Question

You own a bond that pays ​$100 in annual​ interest, with a ​$1,000 par value. It matures in 20 years. The​ market's required yield to maturity on a​ comparable-risk bond is 11 percent.

a.  Calculate the value of the bond.

b.  How does the value change if the yield to maturity on a​ comparable-risk bond​ (i) increases to 16 percent or​ (ii) decreases to 7 ​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 4 years instead of 20 years and recalculate 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) Calculation of value of bond

P.V. factor @11%

Cash flow	Time	P.V. factor @11%	Present Value
$100	(t1-t20)	7.9633	$796.33
$1000	T20	0.1240	$124
Total			$920.33

b) Yield to maturity when comparable risk bond increases to 16%

P.V. factor @16%

Cash flow	Time	P.V. factor @16%	Present Value
$100	(t1-t20)	5.9289	$592.89
$1000	T20	0.0513	$51.39
Total			$644.28

Yield to maturity when comparable risk bond decreases to 7%

P.V. factor @7%

Cash flow	Time	P.V. factor @7%	Present Value
$100	(t1-t20)	10.594	$1059.4
$1000	T20	0.2584	$258.4
Total			$1317.80

c) When the interest rate are high of the bond, the price of bond will decrease as the people will less interested to buy the bonds at higher interest rate and the interest rate is low, then the value of bond will be high because the people will purchase the bond on such lower interest rate. In part B when the interest rate goes to 16% i.e. high, the bond price was $644.28 i.e. less than the price of 11% rate and when the interest rate was 7% I.e. low, the bond price $1317.80 which is more than the price of 11% rate hence the value of bond changes, when there is an change in interest rate. If interest rate will high, the value of bond will decreased and vice versa.

The bond’s market value will be high than the par value if the required rate of return is less than the coupon interest rate and vice versa. When the required rate of return was 7%, the bond price will be $1317.80 which is high than the 11% coupon rate.

When interest rate of bonds is falling then the bond should be for the long term purposes as it provides high return and vice versa. The bond becomes less fluctuating and more stable, when maturity date declines. Short term bonds have less interest rate risk as compare to long term bonds.

d) Yield to maturity @11%

Maturity= 4 years

Cash flow	Time	P.V. factor @11%	Present Value
$100	(t1-t4)	3.1024	$310.24
$1000	T4	0.6587	$658.7
Total			$968.94

Yield to maturity when comparable risk bond increases to 16%

P.V. factor @16%

Cash flow	Time	P.V. factor @16%	Present Value
$100	(t1-t4)	2.7981	$279.81
$1000	T4	0.5523	$552.30
Total			$832.11

Yield to maturity when comparable risk bond decreases to 7%

P.V. factor @7%

Cash flow	Time	P.V. factor @7%	Present Value
$100	(t1-t4)	3.3872	$338.72
$1000	T4	0.7629	$762.9
Total			$1101.62

e) When the interest rate are high of the bond, the price of bond will decrease as the people will less interested to buy the bonds at higher interest rate and the interest rate is low, then the value of bond will be high because the people will purchase the bond on such lower interest rate. In part D, the value of bond changes, when there is a change in interest rate. If interest rate will high, the value of bond will decreased and vice versa. When interest rate of bonds is falling then the bond should be for the long term purposes as it provides high return and vice versa. The bond becomes less fluctuating and more stable, when maturity date declines. The required return is increased because of more discounts or vice versa. The bond’s market value will be high than the par value if the required rate of return is less than the coupon interest rate and vice versa. Short term bonds have less interest rate risk as compare to long term bonds.

Working note-

Present value calculation formula

1/(1+i)+ 1/(1+i)²+1/(1+i)³+………1/(1+i)ⁿ

^{here i = coupon rate or interest rate}