Question

The Frush Corporation has two different bonds currently outstanding.

Bond M has a face value of $30,000 and matures in 20 years. The bond makes no payments for the first six years, then pays $800 every six months over the subsequent eight years, and finally pays $1,000 every six months over the last six years.

Bond N also has a face value of $30,000 and a maturity of 20 years. It makes no coupon payments over the life of the bond.

If the annual percentage rate on both bonds is 6.4%:

A.

What is the current price of Bond M?

B.

What is the current price of Bond N?

Answer 1

Price of bond M= Sum of discounted coupons + Discounted face value

Since the payments are semi annual, we will take the rate as 6.4%/2 = 3.2%

$800 is paid for 16 periods. $1000 is paid for 12 periods

These should be calculated using annuity formula and then the present value of these should be computed

PV of $ 800 paid in years 7 to 14 =C*(1-1/(1+r)^n)/ r divided by (1+r)^6

=800*(1-1/(1+0.032)^16)/ 0.032 divided by (1+0.032)^12

= 9896.94/1.032^12

= $6781.8

PV of $ 1000 paid thereafter =

C*(1-1/(1+r)^n)/ r divided by (1+r)^6

=1000*(1-1/(1+0.032)^12)/ 0.032 divided by (1+0.032)^28

=9836.204 /1.032^28

= $4071.89

PV of face value = 30000/ 1.032^40 = $8510.075

Total price of bond M= 6781.8+ 4071.89+ 8510.075 = $19363.77

Price of Bond N= 30000/ 1.032^40 = $ 8510.07