Answer:
we will find present value of cost over 25 years for both alternatives and would choose one which lowest PV of cost.
Vinyl siding
Cost today (start of year 1) = PV = $13,000
It will last for 25 years
Painting:
Start of year 1:
Cost Incurred today = $3,500
Cost of replacing the boards today (which will last for 25 years) = $2,500
Start of year 6:
Cost Incurred at start of year 6 = $3,500 * (1 + 5%) 5 Annual Inflation rate being 5%
PV of this cost = $3,500 * (1 + 5%) 5 / (1 + 10%) 5
Start of year 11:
Cost Incurred at start of year 11 = $3,500 * (1 + 5%) 10
PV of this cost = $3,500 * (1 + 5%) 10 / (1 + 10%) 10
Start of year 16:
Cost Incurred at start of year 16 = $3,500 * (1 + 5%) 15
PV of this cost = $3,500 * (1 + 5%) 15 / (1 + 10%) 15
Start of year 21:
Cost Incurred at start of year 21 = $3,500 * (1 + 5%) 20
PV of this cost = $3,500 * (1 + 5%) 20 / (1 + 10%) 20
Total PV of all costs = 3500 + 2500 + 3500 * (1 + 5%) 5 / (1 + 10%) 5 + 3500 * (1 + 5%) 10 / (1 + 10%) 10 + 3500 * (1 + 5%) 15 / (1 + 10%) 15 + 3500 * (1 + 5%) 20 / (1 + 10%) 20
= $14,093.94
As such PV of cost Vinyl siding is lower at $13,000 than the PV of cost at $14,093.94 in case of painting.
Thus, you would prefer to install the vinyl siding
