Question

d. How is the value of a bond determined? What is the value of a 10-year, $1,000 par value bond with a 10 percent annual coupon if its required rate of return is 10 percent?

e. (1) What would be the value of the bond described in part d if, just after it had been issued, the expected inflation rate rose by 3 percentage points, causing investors to require a 13 percent return? Would we now have a discount or a premium bond?

    (2) What would happen to the bonds’ value if inflation fell, and r_d declined to 7 percent? Would we now have a premium or a discount bond?

Answer 1

Solution:

d)i)Value of bond is the discounted value of coupon amount of bond and its maturity value.While discounting,required rate of return is uesd.

ii)Calculation value of bond:

=Coupon Amount/(1+required rate of return)^year+Maturity value/(1+required rate of return)^year

Coupon Amount=$1000*10%=$100

Maturity value=$1000(Face value)

Value of bond=$100/1+0.10)^1+$100/1+0.10)^2+$100/1+0.10)^3+$100/1+0.10)^4+$100/1+0.10)^5+$100/1+0.10)^6+$100/1+0.10)^7+$100/1+0.10)^8+$100/1+0.10)^9+$100/1+0.10)^10+$1000/1+0.10)^10

=$1000

You can also onserve that value of bond is equal to its fair value(Bond is trading at Par).This is because the coupon rate and required rate are same.

e1)Calculation of value of bond

=$100/(1+0.13)^1+$100/(1+0.13)^+$100/(1+0.13)^4+$100/(1+0.13)^5+$100/(1+0.13)^6+$100/(1+0.13)^7+$100/(1+0.13)^8+$100/1+0.13)^9+$100/1+0.13)^10+$1000/1+0.13)^10

=$837.21

Since the value of bond is less than its fair value,hence bond is trading at discount.

e2)Calculation of value of bond

=$100/(1+0.07)^1+$100/(1+0.07)^2+$100/(1+0.07)^3+$100/(1+0.07)^4+$100/(1+0.07)^5+$100/(1+0.07)^6+$100/(1+0.07)^7+$100/(1+0.07)^8+$100/(1+0.07)^9+$100/(1+0.07)^10+$1000/(1+0.07)^10

=$1210.71

Since value of bond is higher than its fair value,hence bond is trading at Premium.