Question

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.

Answer 1

a]

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 6% (YTM of bond = market interest rate)

nper = 30 (Years remaining until maturity with 1 coupon payment each year)

pmt = 80 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

The PV is outputted as a negative figure, hence we multiply by -1

Price of bond is calculated to be $1,275.30

b]

(i)

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 12% (YTM of bond = market interest rate)

nper = 30 (Years remaining until maturity with 1 coupon payment each year)

pmt = 80 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

The PV is outputted as a negative figure, hence we multiply by -1

Price of bond is calculated to be $677.79

(ii)

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 5% (YTM of bond = market interest rate)

nper = 30 (Years remaining until maturity with 1 coupon payment each year)

pmt = 80 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

The PV is outputted as a negative figure, hence we multiply by -1

Price of bond is calculated to be $1,461.17

c]

Bonds with long maturity have high interest rate risk. For a small change in the market interest rate, the change in bond price is quite high.

Bonds with a YTM lower than the coupon rate trade above par value - premium bonds.

Bonds with a YTM higher than the coupon rate trade below par value - discount bonds.

d]

a]

Price of a bond is the present value of its cash flows. The cash flows are the coupon payments and the face value receivable on maturity

Price of bond is calculated using PV function in Excel :

rate = 6% (YTM of bond = market interest rate)

nper = 5 (Years remaining until maturity with 1 coupon payment each year)

pmt = 80 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

The PV is outputted as a negative figure, hence we multiply by -1

Price of bond is calculated to be $1,084.25

b]

(i)

Price of bond is calculated using PV function in Excel :

rate = 12% (YTM of bond = market interest rate)

nper = 5 (Years remaining until maturity with 1 coupon payment each year)

pmt = 80 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

The PV is outputted as a negative figure, hence we multiply by -1

Price of bond is calculated to be $855.81

(ii)

Price of bond is calculated using PV function in Excel :

rate = 5% (YTM of bond = market interest rate)

nper = 5 (Years remaining until maturity with 1 coupon payment each year)

pmt = 80 (annual coupon payment)

fv = 1000 (face value receivable on maturity)

The PV is outputted as a negative figure, hence we multiply by -1

Price of bond is calculated to be $1,129.88

e]

Bonds with shorter maturity have lower sensitivity to interest rates, i.e. the change in prices is lower compared to bonds with longer maturity.