Cullumber, Inc., has outstanding bonds that will mature in six years and pay an 8 percent coupon semiannually. If you paid $1,033.85 today and your required rate of return was 6.6 percent.

A. How much should you have paid for the bond? B. Worth of the bond is?

The worth of the bond is $1068.44

Explanation:

Solution

Given that

Supposed that the face of the bond is $1000

Thus

The semiannual coupon payment = 1000*8%*6/12

= 40 (semiannual period in a year comprising of 6 months each)

Then

Semiannual periods = 6 years * 2

=12

The semiannual yield = 6.6*6/12

= 3.3%

So,

The present value of bond = (PVA3.3%,12*semiannual coupon payment) + (PVF3.3%,12*Face value)

= (9.77808*40) + (.67732*1000)

=391.12 + 677.32

=$1068.44

The worth of the bond is $1068.44

nnote: Find present value factor using the formula 1 / (1+i) ^n

(Where i = 3.3%, n = 12) or using financial calculator by putting i = 3.3%, n=12 and FV = 1

Also, Find present value annuity factor using the formula [1 / (1+i) ^1 + 1 / (1+i) ^2 + ... + (1+i) ^11+1 / (1+i) ^12 ] or using financial calculator where i = 3.3%, n = 12 and PMT = 1