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-A firm issues 20-year bonds with a coupon rate of 4.8%, paid semi-annually. The credit spread for this firm's 20-year debt is 1.2%. New 20-year Treasury bonds are being issued at par with a coupon rate of 4.6%. What should the price of the firm's outstanding 20-year bonds be if their face value is $1 000?

Question

Use the information for the question(s)below. 
-A firm issues 20-year bonds with a coupon rate of 4.8%, paid semi-annually. The credit spread for this firm's 20-year debt is 1.2%. New 20-year Treasury bonds are being issued at par with a coupon rate of 4.6%. What should the price of the firm's outstanding 20-year bonds be if their face value is $1 000?

Quizplus · Accepted Answer

Firstly, we need to calculate the semi-annual coupon payment for the firm's bond, which is [($1,000 x 4.8%)/2] = $24.

Next, we can calculate the semi-annual yield on the firm's bond by adding the credit spread of 1.2% to the yield on the 20-year Treasury bond. 
The yield on the 20-year Treasury bond is 4.6%, so the semi-annual yield on the firm's bond is (4.6% + 1.2%)/2 = 2.9%.

Using this yield, we can calculate the present value of each semi-annual coupon payment and the face value at maturity using the formula for the present value of an annuity due: 
PV = C x [(1 - (1+r)^-n) / r] x (1+r)
where PV = present value, C = coupon payment, r = semi-annual discount rate, and n = number of semi-annual periods.

For the coupon payments, we have: 
PV of semi-annual coupon payments = $24 x [(1 - (1+2.9%)^-40) / 2.9%] x (1+2.9%) = $687.97

For the face value at maturity, we have: 
PV of face value = $1,000 x (1+2.9%)^-40 = $194.56

Summing these two present values gives us the total present value of the bond: 
Total PV = $687.97 + $194.56 = $882.53

Therefore, the price of the firm's outstanding 20-year bond should be $882.53.

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