Question

​(Bond valuation​ relationships)  Arizona Public Utilities issued a bond that pays ​$80 in​ interest, with a ​$1,000 par value. It matures in 30 years. The​ market's required yield to maturity on a​ comparable-risk bond is 7 percent.

a.  Calculate the value of the bond.

b.  How does the value change if the​ market's required yield to maturity on a​ comparable-risk bond​ (i) increases to 11 percent or​ (ii) decreases to 6 ​percent?

c.  Explain the implications of your answers in part b as they relate to​ interest-rate risk, premium​ bonds, and discount bonds.

d.  Assume that the bond matures in 10 years instead of 30 years. Recompute your answers in parts a and

b.

e.  Explain the implications of your answers in part d as they relate to​ interest-rate risk, premium​ bonds, and discount bonds.

Answer 1

a. Compuation of the value bond

Value of the Bond today

= present value of the interest + present value of the maturity value

=$80*( PV Annuity factor for 30 years at 7%)+1000* (Present value of 30th year @7%)

= $80*12.41+1000*0.1314

$1124.2

b. Change in the value at different rates

i). Value of bond at 11 %

= present value of the interest + present value of the maturity value

=$80*( PV Annuity factor for 30 years at 11%)+1000* (Present value of 30th year @11%)

= $80*8.69+1000*0.0437

$738.9

ii). Value of bond at 6%

= present value of the interest + present value of the maturity value

=$80*( PV Annuity factor for 30 years at 6%)+1000* (Present value of 30th year @6%)

= $80*13.76+1000*0.1741

$1274.9

C. discount rate and the value of the bond are inversly related. That is why when bond discount rate is 11% and the value of the bond is $738.

And when the rate is 6% the value of the bond is $1274.9. So value is more when the discount rate is lower.

That is because of the value is discounted higher rate will lead lower bond value and visa versa.

d. Value of the bond when the period is 10 years

Value of the Bond today

= present value of the interest + present value of the maturity value

At the rate 7%

=$80*( PV Annuity factor for 10 years at 7%)+1000* (Present value of 10th year @7%)

= $80*7.02+1000*0.5083

$1069.9

i). Value of bond at 11 %

= present value of the interest + present value of the maturity value

=$80*( PV Annuity factor for 10 years at 11%)+1000* (Present value of 10th year @11%)

= $80*5.8892+1000*0.3522

$823.336

ii). Value of bond at 6%

= present value of the interest + present value of the maturity value

=$80*( PV Annuity factor for 10 years at 6%)+1000* (Present value of 10th year @6%)

= $80*7.36+1000*0.5584

$1147.2