Question

A utility company sold an issue of 6 percent bonds 5 years ago. Each bond has a face value (value at maturity) of $1000, which is due in 13 years from now. The bond pays interest twice a year (3 percent per period). Because of market conditions, the bond can now be sold on the bond market for only $760. If a buyer wants his or her investment to earn 10 percent nominal rate per year, compounded semiannually, and must pay a brokerage charge of $20 to purchase each bond, should the buyer purchase the bond?

Answer 1

Period remaining till maturity = 13 years
Coupon amount = 1000*3% = 30 paid semiannually
Required rate of return = 10% compounded semiannually i.e 5% for 6 months compounded semiannually.
No of Periods = 26 half yearly period

Value of Bonds = Present Value of Coupons + PV of Principal Amount
                        = [PVAF (5%,26) * 30] + [PVIF (5%,26) * 1000]
                         = (14.3752 * 30) + (0.2812 * 1000)
                        = 431.26 + 281.20
                         = 712.46

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

Where

r= Required rate of Return (Discount rate)

n= No of Periods

PVAF (5%,26) is calculated by adding the PV Factor of 5% for 26 years

Selling price of bond = $760
Cost to the buyer = Selling price of bond + Brokerage Charge
                            = $760 + $20
                             = $780

Since cost to the buyer is more than the value of the bond calculated at the required rate of return, the buyer should not purchase it.