Question

.Suppose a ten-year bond with a $10,000 face value pays a 5.0% annual coupon (at the end of the year), has 2 years left to maturity, and has a discount rate of 6.5%. Which of the following would give you the present value – i.e. the price – of the bond?

A. Present Value = $10,500/(1.065) 2

B. Present Value = [$500/(1.065)] + [$500/(1.065) 2 ]+ ... +[$500/(1.065) N ], where N = ∞(infinity).

C Present Value = [$500/(1.065)] + [$500/(1.065) 2 ] +[$10,000/(1.065) 2 ]

D. Present Value = [$500/(1.065)] + [$500/(1.065) 2 ]

Answer 1

Face value of bond = $10,000

Annual coupon rate = 5% or 0.05

Annual coupn payment = Face value * Annual coupon rate = $10,000 * 0.05 = $500

Discount rate = 6.5% or 0.065

There is 2 years left to maturity of the bond.

Since, two years has left to maturity of the bond, the bond holder will receive two annual coupon payments.

Thus, the price of the bond will be equal to the sum of the present value of these two coupon payments and the present value of the face value of the bond.

Calculate the pice of the bond -

Price = [Annual coupon payment/(1 + r)ⁿ] + [Annual coupon payment/(1+r)ⁿ] + [Face value of bond/(1 + r)ⁿ]

Price = [$500/(1+0.065)¹] + [$500/(1+0.065)²] + [$10,000/(1+0.065)²]

Price = [$500/(1.065)] + [$500/(1.065)²] + [$10,000/(1.065)²]

Hence, the correct answer is the option (C).