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Math Help - To buy or not to buy?

  1. #1
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    To buy or not to buy?

    Chaotic Industries is considering an investment in a fleet of 10 delivery vans to take its products to customers. The vans will cost $15,000 each to buy, payable immediately. The annual maintenance and operating costs are expected to total $20,000 for each van, including the driver’s salary. The vans are expected to operate successfully for six years, at the end of which period they will all be sold, with disposal proceeds expected to be $3,000 per van. At present, the business uses a commercial carrier for all of its deliveries. It is expected that this carrier will charge a total of $230,000 each year for the next five years to undertake the deliveries. The Company’s discount rate is 8%. As the financial manager of Chaotic, would you recommend this investment?

    Im not even sure where to start, although somethin tells me Im missing something. Thanks.

    Ibrox
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  2. #2
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    Quote Originally Posted by ibrox View Post
    Chaotic Industries is considering an investment in a fleet of 10 delivery vans to take its products to customers. The vans will cost $15,000 each to buy, payable immediately. The annual maintenance and operating costs are expected to total $20,000 for each van, including the driver’s salary. The vans are expected to operate successfully for six years, at the end of which period they will all be sold, with disposal proceeds expected to be $3,000 per van. At present, the business uses a commercial carrier for all of its deliveries. It is expected that this carrier will charge a total of $230,000 each year for the next five years to undertake the deliveries. The Company’s discount rate is 8%. As the financial manager of Chaotic, would you recommend this investment?

    Im not even sure where to start, although somethin tells me Im missing something. Thanks.

    Ibrox
    List what you know
    For all vans:

    Initial cost: -$15000*10 = -$150,000
    Maintenance: -$20000 * 10 * 5 =- $1,000,000
    Sell: $3000 * 10 = $30,000
    Savings: $230,000*5 = $1,150,000

    Taking the sum of these gives +$30,000 so it would make sense to invest
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  3. #3
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    You need the Present Value of each alternative.

    150000 + PV of [200000 (n=6) - 30000] = 1,055,671 ****

    PV of 230000 (n=6) = 1,063, 262

    **** take this one: cheaper (not by much!)
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  4. #4
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    ibrox, check the wording of the original problem carefully. According to your posting, the annual cost to Chaotic under the "no buy" decision is $230K for each of the next five years, using the outsourced carrier service. Should that actually be six years (matching the expected service life of the proposed trucks--pretty typical for a question like this)?

    By assuming that it's supposed to be $230K for the next six years, then the present value of the "purchase" decision is a positive $7,591, just as Wilmer has computed.

    Best regards,
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  5. #5
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    I know, it did look wierd too on my end. It's not due until Friday, so I'll have a chat with my prof and confirm it...
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  6. #6
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    I did check with the prof and it is for five years and not six. However, I think the best approach now would be to take the NPV of each alternative and then do the annual eqiuvelent cost and then base my decision from there.
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  7. #7
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    Ok, I figured it out, can someone check my work?

    Vans - $15,000 each -> 10 vans will be purchased, so $15,000 x 10 = $150,000
    Maintenance cost - $20,000 each -> again for 10 vans it’s $20,000 x 10 = $200,000
    Life of each van = 6 years
    Salvage value = $3,000 x 10 vans = $30,000

    Cost of commercial carrier service = $230,000 each year x 5 years = $1,150,000
    Discount rate – 8%

    For buying the vans

    $324,074.07 = ($150,000 [van cost] + $200,000 [maintenance cost] )/1.08 [discount rate]
    $171,467.76 = $200,000/1.08^2
    $158,766.45 = $200,000/1.08^3
    $147,005.97 = $200,000/1.08^4
    $136,116.64 = $200,000/1.08^5
    +$107,128.84 = $200,000 - $30,000 [salvage value]/1.08^6
    $1,044,559.73 grand total

    For the outsourcing option, we are going to use the following formula to get the answer quicker:

    Annuity present value = dollars per period [C] x (1 – 1/(1+r)^t)/ r
    = $230,000 x (1 – 1/1.08^5)/0.08
    = $230,000 x (0.3194)/0.08
    = $230,000 x 3.9925
    = $918,275



    Now, because of differing services lives, we have to figure out equivalent annual cost:

    NPV of costs = EAC x annuity factor

    Annuity factor simply is: (1 – 1/1+r^t)/r -> which is 3.9927

    $918,275 = 3.9927EAC
    $229,988.48 = EAC

    For the in-house (van) option, it’s

    NPV of costs = EAC x annuity factor

    Annuity factor = 1-1/1+r^t/r
    = (1-1/1+.08^6)/.08
    = 4.6229

    NPV of costs = EAC x annuity factor

    $1,044,559.73 = 4.6229EAC
    $225,953.35 = EAC

    Based on the analysis, we should purchase the vans as it effectively costs $225,953.35 a year against the $229,988.48 for outsourcing.
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  8. #8
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    Quote Originally Posted by ibrox View Post
    For buying the vans
    $324,074.07 = ($150,000 [van cost] + $200,000 [maintenance cost] )/1.08 [discount rate]
    $171,467.76 = $200,000/1.08^2
    $158,766.45 = $200,000/1.08^3
    $147,005.97 = $200,000/1.08^4
    $136,116.64 = $200,000/1.08^5
    +$107,128.84 = $200,000 - $30,000 [salvage value]/1.08^6
    $1,044,559.73 grand total
    You need to start like this:
    150,000 = 150,000 / 1.08^0
    185,185 = 200,000 / 1.08^1
    Your years 2 to 6 are ok.
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