Consider a security with a face value of $100 000 to be repaid at maturity. The maturity of the security is 3 years. The coupon rate is 9 per cent p.a. and coupon payments are made semi-annually. The current discount rate is 12 per cent p.a. What is the security's duration (round your answer to two decimals)?
A) 2.68 years
B) 2.68 half-years
C) 3 years
D) 0.38 years

Question

Quizplus · Accepted Answer

To calculate the duration, we can use the following formula:
Duration = (Present value of bond's cash flows * time until cash flow) / Present value of bond
The present value of the bond's cash flows can be calculated as follows:
PV of bond's cash flows = (Coupon payment/ (1 + r/2)^t) + (Coupon payment/ (1 + r/2)^(t+0.5)) + (Coupon payment/ (1 + r/2)^(t+1)) + ... + (Coupon payment + Face value/ (1+r/2)^(2t))
PV of bond's cash flows = (4500/1.06) + (4500/1.06^2) + (4500/1.06^3) + ... + (4500/1.06^6) + (100,000/1.06^6)
PV of bond's cash flows = $94,792.09

Using the same formula, the present value of the bond can be calculated as follows:
PV of bond = (Coupon payment/ (1 + r/2)^t) + (Coupon payment/ (1 + r/2)^(t+0.5)) + (Coupon payment/ (1 + r/2)^(t+1)) + ... + (Coupon payment + Face value/ (1+r/2)^(2t))
PV of bond = (4500/1.06) + (4500/1.06^2) + (4500/1.06^3) + ... + (4500/1.06^6) + (100,000/1.06^6)
PV of bond = $82,172.83

Using these values, we can calculate the duration as follows:
Duration = (PV of bond's cash flows * time until cash flow) / PV of bond
Duration = ($94,792.09 * 2.5) / $82,172.83
Duration = 2.68 years (rounded to two decimals)

Therefore, the best choice is A.

Consider a Security with a Face Value of $100 000