only 3.1% per half-year. The bond has six years until maturity. a. Find the bond?s price today and twelve months from now after the next coupon is paid. (Do not round intermediate calculations. Round your answers to 2 decimal places.) Current price $ Price after twelve months $ b. What is the total rate of return on the bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Total rate of return % per six months

Explanation / Answer

Part a)

To calculate the price of bond, we need to the find the present value of all the future interest payments and the face value at the maturity of bond. The present value of annuity (interest payments, made half yearly) will be calculated with the use present value of ordinary annuity formula:

Present Value of Interest Payments =P*[((1-(1+r)^-n)/r] where r is market rate of interest, n is the period (which will involve semi-annual payments) and P is the amount of semi-annual interest payment.

Present Value of Face Value (which is taken as $1,000 unless specified otherwise) = $1,000(1+r)^n (on the day of maturity)

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Solution:

Current Price

Here, P = 1,000*7.75%*1/2 = $38.75, n = 6*2 = 12, and r = 3.1%

Using these values, we get:

Present Value of Interest Payments = 38.75[((1+(1+3.1%)^-12)/3.1%] = $383.43

Present Value of Face Value = 1000/(1+3.1%)^12 = $693.26

Current Price = $383.43 + $693.26 = $1076.69

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Price after 12 months,

After, 12 months, the price of the bond will be calculated for a period of 5 years. That is, the remaining maturity period will be only 5 years, since 1 year has already passed.

Here, P = 1,000*7.75%*1/2 = $38.75, n = 5*2 = 10, and r = 3.1%

Using these values, we get:

Present Value of Interest Payments = 38.75[((1+(1+3.1%)^-10)/3.1%] = $328.86

Present Value of Face Value = 1000/(1+3.1%)^10 = $736.91

Current Price = $328.86 + $736.91 = $1065.77

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Tabular Representation:

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Part b:

We will calculate the total return with the use of prices calculated above. We will also include the amount of interest payments that the bond pays, since, it is a semi-annual bond, we will consider 2 interest payments in the calculation. First we, will calculate the return for 1 Years and than divide it by 2 to calculate return per six months.

Total Return (Annual) = (Price after 12 Months - Current Price + Total Interest)/Current Price*100 = (1065.77-1076.69 + 2*38.75)/1076.69*100 = 6.18%

Total Return (Per Six Months) = Total Return (Annual)/2 = 6.18%/2 = 3.09%

Current Price $1,076.69 Price after 12 Months $1,065.77

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