Question 5: (15 points). (Bond valuation relationships) Arizona Public Utilities
ID: 2768378 • Letter: Q
Question
Question 5: (15 points).
(Bond valuation relationships) Arizona Public Utilities issued a bond that pays $70 in interest, with a $1,000 par value and matures in 25 years. The markers required yield to maturity on a comparable-risk bond is 8 percent. (Round to the nearest cent.) For questions with two answer options (e.g. increase/decrease) choose the best answer and write it in the answer block. Question Answer
a. What is the value of the bond if the markers required yield to maturity on a comparable-risk bond is 8 percent? $
b. What is the value of the bond if the markers required yield to maturity on a comparable-risk bond increases to 11 percent? $
c. What is the value of the bond if the market's required yield to maturity on a comparable-risk bond decreases to 7 percent? $
d. The change in the value of a bond caused by changing interest rates is called interest-rate risk.
Based on the answer: in parts b and c, a decrease in interest rates (the yield to maturity) will cause the value of a bond to (increase/decrease): By contrast in interest rates will cause the value to (increase/decrease): Also, based on the answers in part b, if the yield to maturity (current interest rate) equals the coupon interest rate, the bond will sell at (par/face value): exceeds the bond's coupon rate, the bond will sell at a (discount/premium): and is less than the bond's coupon rate, the bond will sell at a (discount/premium): e. Assume the bond matures in 5 years instead of 25 years, what is the value of the bond if the yield to maturity on a comparable-risk bond is 8 percent? $ 960.07 Assume the bond matures in 5 years instead of 25 years, what is the value of the bond if the yield to maturity on a comparable-risk bond is 11 percent? $ f. Assume the bond matures in 5 years instead of 25 years, what is the value of the bond if the yield to maturity on a comparable-risk bond is 7 percent? $ g. From the findings in part e, we can conclude that a bondholder owning a long-term bond is exposed to (more/less) interest-rate risk than one owning a short-term bond.
Explanation / Answer
(a) Computation of the value of bond.We have,
Value of bond = C[1-1/(1+r)n ] / r + F.V /(1+r)n
Where,
C = Coupon payment = $ 70
r = YTM = 8%
n = Number of years =25 years
FV = face value = $ 1,000
putting these value in above equation.We have,
Value of bond = 70[ 1 - 1/(1.08)25] / 0.08 + 1,000/(1.08)25
Value of bond = 70[ 1 - 0.14602] / 0.08 + 1,000 x 0.14602
value of bond = 70 x 10.67 + 146.02 = 746.90 + 146.02 = $ 892.92
Hence, the value of bond is $ 892.92
(b) Computation of the value of bond.We have,
Value of bond = C[1-1/(1+r)n ] / r + F.V /(1+r)n
Where,
C = Coupon payment = $ 70
r = YTM = 11%
n = Number of years =25 years
FV = face value = $ 1,000
putting these value in above equation.We have,
Value of bond = 70[ 1 - 1/(1.11)25] / 0.11 + 1,000/(1.11)25
Value of bond = 70[ 1 - 0.07361] / 0.11 + 1,000 x 0.07361
value of bond = 70 x 8.42 + 73.61 = 589.4 + 73.61 = $ 663.01
Hence, the value of bond is $ 663.01
(c) Computation of the value of bond.We have,
Value of bond = C[1-1/(1+r)n ] / r + F.V /(1+r)n
Where,
C = Coupon payment = $ 70
r = YTM = 7%
n = Number of years =25 years
FV = face value = $ 1,000
putting these value in above equation.We have,
Value of bond = 70[ 1 - 1/(1.07)25] / 0.07 + 1,000/(1.07)25
Value of bond = 70[ 1 - 0.18425] / 0.07 + 1,000 x 0.18425
value of bond = 70 x 11.65 + 184.25 = 815.50 + 184.25 = $ 1,000
Hence, the value of bond is $ 1,000
(d) A decrease in interest rate of bond will cause value of bond is increase.
If yield to maturity is equal to coupon interest rate.Then, the bond is sell at par value.
The exceeds the bond's coupon rate from yield to maturiy,the bond will sell at a premium.
The bond's coupon rate is less than yield to maturity, the bond will sell at a discount.
(e) (i) Computation of the value of bond.We have,
Value of bond = C[1-1/(1+r)n ] / r + F.V /(1+r)n
Where,
C = Coupon payment = $ 70
r = YTM = 8%
n = Number of years =5 years
FV = face value = $ 1,000
putting these value in above equation.We have,
Value of bond = 70[ 1 - 1/(1.08)5] / 0.08 + 1,000/(1.08)5
Value of bond = 70[ 1 - 0.68058] / 0.08 + 1,000 x 0.68058
value of bond = 70 x 3.99 + 680.58= 279.49 + 680.58 = $ 960.07
Hence, the value of bond is $ 960.07
(ii)Computation of the value of bond.We have,
Value of bond = C[1-1/(1+r)n ] / r + F.V /(1+r)n
Where,
C = Coupon payment = $ 70
r = YTM = 11%
n = Number of years =5 years
FV = face value = $ 1,000
putting these value in above equation.We have,
Value of bond = 70[ 1 - 1/(1.11)5] / 0.11 + 1,000/(1.11)5
Value of bond = 70[ 1 - 0.59345] / 0.11 + 1,000 x 0.59345
value of bond = 70 x 3.695897 + 593.45 = 258.71 + 593.45 = $ 852.16
Hence, the value of bond is $ 852.16
(f) Computation of the value of bond.We have,
Value of bond = C[1-1/(1+r)n ] / r + F.V /(1+r)n
Where,
C = Coupon payment = $ 70
r = YTM = 7%
n = Number of years =5 years
FV = face value = $ 1,000
putting these value in above equation.We have,
Value of bond = 70[ 1 - 1/(1.07)5] / 0.07 + 1,000/(1.07)5
Value of bond = 70[ 1 - 0.71299] / 0.07 + 1,000 x 0.71299
value of bond = 70 x 4.10 + 712.99 = 287.01+ 712.99 = $ 1,000
Hence, the value of bond is $ 1,000
(g) The bondholder owning a long-term bond is exposed to more interest rate risk than owning a short term bond.
Interest rate 5 year 25 year 7% $ 1,000 $ 1,000 8% $ 960.07 892.92 11% $ 852.16 $ 663.01Related Questions
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