Polycorp Treasury a company in the land of Zanadu is holding a parcel of Zanadu Government Bonds with a face value of $2,000,000. The bonds were issued seven years and nine months ago and still have two years and three months to maturity. They pay a coupon rate of interest of 6.25% pa, with interest being paid semi-annually. Currently the market yield quoted for Zanadu bonds is 4.62% pa. The convention in Zanadu financial markets is that the market yield and coupon rate are quoted as annual nominal rates. What is the current market value of the bonds?
To calculate the current market value of the Zanadu Government Bonds, we need to discount the future cash flows from the bond using the market yield.
Here are the steps to calculate the current market value:
1. Determine the number of coupon payments remaining: Since the bonds were issued seven years and nine months ago and have two years and three months to maturity, there are a total of 10 coupon payments remaining (5 years * 2 semi-annual payments per year).
2. Calculate the coupon payment: The coupon rate is 6.25% per annum, and since it is paid semi-annually, the coupon payment is (6.25% / 2) = 3.125% every six months. We need to convert this to a decimal form, so the coupon payment is 0.03125.
3. Calculate the present value of the coupon payments: To find the present value of each coupon payment, we need to discount them using the market yield of 4.62%. Since the coupon payments occur semi-annually, the discount rate per period is half of the annual market yield, which is (4.62% / 2) = 2.31%.
Using the formula for the present value of an ordinary annuity:
PV = C * (1 - (1 + r)^-n) / r
Where:
PV = Present Value of the coupon payments
C = Coupon payment
r = Discount rate per period
n = Number of coupon payments remaining
Using the values we have:
PV = 0.03125 * (1 - (1 + 0.0231)^-10) / 0.0231
4. Calculate the present value of the face value: The face value of the bond is $2,000,000, which will be received at maturity. Since it is not a coupon payment, we discount it for the remaining period using the market yield of 4.62%.
PV = F / (1 + r)^n
Where:
PV = Present Value of the face value
F = Face value
r = Discount rate per period
n = Number of periods remaining
Using the values we have:
PV = 2,000,000 / (1 + 0.0462)^10
5. Add the present values of the coupon payments and the face value to get the current market value:
Current Market Value = Present Value of the coupon payments + Present Value of the face value
Now you can perform the calculations to find the current market value of the Zanadu Government Bonds.