A company issues a bond with a face value of 7,000,000 dollars and a maturity of 15 years, where the coupon rate is 15% per year and agrees to pay the bondholders quarterly coupons. Calculate the price of the bond if the yield rate is 18% per year.

1. Calculate the annual coupon payment:

C_{\text{annual}} = 7,000,000 \times 0.15 = 1,050,000

2. Determine the quarterly coupon payment:

C_{\text{quarterly}} = \frac{1,050,000}{4} = 262,500

3. Calculate the number of periods (\(n\)) in 15 years with quarterly payments:

n = 15 \times 4 = 60

4. Determine the quarterly yield rate (\(r\)):

r = \frac{0.18}{4} = 0.045

5. Calculate the price of the bond (Present Value of all future cash flows). The price of the bond \(B\) is given by:

B = C_{\text{quarterly}} \times \frac{1 - (1 + r)^{-n}}{r} + \frac{7,000,000}{(1 + r)^n}

Plug in the known values:

B = 262,500 \times \frac{1 - (1 + 0.045)^{-60}}{0.045} + \frac{7,000,000}{(1 + 0.045)^{60}}

6. Simplify the equations:

B = 262,500 \times \frac{1 - (1.045)^{-60}}{0.045} + \frac{7,000,000}{(1.045)^{60}}

7. Using a calculator to compute:

B\approx262,500\times20.6380+499,023.05796517\approx5,916,498.06

Hence, the price of the bond is:

B=5,916,498.06