Question

22) On January 1, 2017, bonds with a face value of $94,000 were sold. The bonds mature on January 1, 2027. The stated interest rate is 8% annually. The bonds pay interest semiannually on July 1 and January 1. The market rate of interest is 10% annually. What is the market price of the bonds? (Round your final answer to the nearest dollar.)

Answer 1

Calculation of present value of interest payments

PV of annuity factor = (1 - (1/(1+r)^n))/r

where,

n = number of intervals of payments (Here, it is 20 which is 10 years of semi annual payments)

r = Market interest rate (here, it is 5% which is 10% annual / 2 = 5% semi annual)

PV of annuity factor = (1 - (1/(1 + 0.05)^20))/0.05

                                = (1 - (1/(1.05)^20))/0.05

                                = (1 - (1/2.653297795)/0.05

                                = (0.6231105299/0.05)

                                = 12.4622

Annuity Payments = 94000 x 4% (8%/2 = 4% semi annual rate)

                             = 3,760

PV of annuity payments = Annuity payments x PV of annuity factor

                                       = 3,760 x 12.4622

                                       = 46,858

PV of maturity value of bond

The bond matures in 10 years and the maturity value is $94,000. The market interest rate is used to discount it which is 10%.

The discount factor = 1/(1+r)^n

                                = 1/(1+0.1)^10

                                = 1/2.59374246

                                = 1/2.59374246

                                = 0.3855

Present value = Face value x discount factor

                       = 94,000 x 0.3855

                       = $36,237

Market value of bond = PV of annuity payments + PV of maturity amount

                                  = 46,858 + 36,237

                                 = $83,095