Applied Foundations of Finance Tutorial Quiz 2
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Question:
Your friend owns a restaurant business. She has decided to issue bonds as a way of raising monies to fund a new project. These bonds will pay coupons at a rate of p.a. and will mature exactly 7.25 years after being issued. If the rate of return required by financiers on these instruments has been estimated at p.a., how much will your friend raise upon issuing a bond like this with a face value of ?
What will happen to the value of the bond immediately after a coupon is paid? Why?
To determine how much your friend will raise upon issuing the bond, we need to calculate the present value of the bond's cash flows, which consist of the annual coupon payments and the face value at maturity.
1.
Coupon Payment: The bond pays a coupon of 6% on a face value of $125,000. Therefore, the annual coupon payment is:
\[
\text{Coupon Payment} = 0.06 \times 125,000 = 7,500
\]
2.
Present Value of Coupon Payments: Since the bond matures in 7.25 years, we will discount each of the coupon payments back to the present value using the required rate of return of 8%. The present value of an annuity formula can be used here:
where is the annual coupon payment, is the required rate of return, and is the number of years until maturity.
Plugging in the values:
3.
Present Value of Face Value: The present value of the face value of the bond is calculated using the formula:
where is the face value of the bond.
Plugging in the values:
4.
Total Present Value: The total amount your friend will raise from issuing the bond is the sum of the present values of the coupon payments and the face value:
Now, regarding what happens to the value of the bond immediately after a coupon is paid:
When a coupon payment is made, the bond's price typically decreases by the amount of the coupon payment. This is because the bondholder receives cash, which reduces the future cash flows associated with the bond. Therefore, the bond's market value will drop by the amount of the coupon paid, reflecting the fact that there is now one less coupon payment to be received in the future.
If you need help with the calculations or further clarification, feel free to ask!
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