Final answer:
The present value (PV) of leasing the truck is calculated using the annuity due formula, taking into account the annual lease payment, the company's discount rate, and the number of payment periods.
Step-by-step explanation:
To calculate the present value (PV) of leasing the truck, we need to discount the lease payments back to their present value at the company's borrowing rate. Since lease payments are $50,000 per year, due at the beginning of each year (annuity due), we need to use the beginning of period formula to calculate their present value.
The formula for the present value of an annuity due is PV = Pmt * [(1 - (1 + r)^-n) / r] * (1 + r), where Pmt is the annual lease payment, r is the discount rate (8% or 0.08 in decimal form), and n is the number of periods (5 years in this case).
The company's tax rate or capital cost allowance rate do not directly affect the calculation of the PV of the lease payments; however, they could be relevant for a comparison with the cost of buying the truck and taking depreciation into account.
For this example, let's calculate the PV of leasing:
- Lease Payment (Pmt): $50,000
- Discount Rate (r): 0.08
- Number of Periods (n): 5
Therefore, the PV of the lease is:
PV = $50,000 * [(1 - (1 + 0.08)^-5) / 0.08] * (1 + 0.08)
After calculating the above formula, we get the present value of the lease as a dollar amount, which would be the answer to the student's question.