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19 March, 23:32

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

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  1. 20 March, 02:58
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    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
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Home » Business » 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.
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