Answer:
the price of the zero-coupon bond is approximately GBP 4,524.21. This means that an investor would need to pay GBP 4,524.21 upfront to purchase the bond and would receive GBP 10,000 at maturity in 16 years.
Step-by-step explanation:
A zero-coupon bond is a type of bond that does not pay any interest to the bondholders. Instead, it is issued at a discount from its face value and matures at a future date when the bondholder receives the full face value of the bond.
In this case, the company has issued a zero-coupon bond with a face value of GBP 10,000 and a maturity period of 16 years. The market rate for such bonds is 8%, compounded semiannually.
To calculate the price of the bond, we need to discount the future cash flow of GBP 10,000 back to the present value using the market rate of 8%. Since the interest is compounded semiannually, we need to adjust the interest rate accordingly.
The formula to calculate the present value of a future cash flow is:
PV = FV / (1 + r/n)^(n*t)
Where:
PV = Present Value
FV = Future Value
r = Interest Rate
n = Number of compounding periods per year
t = Number of years
In this case, FV is GBP 10,000, r is 8% (0.08), n is 2 (semiannual compounding), and t is 16 years.
Using the formula, we can calculate the present value as follows:
PV = 10,000 / (1 + 0.08/2)^(2*16)
PV = 10,000 / (1.04)^(32)
PV = 10,000 / 2.208
PV ≈ GBP 4,524.21