Question

BOND VALUATION

Bond X is noncallable and has 20 years to maturity, a 8% annual coupon, and a $1,000 par value. Your required return on Bond X is 8%; if you buy it, you plan to hold it for 5 years. You (and the market) have expectations that in 5 years, the yield to maturity on a 15-year bond with similar risk will be 10%. How much should you be willing to pay for Bond X today? (Hint: You will need to know how much the bond will be worth at the end of 5 years.) Do not round intermediate calculations. Round your answer to the nearest cent.

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Answer 1

To find out the amount that we will be willing to pay today, we need to find out the value of bond today.

Given:

Time to maturity (n) = 20 years

Annual coupon = 8%; 8%*1000= $80

Par value = $1000

Required rate of return = 8%

YTM after 5 years on a 15 year bond with similar risk = 10%

Solution:

Assuming annual compounding, we will first of all calculate the value of bond at the end of 5 years

Value of bond at the end of 5 year = (Annual coupon/(1+YTM)) + (Annual coupon/(1+YTM)^2)) + ................((Annual coupon+Par value)/(1+YTM)^15)

= ($80/(1+10%)) + ($80/(1+10%)^2) + ....................(($80+$1000)/(1+10%)^15))

= $ 847.88

Since, required rate of return today is 8% and the plan is to hold for 5 years, to calculate the value of bond today, the coupon and value at the end of 5 years will be discounted by 8%

Value of bond today = (Annual coupon/(1+YTM)) + (Annual coupon/(1+YTM)^2)) + ................((Annual coupon+Value at the end of 5 years)/(1+YTM)^15)

= ($80/(1+8%)) + ($80/(1+8%)^2) + ....................(($80+$847.88)/(1+8%)^5))

= $896.47

Value of bond today is $896.47. Therefore, we will be willing to pay $ 896.47 for 20 years non-callable bond with coupon rate of 8%.