Determine the value of a $500 Canadian Pacific Limited perpetual 8 percent debenture if the required rate of return is 14%
To determine the value of a debenture, we need to use the present value formula. The present value formula calculates the current worth of future cash flows by discounting them using the required rate of return.
In this case, the required rate of return is given as 14%, and we know that the debenture pays an 8% interest annually.
Step 1: Calculate the interest payment
The interest payment is a fixed amount each year based on the debenture's face value. The face value is $500.
Interest payment = Face value x Interest rate
Interest payment = $500 x 8% = $40
Step 2: Determine the present value of the interest payments
To find the present value of the interest payments, we need to discount each future payment to its present value. We can use the present value of an ordinary annuity formula for this calculation.
Present value of an ordinary annuity = Payment x (1 - (1 + r)^(-n)) / r
where:
- Payment is the annual interest payment
- r is the required rate of return (as a decimal)
- n is the number of years
In this case, the payment is $40, the required rate of return (r) is 14% or 0.14, and the debenture is perpetual, meaning it has no specific maturity date. So, we can assume a very long term, such as 100 years, to calculate the present value effectively.
Present value of interest payments = Payment x (1 - (1 + r)^(-n)) / r
Present value of interest payments = $40 x (1 - (1 + 0.14)^(-100)) / 0.14
Using a financial calculator or spreadsheet, the present value of the interest payments is approximately $280.51.
Step 3: Determine the present value of the principal repayment
Since the debenture is perpetual, it doesn't have a specific maturity date. Therefore, the principal repayment amount is infinite. To calculate the present value of an infinite cash flow, we can use the Gordon Growth Model, assuming that the principal payment grows at a constant rate perpetually.
Gordon Growth Model formula:
Present value of infinite cash flow = Cash flow / (r - g)
where:
- Cash flow is the cash flow in the first year
- r is the required rate of return (as a decimal)
- g is the growth rate of the cash flow
In this case, the cash flow is the principal repayment, which is $500, the required rate of return (r) is 14% or 0.14, and we need to assume a growth rate (g). Let's assume a conservative growth rate of 2% annually.
Present value of principal repayment = Principal repayment / (r - g)
Present value of principal repayment = $500 / (0.14 - 0.02)
Using a financial calculator or spreadsheet, the present value of the principal repayment is approximately $3,846.15.
Step 4: Calculate the total value of the debenture
To determine the total value of the debenture, we need to sum up the present value of the interest payments and the present value of the principal repayment.
Total value of the debenture = Present value of interest payments + Present value of principal repayment
Total value of the debenture = $280.51 + $3,846.15
Calculating this sum, the total value of the debenture is approximately $4,126.66.
Therefore, the value of the $500 Canadian Pacific Limited perpetual 8 percent debenture, with a required rate of return of 14%, is approximately $4,126.66.