Question

On 31 December 20X0, Columbia Inc. entered into an agreement with Scotia Ltd. to lease equipment with a useful life of 6 years. Columbia Inc. will make four equal payments of $153,000 at the beginning of each lease year. Columbia Inc. anticipates that the equipment will have a residual value of $88,800 at the end of the lease, net of removal costs. Columbia Inc. has the option of extending the lease by (1) paying $88,800 to retain the equipment or (2) allowing Scotia Ltd. to remove it. Scotia Ltd.’s implicit interest rate in this lease is 9%. Columbia Inc.’s incremental borrowing rate is 10%. Columbia Inc. depreciates the leased equipment on a straight-line basis. The lease commences on 1 January 20X1. Assume that the fair value of the equipment on the open market is greater than the present value of the lease payments. (PV of $1, PVA of $1, and PVAD of $1.)

Answer 1

The concept of present value helps calculate the worth of future cash flows in today's terms, which is essential in finance for evaluating bonds, leases, and loans. Applying present value, one can determine the current worth of a bond or the lease payments by discounting future cash flows using the appropriate interest rate. This concept illustrates how sensitive present value is to interest rate changes.

Step-by-step explanation:

Present Value Calculations for Bonds and Leases

The concept of present value is a fundamental principle in finance, used to determine the value of future cash flows in today's terms. When assessing the value of a bond, which provides periodic interest payments and a return of principal at maturity, or a lease, which involves regular payments for the use of an asset, understanding how to calculate present value is crucial.

For instance, if we consider a simple two-year bond issued for $3,000 with an 8% interest rate, it will pay $240 in the first year and both $240 in interest plus the $3,000 principal in the second year. To calculate the present value with an 8% discount rate, we would use the formula:

PV = $C1 / (1+r) + $C2 / (1+r)^2

where PV is present value, C1 is the cash flow in the first year, C2 is the cash flow in the second year, and r is the discount rate.

If interest rates rise to 11%, the present value needs to be recalculated because future cash flows are now worth less in today's dollars due to the higher opportunity cost of capital. This calculation emphasizes the sensitivity of present value to interest rate fluctuations.

In the scenario given, where Mackenzie takes out a student loan or Columbia Inc. enters into a lease agreement, each would require calculating the present value of the lease payments or the student loan payments using the given interest rates, and those calculations would drive decisions about the advisability and affordability of the loan or lease.