Question

A country plans to use an 83.74-acre plot for a road link 12.6 years from now. In the meantime (in the next 5 years) this land will be used as a sports field (football-basketball) together with the parking area.

The development cost of the land is $96413 and the annual operating cost is $6013. The football field will serve 3119 people in the first year and will increase by 42% per year. The basketball court will serve 1111 people in its first year and there will be an increase of 7% per year.
If the interest rate is 11%, find the present value and the equivalent annuity.

Answer 1

To find the present value and equivalent annuity, calculate the present value of the development cost and annual operating costs, as well as the present value of the expected cash flows from the sports field.

Step-by-step explanation:

To find the present value and equivalent annuity, we need to calculate the present value of the development cost and annual operating costs, as well as the present value of the expected cash flows from the sports field.

First, we calculate the present value of the development cost and annual operating costs using the formula for present value: PV = FV / (1+r)^t,

where PV is the present value, FV is the future value, r is the interest rate, and t is the time period.

Next, we calculate the present value of the expected cash flows from the sports field. The football field will generate cash flows for the next 5 years, and the basketball court will also generate cash flows for the next 5 years. We use the formula for the present value of an annuity to calculate the present value of both sets of cash flows.

Finally, we add the present value of the development cost and annual operating costs to the present value of the expected cash flows from the sports field to get the total present value. To find the equivalent annuity, we divide the total present value by the present value of a $1 annuity factor for the corresponding interest rate and time period.