Question

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% return? Would we now have a discount or a premium bond?

(B- pertaining to the question above

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

Answer 1

Question 1.

Rate of return become 13% which is more than coupon rate.

Which means investor expects higher return as compare to return provided by bonds. it will reduce the value of bond and hence it is now a discount bond.

Value of bond = [Coupon rate in year 1 / ( 1 + Investor return )¹ + Coupon rate in year 2 / ( 1 + Investor return )² + Coupon rate in year ⁿ / ( 1 + Investor return )ⁿ ] + ​​​​​​​ Par value / ( 1 + investor return )ⁿ

= [ $100 / (1 + 0.13)¹ + $100 / ( 1 + 0.13)².........$100 / ( 1 + 0.13)¹⁰ ] + $1000 / ( 1 + 0.13 )¹⁰

= $542.62 + 294.58

= $837.21

Value of bond will be = 837.213

Question 2.

Value of bond is determined by discounting all the future cash flows at the rate of return of investor.

Face value = $1000

Coupon rate = 10%

Coupon amount = $1000 * 10% = $100

Required rate of return = 10%

Life of bond = 10 years.

Value of bond = [ $100 / ( 1 + 0.10)¹ + $100 / ( 1 + 0.10)² ..........$100 / ( 1 + 0.10)¹⁰ ] + $1000 / ( 1 + 0.10)¹⁰

= $614.46 + $385.54

= $1000

Since the coupon rate and investor rate of return is same bond is valued at par.