Question

The Lone Star Company has $1.000 par value bonds outstanding at 10 percent interest. The bonds will mature in 20 years Use Appendix B and Appendix D for an approximate answer but calculate your final answer us methods ing the formula and financial calculator Compute the current price of the bonds if the present yield to maturity is: (Do not round intermediate calculations. answers to 2 decimal places. Assume interest payments are annual.) Bond Price a. 6 percent b. 9 percent C. 13 percent

Answer 1

Current Price of the bond will be the Present Value of all the cash flows (i.e. Interest and Principal maturity amount) till the maturity date.

The current price of the bonds is calculated as below:

Present Value of Interest Payment (PV_A ) + Present Value of Principal on Maturity (PV_F)

PV_A = A * PV_IFA where A = Interest Amount and IFA is Interest factor of Annuity for given number of peiords (n) and the particular rate (i) AND

PV_F = FV * PV_IF where FV = Principal Maturity Amount and IF is Interest factor at a given time (n) and at a particular rate (i)

Interest payment per year is $ 100 ($1,000 * 10%) and the maturity is after 20 years (so n = 20, i=10%, A=$100 and FV = $1,000).

a. Current Price of Bond if the yield to maturity is 6%

IFA for n=20 and i=6% is 11.470 and IF for n=20 and i=6% is 0.312

Present Value of Interest Payment = $100*11.470=                                      $1,147.00

Present Value of Principal on Maturity = $1000*0.312= $312.00

Price of Bond                                                                                         $1,459.00

b. Current Price of Bond if the yield to maturity is 9%

IFA for n=20 and i=9% is 9.129 and IF for n=20 and i=9% is 0.178

Present Value of Interest Payment = $100*9.129=                                        $912.90

Present Value of Principal on Maturity = $1000*0.178= $178.00

Price of Bond                                                                                          $1,090.90

c. Current Price of Bond if the yield to maturity is 13%

IFA for n=20 and i=13% is 7.025 and IF for n=20 and i=13% is 0.087

Present Value of Interest Payment = $100*7.025=                                        $702.50

Present Value of Principal on Maturity = $1000*0.087= $87.00

Price of Bond                                                                                              $789.50