Question

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

Answer 1

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