On January 1, 2019, East Lansing, Inc., issues $2,000,000 of 10 percent, 5-year bonds that pay interest of $100,000 semiannually

Question

3 years ago

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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 _____.

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1 answer:

xenn [34] · Answer 1 · 2022-08-11T10:59:24+03:00

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 <u>1,418,684.75</u>