Final answer:
To determine the future and present values of cash flows for Canine, Inc., we apply varying discount rates over different periods. Calculations involve compounding received cash flows for future value and discounting future cash flows to find present value. A two-year bond example illustrates the impact of discount rates on investment valuation.
Step-by-step explanation:
To calculate the future and present values of cash flows for Canine, Inc., we need to apply different discount rates for different periods. The cash flows will be discounted at 8% for the first two years and at 6% from the third year onwards.
Future Value Calculations
For the future value in Year 5, we have cash flow from Year 1 to Year 4 that needs to be compounded at the respective rates for the remaining periods.
Future Value of Year 1 Cash Flow in Year 5 = $1,075 * (1 + 0.08)4
Future Value of Year 2 Cash Flow in Year 5 = $1,235 * (1 + 0.08)3
Future Value of Year 3 Cash Flow in Year 5 = $1,510 * (1 + 0.06)2
Future Value of Year 4 Cash Flow in Year 5 = $1,965 * (1 + 0.06)
Sum up all these future values to find the total future value in Year 5.
For the future value in Year 10, the cash flow in Year 7 needs to be compounded at 6% for 3 years.
Future Value of Year 7 Cash Flow in Year 10 = $10,000 * (1 + 0.06)3
Present Value Calculations
The present value of each cash flow is calculated by discounting them at the respective rates:
Present Value of Year 1 Cash Flow = $1,075 / (1 + 0.08)
Present Value of Year 2 Cash Flow = $1,235 / (1 + 0.08)2
Present Value of Year 3 Cash Flow = $1,510 / (1 + 0.06)3
Present Value of Year 4 Cash Flow = $1,965 / (1 + 0.06)4
Present Value of Year 7 Cash Flow = $10,000 / (1 + 0.06)7
Sum all these present values to get the total present value of the cash flows.
To understand the impact of changing discount rates, consider the given example of a two-year bond issued at $3,000 paying 8% interest annually. When discounted at the same rate (8%), the present value of interest payments and the principal remains equal to the nominal amounts.
However, if the discount rate increases to 11%, the present value of these payments decreases, showing that the value of the investment drops with rising discount rates.