Question

​(Bond valuation​) National​ Steel's 20​-year, ​$1 000 par value bonds pay 12 percent interest annually. The market price of the bonds is ​$1050​, and your required rate of return is 13 percent.

a. Compute the​ bond's expected rate of return.

b. Determine the value of the bond to​ you, given your required rate of return.

c. Should you purchase the​ bond?

Answer 1

Price of the bond is calculated using the formula: P= C/(1+r)+C/(1+r)^2+....C/(1+r)^n+P/(1+r)^n; where C is the coupon payment per period, P is the face value of the bond, r is the yield to maturity and n is the number of years to maturity.

a).

Given that Par value is $1000 with 12% interest annually, for 20 years.

So, Price of the bond= 1050= 120/(1+r)+120/(1+r)^2+....120/(1+r)^20+1000/(1+r)^20

For the coupons part, we can use the formula of present value of annuity which is C*(1-(1+r)^-n)/r; where C is the annual cashflow, r is the discount rate and n is the number of years.

So, 1050= (120*(1-(1+r)^-20)/r)+1000/(1+r)^20

r= 11.36%

b).

Given that required rate is 13%,

So, Price of the bond= 120/1.13+120/1.13^2+...120/1.13^20+1000/1.13^20

= 120*(1-1.13^-20)/0.13+(1000/1.13^20)

= $929.75

c).

The bond is giving a return of 11.36% which is less than the required return of 13%. So, we should not purchase the bond.