The Only Organic (OO) golf complex has a first cost of $55M, annual O&M costs of $10M, salvage value in year 100 of $25M, clubhouse renovation every 10 years costing $19M (but not in year 100), and reseeding every 4 years starting in year 4 costing $8M. Additional miscellaneous work will be done every 5 years starting in year 5 costing $2M (but not in year 100), and other annual costs of $1M. Find the EAC for a 100-year horizon if i = 10%. Roughly 500 golfers are expected to use the golf complex daily. What is the benefit (or cost) per daily golfer to justify the golf complex?

I am uncertain what you question is. The problem is straightforward: Ammoritize the cost over a 100 year term. The only question I had on the problem is whether the costs (OM, renovation, and misc work) are given in present value or future value. In my experience, it would be present value, but the question does not seem written that way. We can check your work if you need.

To find the Equivalent Annual Cost (EAC) for a 100-year horizon, we need to calculate the present value of all the costs and benefits associated with the golf complex and then distribute them evenly over the 100-year period.

First, let's calculate the present value of each cost and benefit:

1. First cost: The first cost of $55M is already in present value, so we can use it directly.

2. O&M costs: The annual O&M costs of $10M need to be converted to present value. We can use the formula for the present value of a perpetuity:

Present Value = Annual Cost / Discount Rate

PV(O&M) = $10M / 0.1 = $100M

3. Salvage value: The salvage value in year 100 of $25M is already in present value, so we can use it directly.

4. Clubhouse renovation: The renovation cost of $19M every 10 years needs to be converted to present value. We can use the formula for the present value of an annuity:

PV(Renovation) = Annual Cost * (1 - (1 + discount rate)^-n) / discount rate

PV(Renovation) = $19M * (1 - (1 + 0.1)^-10) / 0.1 = $132.59M

5. Reseeding: The reseeding cost of $8M every 4 years starting in year 4 needs to be converted to present value. Similar to the clubhouse renovation, we can use the formula for the present value of an annuity:

PV(Reseeding) = Annual Cost * (1 - (1 + discount rate)^-n) / discount rate

PV(Reseeding) = $8M * (1 - (1 + 0.1)^-24) / 0.1 = $81.35M

6. Miscellaneous work: The miscellaneous cost of $2M every 5 years starting in year 5 also needs to be converted to present value. Again, we can use the formula for the present value of an annuity:

PV(Miscellaneous) = Annual Cost * (1 - (1 + discount rate)^-n) / discount rate

PV(Miscellaneous) = $2M * (1 - (1 + 0.1)^-20) / 0.1 = $31.52M

7. Other annual costs: These costs are already in present value, so we can use them directly.

Now, let's add up all the present values to calculate the total present value of costs and benefits:

Total Present Value = First cost + PV(O&M) + Salvage value + PV(Renovation) + PV(Reseeding) + PV(Miscellaneous)

Total Present Value = $55M + $100M + $25M + $132.59M + $81.35M + $31.52M = $425.46M

Finally, we can calculate the Equivalent Annual Cost by dividing the total present value by the number of years (100) and adjusting for the number of daily golfers (500):

EAC = Total Present Value / (Number of Years * Number of Daily Golfers)

EAC = $425.46M / (100 * 500) = $850.92

So the Equivalent Annual Cost for a 100-year horizon, considering a discount rate of 10% and approximately 500 golfers using the complex daily, is approximately $850.92.

To calculate the benefit (or cost) per daily golfer to justify the golf complex, we divide the EAC by the number of daily golfers:

Benefit (or Cost) per Daily Golfer = EAC / Number of Daily Golfers

Benefit (or Cost) per Daily Golfer = $850.92 / 500 = $1.70

Therefore, approximately $1.70 per daily golfer is needed to justify the golf complex.