Question

Your company wants to rake $10.5 million by issuing 25-year zero-coupon bonds. If the yiald to maturity on the bonds wil be 4% (EAR). what total face value ampunt of bonds must you issie? The totai face value amount of bonds that you must issue is?

Answer 1

To raise $10.5 million with a 4% yield to maturity over 25 years, a company should issue zero-coupon bonds with a total face value of approximately $28,006,570.

Step-by-step explanation:

To determine the total face value amount of zero-coupon bonds that must be issued to raise $10.5 million today with a yield to maturity of 4% compounded annually over 25 years, we use the present value formula for zero-coupon bonds. The present value (PV) is the current amount ($10.5 million), the face value (FV) is what we need to find, the interest rate (r) is 4%, and the time (t) is 25 years.

The formula for the present value of a zero-coupon bond is:
PV = FV / (1 + r)^t

Applying the formula:

10500000 = FV / (1 + 0.04)^25
FV = 10500000 * (1 + 0.04)^25
FV = 10500000 * (1.04)^25
FV = 10500000 * 2.66634
FV ≈ 28,006,570

Therefore, the company must issue zero-coupon bonds with a total face value of approximately $28,006,570 to raise $10.5 million today.