Question

On January 1, 2019, East Lansing, Inc., issues $2,000,000 of 10 percent, 5-year bonds that pay interest of $100,000 semiannually. The market rate is 8 percent at the time of issuance. The present value of 1 at 4% for 10 periods is 0.6756. The present value of an annuity at 4% for 10 periods is 8.1109. The issue price of the bonds is _____.

Answer 1

Answer:

The issue price of the bond is the present value of  the future cash flows of the bond,which is $2,162,217.92.  

The calculation of the issue price is shown below.

Explanation

The bond will pay interest of $100000 for 10 periods plus $2000000 par at the end of the tenth period.

The formula applicable is: Future value of each period multiplied by applicable discounting factor.

Even though the bond is issued for only 5 years,but the fact that it pays interest semi-annually makes it 10 period duration(5years*2).

Interest rate should also be adjusted to show the time horizon of six month each by dividing 8% per year by 2.

The detailed computation of present value is as follows:

 Periods   Coupon Interest @10%/2   DCF=1/(1+r)^n   PV  

1.00                 100,000.00                     0.9615            96,153.85  

2.00                  100,000.00                       0.9246     92,455.62  

3.00                  100,000.00                        0.8890      88,899.64  

4.00                   100,000.00                          0.8548      85,480.42  

5.00                    100,000.00                            0.8219      82,192.71  

6.00                    100,000.00                            0.7903     79,031.45  

7.00                    100,000.00                             0.7599    75,991.78  

8.00                    100,000.00                             0.7307    73,069.02  

9.00                    100,000.00                             0.7026     70,258.67  

10.00                    2,100,000.00                     0.6756   1,418,684.75  

                                                                            2,162,217.92