Question

Need all parts of D and E answered step by step.

How do you determine the value of a bond? What is the value of a one-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent? What is the value of a similar 10-year bond? (1) c. value resent u can What would be the value of the 10-year bond described in part (c) if, just after it had been issued, the expected inflation rate rose by 3 per- centage points, causing investors to require a 13 percent return? Is the security now a discount bond or a premium bond? d. Equa ear 6, (2) What would happen to the bond's value if inflation fell and r declined to 7 percent? Would it now be a premium bond or a dis- count bond? What would happen to the value of the 10-year bond over time if the required rate of return remained at (0) 13 percent or (i) remained at 7 percent? What is the yield to maturity on a 10-year, 9 percent annual coupon, $1,000 par value bond that sells for $887.00? That sells for $1,134.202 What does the fact that a bond sells at a discount or at a premium tell you about the relationship between ra and the bond's coupon rate? r this ield is same (3) e. (1) th rate

Answer 1

d. 1.

Value of a bond is the sum of the Present Values of:

all its future coupons   &

face value that will be recieved at maturity

which is found out using the formula

PV of a bond=(Pmt.*(1-(1+r)^-n)/r)+(FV/(1+r)^n)

where,

Pmt.= Annual $ coupon amt.--here (1000*10%)= $ 100

r= Reqd. rate of return/yield to maturity,13%

n=No.of coupon periods still pending to maturity,10

FV=Face value of the bond, $ 1000

Substituting the values in the formula,

PV of the bond=(100*(1-(1+0.13)^-10)/0.13)+(1000/(1+0.13)^10)

837.21

It is a DISCOUNT bond as it sells below the $ 1000 par

2..Rd deciling to 7%

PV of the bond=(100*(1-(1+0.07)^-10)/0.07)+(1000/(1+0.07)^10)

1210.71

It is a PREMIUM bond as its price > the $ 1000 par

3….

If the reqd. return remained at 13%

Value when 10 yrs. Pending to maturity:

PV of the bond=(100*(1-(1+0.13)^-10)/0.13)+(1000/(1+0.13)^10)

837.21

Value when 7 yrs. Pending to maturity:

PV of the bond=(100*(1-(1+0.13)^-7)/0.13)+(1000/(1+0.13)^7)

867.32

Value when 4 yrs. Pending to maturity:

PV of the bond=(100*(1-(1+0.13)^-4)/0.13)+(1000/(1+0.13)^4)

910.77

From the above, over time,as the bond nears maturity, its value INCREASES when the reqd. return > Coupon rate

If the reqd. return remained at 7%

Value when 10 yrs. Pending to maturity:

PV of the bond=(100*(1-(1+0.07)^-10)/0.07)+(1000/(1+0.07)^10)

1210.71

Value when 7 yrs. Pending to maturity:

PV of the bond=(100*(1-(1+0.07)^-7)/0.07)+(1000/(1+0.07)^7)

1161.68

Value when 4 yrs. Pending to maturity:

PV of the bond=(100*(1-(1+0.07)^-4)/0.07)+(1000/(1+0.07)^4)

1101.62

From the above, over time,as the bond nears maturity, its value DECREASES when the reqd. return < Coupon rate

e.1.Yield to Maturity:

887=(90*(1-(1+YTM)^-10)/YTM)+(1000/(1+YTM)^10)

Solving for YTM we get,

10.91%

1134.20=(90*(1-(1+YTM)^-10)/YTM)+(1000/(1+YTM)^10)

Solving for YTM we get,

7.08%

When Rd > Coupon rate, Price < par & it sells as a DISCOUNT bond

When Rd < Coupon rate, Price > par & it sells as a PREMIUM bond