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24 August, 15:14

You are considering two home security companies for your new house. The first company offers free installation and equipment, but will charge you $401.00 per year forever. The second company charges $783.00 for installation, but will charge you $204.00 per year forever. Assume that payments are at the END of the year. Your personal interest rate is 5.00% per year, and you want to evaluate each proposal. What is the present value (PV) of the free installation?

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  1. 24 August, 17:53
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    The second option is the cheapest.

    Explanation:

    Giving the following information:

    The first company offers free installation and equipment, but will charge you $401.00 per year forever. The second company charges $783.00 for installation, but will charge you $204.00 per year forever. Assume that payments are at the END of the year. Your personal interest rate is 5.00% per year

    To calculate the present value, we need to use the formula for a perpetual annuity:

    PV = Cf/i

    Cf = cash flow

    i = interest rate

    Option 1:

    PV = 401/0.05 = $8,020

    Option 2:

    PV = 204/0.05 + 783/1.05 = $4,825.71

    The second option is the cheapest.
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