Question

Bond value and time—Changing required returns 

Lynn Parsons is considering investing in either of two outstanding bonds. The bonds both have​ $1,000 par values and 12​% coupon interest rates and pay annual interest. Bond A has exactly 9 years to​ maturity, and bond B has 19

years to maturity.  

a. Calculate the present value of bond A if the required rate of return​ is: (1) 9​%, ​(2) 12​%, and​ (3)

15​%.

b. Calculate the present value of bond B if the required rate of return​ is: (1) 9​%, ​(2) 12​%, and​ (3) 15​%.

c. From your findings in parts a and b​, discuss the relationship between time to maturity and changing required returns.

d. If Lynn wanted to minimize interest rate​ risk, which bond should she​ purchase? ​ Why?

Answer 1

Characteristics of the two bonds :

Par value - $1,000 for both bonds

Coupon rate - 12% for both bonds. Coupon amount = Par value x Coupon rate = $1,000 x 12% = $120

Time to maturity - Bond A : 9 years, Bond B : 19 years

a. Calculate the present value of bond A :

We will use the PV formula in Excel to calculate the bond's present value for each rate of return.

The Inputs for the PV formula are : Rate - The required rate of return, Nper - number of payment periods = 9, Pmt - the annual coupon interest amount = 120, Fv - the future value which is the bond's par value redeemed on maturity = 1,000. The last input "Type" is not required and will be left blank.

Required rate of return​ is: (1) 9​% :

Ignore the negative sign in the formula result.

Present Value with Required rate of return of 9% = $1,179.86 (rounded off)

Required rate of return​ is: (2) 12​% :

We use the PV formula with the same inputs as above, except now Rate = 12%

Present Value with Required rate of return of 12% = $1,000

Required rate of return​ is: (3) 15​% :

Rate = 15%. All other inputs remain the same.

Present Value with Required rate of return of 15% = $856.85 (rounded off)

b. Calculate the present value of bond B :

Required rate of return​ is: (1) 9​% :

Inputs for the PV formula : Rate = 9%, Nper = 19 (Bond B has 19 years to maturity), Pmt = 120, Fv = 1,000

Present Value with Required rate of return of 9% = $1,268.50 (rounded off)

Required rate of return​ is: (2) 12​% :

Present Value with Required rate of return of 12% = $1,000

Required rate of return​ is: (3) 15% :

Present Value with Required rate of return of 15% = $814.05 (rounded off)

c. Relationship between time to maturity and changing required returns :

First compare the Present Values of both bonds if the Required Rate of Return is 9% for both the bonds. This required return is less than the Coupon rate on both the bonds. Bond A has a lower present value than Bond B.

Thus we can say that when the Required Return is less than the Coupon rate, the Bond with the longer time to maturity (Bond B) has a higher Present Value.

When the Required Rate of Return is 12%, which is equal to the Coupon rate on both the bonds, the Present Values of the bonds is equal to their Par Value, irrespective of the time to maturity.

When the Required Rate of Return is 15% for both the bonds, which is more than the Coupon rate on both the bonds, Bond A has a higher present value than Bond B.

Thus we can say that when the Required Return is more than the Coupon rate, the Bond with the shorter time to maturity (Bond A) has a higher Present Value.

d. If Lynn wanted to minimize interest rate​ risk, which bond should she​ purchase? Why? :

For each of the bonds, notice that their present value becomes lower as the required rate of return increases. Bond prices and Interest rates are inversely related to each other.

For Bond B which has a longer time to maturity, the present value falls more sharply with an increase in required rate of return, and is lower than that of Bond A at a required return of 15%.

Thus, Interest Rate Risk is higher for longer maturity bonds because interest rates are more likely to rise in the long term and adversely affect the bond price or present value, which means that the bond's present value may fall below its par value and the investors who want to sell the bond may be faced with a loss.

Hence, in order to minimize interest rate​ risk, Lynn should purchase Bond A because it has a shorter time to maturity at 9 years. Interest rates have a lower probability of rising in the short term and the present value is less likely to be adversely affected.

We can also see this above, since Bond A's present value at a 15% required return with 9 years to maturity is more than Bond B's present value at the same required return with 19 years to maturity.