Question

Katie Pairy Fruits Inc. has a $2,100, 22-year bond outstanding with a nominal yield of 18 percent (coupon equals 18% × $2,100 = $378 per year). Assume that the current market required interest rate on similar bonds is now only 12 percent. Use Appendix B and Appendix D for an approximate answer but calculate your final answer using the formula and financial calculator methods.    
  
a. Compute the current price of the bond. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.

b. Find the present value of 6 percent × $2,100 (or $126) for 22 years at 12 percent. The $126 is assumed to be an annual payment. Add this value to $2,100. (Do not round intermediate calculations. Round your final answer to 2 decimal places. Assume interest payments are annual.)
  

Answer 1

(a) Bond Nominal Yield = 18 %, Bond Face Value = $ 2100, Bond Tenure = 22 years and Yield = 12 %

Annual Coupon Payment = Bond Nominal Yield x Bond Face Value = 0.18 x 2100 = $ 378

The current bond price will be equal to the total present value of the bond's expected cash flow in the form of bond coupon payments and the redeemed face value at bond maturity.

Therefore, current bond price = 378 x (1/0.12) x [1-{1/(1.12)^(22)}] + 2100 / (1.12)^(22) = $ 3063.22

(b) Present Value of 6 % of $ 2100 for 22 years at 12 % will be calculated as shown below:

6 % of $ 2100 = 0.06 x 2100 = $ 126

PV of these payments for 22 years at 12 % = 126 x (1/0.12) x [1-{1/(1.12)^(22)}] = $ 963.22

Total Value = 2100 + 963.22 = $ 3063.22