You are trying to decide whether to repaint your house or install vinyl siding. The vinyl siding will cost $13,000 today and will last 25 years. Painting your house will cost $3,500 today. However, a paint job only lasts 5 years. Additionally, there will be some weather damaged boards that need replacing if you choose to paint. Replacing the boards will cost $1,000, last 5 years as well. If you keep your money in a bank account that earns 10% (EAR), would you prefer to paint or install the siding

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