Question

PROBLEM:

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 6

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 12 percent or​ (ii) decreases to 5 ​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 5 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.

QUESTIONS:

a. What is the value of the bond if the​ market's required yield to maturity on a​ comparable-risk bond is 6 ​percent? ($) (Round to the nearest​ cent.)

b. ​(i) What is the value of the bond if the​ market's required yield to maturity on a​ comparable-risk bond increases to 12 ​percent? ​($) ​(Round to the nearest​ cent.)

b. ​(ii) What is the value of the bond if the​ market's required yield to maturity on a​ comparable-risk bond decreases to 5 ​percent? ​($)​ (Round to the nearest​ cent.)

c. The change in the value of a bond caused by changing interest rates is called​ interest-rate risk. Based on the answers in part b​, a decrease in interest rates​ (the yield to​ maturity) will cause the value of a bond to (increase, not changed, decrease)​; by​ contrast, an increase in interest rates will cause the value to (increase, not changed, decrease). ​(Choose between the 3 options)

​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, a discount, a premium)​; (Choose between the 3 options)

exceeds the​ bond's coupon​ rate, the bond will sell at (par, a discount, a premium); (Choose between the 3 options)

and is less than the​ bond's coupon​ rate, the bond will sell at (para, a discount ,a premium). ​ (Choose between the 3 options)

d. Assume the bond matures in 5 years instead of 30 years, what is the value of the bond if the yield to maturity on a​ comparable-risk bond is 6 percent? ($) ​(Round to the nearest​ cent.)

Assume the bond matures in 5 years instead of 30 ​years, what is the value of the bond if the yield to maturity on a​ comparable-risk bond is 12 ​percent? ​($) ​(Round to the nearest cent.)

Assume the bond matures in 5 years instead of 30 ​years, what is the value of the bond if the yield to maturity on a​ comparable-risk bond is 5 ​percent? ​($) ​(Round to the nearest​ cent.)

e. From the findings in part d​, we can conclude that a bondholder owning a​ long-term bond is exposed to (more, the same, less) more the same less ​interest-rate risk than one owning a​ short-term bond. (Choose between the 3 options)

Answer 1

Solving First 4 parts

Answer A.)

Interest Rate	6%
Time Period (Years)	30
Future Value (Par Value)	1,000
Coupon	80

Using financial calculator:

1. Insert 30 and press N.

2. Insert 80 and press PMT (coupon)

3. Insert 6% and press I/Y.

4. Insert 1000 and press FV.

5. Press CPT and Press PV

Present Value = 1275.30

Answer B.)

Part 1. Market Interest Increases to 12%.

Using financial calculator:

1. Insert 30 and press N.

2. Insert 80 and press PMT (coupon)

3. Insert 12% and press I/Y.

4. Insert 1000 and press FV.

5. Press CPT and Press PV

Present Value = 677.79

Part 1. Market Interest Decreases to 5%.

Using financial calculator:

1. Insert 30 and press N.

2. Insert 80 and press PMT (coupon)

3. Insert 5% and press I/Y.

4. Insert 1000 and press FV.

5. Press CPT and Press PV

Present Value = 1461.17

Answer C.)

As market interest rate (Yield to maturity) increases over the coupon (interest earned on bond), the bond becomes less valuable. This happens because the bond is paying less interest than the market rate of interest. As a result, such bonds will be worth or are issued at discount to their par value to compensate the investors for less coupon rate.

On the other hand, As market interest rate (Yield to maturity) decreases in comparison to the coupon (interest earned on bond), the bond becomes more valuable. This happens because the bond is paying higher interest than the market rate of interest. As a result, such bonds will be worth more and are issued at premium to their par value since they offer higher coupon interest.

Answer D.)

Time period reduces to 5 years.

Part 1. When market interest rate is 6%

Using financial calculator:

1. Insert 5 and press N.

2. Insert 80 and press PMT (coupon)

3. Insert 6% and press I/Y.

4. Insert 1000 and press FV.

5. Press CPT and Press PV

Present Value = 1084.25

Part 2. When market interest rate is 12%

Using financial calculator:

1. Insert 5 and press N.

2. Insert 80 and press PMT (coupon)

3. Insert 12% and press I/Y.

4. Insert 1000 and press FV.

5. Press CPT and Press PV

Present Value = 855.81

Part 3. When market interest rate is 5%

Using financial calculator:

1. Insert 5 and press N.

2. Insert 80 and press PMT (coupon)

3. Insert 5% and press I/Y.

4. Insert 1000 and press FV.

5. Press CPT and Press PV

Present Value = 1129.88