A CBS bond with a par value of $1,000, an interest rate of 7.625 percent, and a maturity of 10 years The bond is selling for $986.
The required rates of return is 6 percent for the bond.
To calculate the present value of cash flows for the CBS bond, you can use the formula:
PV = (C / (1 + r)) + (C / (1 + r)^2) + ... + (C / (1 + r)^n) + (F / (1 + r)^n)
Where:
PV = Present Value of the bond
C = Coupon or interest payment
r = Required rate of return
n = Number of periods
F = Par value of the bond
Given information:
Par value (F) = $1,000
Coupon rate = 7.625%
Required rate of return (r) = 6%
Maturity (n) = 10 years
Selling price = $986
Step 1: Calculate the annual coupon payment
Coupon payment = Coupon rate * Par value
Coupon payment = 7.625% * $1,000
Coupon payment = $76.25
Step 2: Calculate the present value of the coupon payments
PV of coupon payments = (C / (1 + r)) + (C / (1 + r)^2) + ... + (C / (1 + r)^n)
PV of coupon payments = ($76.25 / (1 + 0.06)) + ($76.25 / (1 + 0.06)^2) + ... + ($76.25 / (1 + 0.06)^10)
Step 3: Calculate the present value of the par value (face value)
PV of par value = F / (1 + r)^n
PV of par value = $1,000 / (1 + 0.06)^10
Step 4: Calculate the present value of the bond
PV of the bond = PV of coupon payments + PV of par value
PV of the bond = PV of coupon payments + PV of par value
Now, let's perform the calculations:
PV of coupon payments = ($76.25 / (1 + 0.06)) + ($76.25 / (1 + 0.06)^2) + ... + ($76.25 / (1 + 0.06)^10)
Using the financial calculator or Excel, this sum is approximately $680.98.
PV of par value = $1,000 / (1 + 0.06)^10
Using the financial calculator or Excel, this value is approximately $558.39.
PV of the bond = $680.98 + $558.39
PV of the bond = $1,239.37
Since the selling price of the bond is $986 and the calculated present value is $1,239.37, it indicates that the bond is selling at a discount.
To calculate the value of a bond, you can use the present value formula. The present value represents the current worth of future cash flows, which in the case of a bond, are the periodic interest payments and the principal repayment at maturity.
The formula to calculate the present value of a bond is:
PV = (C / r) * (1 - (1 / (1 + r)^n) ) + (F / (1 + r)^n)
Where:
PV = Present value or price of the bond
C = Coupon payment (interest payment)
r = Required rate of return
n = Number of periods (maturity in years)
F = Par value (face value)
Given the information:
C = $1,000 * 7.625% = $76.25 (annual coupon payment)
r = 6% (required rate of return)
n = 10 (maturity in years)
F = $1,000 (par value)
To calculate the present value, plug in the values into the formula:
PV = ($76.25 / 0.06) * (1 - (1 / (1 + 0.06)^10) ) + ($1,000 / (1 + 0.06)^10)
Now, calculate the present value:
PV = ($76.25 / 0.06) * (1 - (1 / (1.06)^10) ) + ($1,000 / (1.06)^10)
PV = $1270.80 + $558.39
PV = $1,829.19
So, the value or price of the bond should be approximately $1,829.19.
Comparing this calculated value to the actual selling price of $986, we can see that the bond is selling at a discount.