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The Apple plan offers to pay $5,824 starting from the first year. The annual amount will increase at 4 percent per year for the next 45 years. Assuming a discount rate of 11%, what is the present value of this investment plan?

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Final answer:

To calculate the present value of the investment plan, we use the formula PV = CF / (1+r)n, where PV is the present value, CF is the future cash flow, r is the discount rate, and n is the number of years. Each future cash flow can be calculated using the formula CFn = CF1 * (1+growth rate)^n. By discounting and summing up all the future cash flows, we can find the present value.

Step-by-step explanation:

To calculate the present value of the investment plan, we need to discount each future payment back to the present using the discount rate of 11%. The formula to calculate the present value of an investment or cash flow is PV = CF / (1+r)n, where PV is the present value, CF is the future cash flow, r is the discount rate, and n is the number of years.

In this case, the future cash flows are increasing at a rate of 4% per year, starting with $5,824 in the first year. So, the future cash flows in each year can be calculated as follows:

  • Year 1: $5,824
  • Year 2: $5,824 * (1+4%) = $6,061.76
  • Year 3: $6,061.76 * (1+4%) = $6,311.41
  • ...continue this calculation for the next 45 years

After calculating the future cash flows, we can apply the formula to calculate the present value:

PV = $5,824 / (1+11%)^1 + $6,061.76 / (1+11%)^2 + $6,311.41 / (1+11%)^3 + ... + (last year cash flow) / (1+11%)^45

By summing up all the present values, we can find the present value of this investment plan.

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