Final answer:
The cash payback period for The Bell Company's project is 2 years. For a given future value, the lowest interest rate (2%) results in the highest present value. When calculating the present value of bond payments, lower discount rates result in higher present values.
Step-by-step explanation:
Cash Payback Period
The cash payback period for an investment is the time it takes for the project to generate enough cash flow to cover the initial investment cost. In this case, The Bell Company invested $14,000 in a project with cash flows of $6,000 in year 1, $6,000 in year 2, and $4,000 in year 3. To calculate the payback period, we sum the cash flows until the initial investment is recovered.
Year 1 cash flow: $6,000
Year 2 cumulative cash flow: $6,000 + $6,000 = $12,000
By the end of year 2, the project has not yet paid back the full investment. In year 3, it generates additional $4,000, taking the cumulative cash flow to $16,000, which covers the investment cost. The investment is fully paid back in year 3. So, the payback period is 2 years.
Present Value and Interest Rate
Given a future value, the lowest interest rate would result in the highest present value since there is an inverse relationship between interest rates and present values. Therefore, the correct answer is 2% (c).
Present Value Calculation for a Bond
To find the present value (PV) of a simple two-year bond that pays an annual interest of $240 and returns the principal of $3,000 at the end of the second year, we use the present value formula for each cash flow and sum them up. If the discount rate is 8%, the PV of the first interest payment is $240/(1+0.08) and the PV of the second payment plus principal is ($240+$3,000)/(1+0.08)^2. If the discount rate rises to 11%, the calculations would use these new rates respectively.
When the applicable discount rate is 11%, each cash flow's present value would be lower, resulting in a lower overall PV for the bond, due to the higher discount factor being applied.