Question

You have been looking for the perfect investment all your life. You finally found it yesterday when you were studying for this exam. It is 10 percent coupon bond on the market that sells for par value. you decide to celebrate your finding by throwing a big party on the maturity date of this bond. when is your party? Please answer in Year-Month-Date format and show the steps to justify your answer.

That is how my Professor asked the question

Answer 1

In this case as the bond sells for par value it means that the bond’s coupon rate is the same as its yield to maturity.

Thus in this case coupon rate = yield to maturity = 10%

The maturity date can be 1 year, or 2 years, or 3 years. In all these cases the bond will sell for par value.

Let’s assume that maturity is after 1 year and that yesterday was 2019-04-13. Thus the party will be after 1 year i.e. on 2020-04-12.

Present value of a bond (or its selling price) = present value of coupon + present value of maturity amount

Now face value is usually $1,000. Thus coupon is 10% of $1000 = $100. Present value will be computed using the YTM of 10%.

So, $1,000 = $100/1.1^1 + $1000/1.1^1

= 90.91 + 909.09

= $1,000

So assuming that yesterday was 2019-04-13 the party will be given on 2020-04-12.