There is a safe bond B which has 4 years before maturity and pays a coupon
of 12% at regular annual intervals and a face value of $100 at maturity.
(a) What will be the current price of bond B?
To calculate the current price of a bond, you need to use the present value formula. The present value is the discounted value of future cash flows.
In this case, bond B pays a coupon of 12% annually until maturity, and a face value of $100 at maturity. The current price will be equal to the present value of these future cash flows.
To calculate the present value, you need to discount each cash flow using an appropriate discount rate. The discount rate depends on prevailing market interest rates and the risk associated with the bond.
Assuming a discount rate of 10%, you can calculate the present value of the coupon payments and the face value at maturity.
Step 1: Calculate the present value of the coupon payments:
Coupon payment = Coupon rate x Face value = 12% x $100 = $12
Using the formula for present value of an ordinary annuity:
PV of coupon payments = Coupon payment x [1 - (1 + discount rate)^(-number of periods)] / discount rate
PV of coupon payments = $12 x [1 - (1 + 10%)^(-4)] / 10%
Step 2: Calculate the present value of the face value at maturity:
PV of face value = Face value / (1 + discount rate)^number of periods
PV of face value = $100 / (1 + 10%)^4
Step 3: Calculate the current price of bond B:
Current price of bond B = PV of coupon payments + PV of face value
Substituting the values computed in steps 1 and 2:
Current price of bond B = PV of coupon payments + PV of face value
Now you can calculate the current price of bond B using the discount rate of 10%.