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. The cost of painting a house is expected to grow at 5% per year. Additionally, there are some weather damaged boards that will need replacing if you choose to paint. Replacing the boards will cost $2,500 today. The new boards will last 25 years. The boards do not have to be replaced if you choose vinyl siding. If you keep your money in a bank account that earns 10% (EAR), would you prefer to paint or install the siding? Please ignore aesthetics in this question.

Answer 1

Answer:

To compare 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.

As such you would prefer to install the vinyl siding