Question

6. A friend sells you a AAA bond purchased in 1999 with a 10-year maturity at $ 1010.00. The bonus has a coupon rate of $ 80. The prevailing market rate is 7.0%. What is the value of the bond? Would you buy it if interest rates plan to drop?

a) I would buy it, total to pay $ 1009.35, if interest rates go down it favors

b) You would not buy it, total to pay $ 1080, changes in interest rates do not affect you

c) I would buy it, total to pay $ 1000, if interest rates go down it favors

d) I would not buy it, the offer is equal to the value of the Bond, changes in interest rates affect it

Answer 1

Coupon amount = $80
Period remaining till maturity = 10 years
Discount Rate = 7%

Value of Bonds = Present Value of Coupons + PV of Principal Amount
                   = [PVAF (7%,10) * 80] + [PVIF (7%,10) * 1000]
                         = (7.0236 * 80) + (0.5083 * 1000)
                  = $561.89 + $508.30
                         = $1070.19 (rounded off)

Present Value Factor have been calculated as = (1/1+r)n

Where
r= Required rate of Return (Discount rate)
n= No of Periods

PVAF (7%,10) is calculated by adding the PV Factor of 7% for 10 years
NOTE : We have assumed the Face Value of the bond to be $1000.

Since the intrinsic value of the bond ($1070.19) is more than the price of the bond, the bond is trading cheap and should be purchased.

The price we will pay to the seller will be $1010.

Bond price has inverse relation with interest rate. If interest rate are expected to fall bond price will rise and vice versa. Since the expectation of interest rate is to fall, the bond prices will increase.

Option a) is correct.
I would buy it, total to pay $1009.35, if interest rates go down it favours.