Question

National Steel 15-year, $1,000 par value bonds pay 8 percent interest annually. The market price of the bonds is $1,085, and your required rate of return is 10percent.
• 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

a. Calculate bond’s expected rate of return:

Formula:

Substitute

Calculate

Therefore, expected rate of return is 7%

b. Determine the value of the bond at 10% rate of return:

Formula:

Substitute

Calculate

Therefore, value of the bond is $847.78

c. we should not purchase the bond because the market price of the bond lower than par value of the bond (Discount bond).

Answer 2

SOLUTION :

a.

Coupon amount = 1000 * 0.08 = 80 ($) annually.

Market price, P = 1085($)

Required rate of return, k = 10% = 0.1

Bond period = 15 years

Let expected rate of return be r (in decimals). At this return rate, PV of all inflows of cash through coupons and final redemption  of the bond is equal to the price of the bond.

This means :

1085 = 80((1+r)^15 - 1)/(r(1+r)^15) + 1000/(1 + r)^15

By trial and error,  r = 0.07063 = 7.063 % = 7.06% approx.

Hence, expected return of the bond = 7.06 % (ANSWER).

b.

Required rate of return, k = 0.1

=> (1 + k)  = 1.1

Value of the bond 

= 80(1.1^15 - 1)/(0.1*1.1^15) + 1000/1.1^15

= 847.88 ($).  (ANSWER).

c. 

Return of the bond of 7.06% is less than the required rate of return of 10%. So, it should not be purchased (ANSWER).