Question

In: Economics

A new cement mixing truck can be purchased for $100,000 and will have a salvage value...

A new cement mixing truck can be purchased for $100,000 and will have a salvage value of $50,000 at the end of 5 years. The cost of concrete mix for the truck is $100 per cubic yard. Alternatively, the construction company can pay $105 per cubic yard to have concrete delivered by a third party.

Assume the construction company can order the concrete mix or delivery for the whole year on their account, and pay the full balance at the end of each year. At an interest rate of 10% per year, the minimum cubic yards of concrete that must be used each year to justify the purchase of a truck is closest to:

1,050
2,650
3,650
5,550

The answer is C. Why?

I need an explanation.

Expert Solution

Let the number of cubic yards of concrete bought in a year be x

The interest rate is 10%, therefore the discount factor= 1/(1+0.1)

The total present value Of costs buying the truck and the concrete mix- the salvage value=100,000+100x/(1+0.1)+100x/(1+0.1)²+100x/(1+0.1)³+100x/(1+0.1)⁴+100x/(1+0.1)⁵-50,000/(1+0.1)⁵

Similarly, the total present value of buying the concrete mix

=105x/(1+0.1)+105x/(1+0.1)²+105x/(1+0.1)³+105x/(1+0.1)⁴+105x/(1+0.1)⁵

At minimum number of cubic yards of concrete For it to be worthwhile to buy a truck, both should be equal

100,000+100x/(1+0.1)+100x/(1+0.1)²+100x/(1+0.1)³+100x/(1+0.1)⁴+100x/(1+0.1)⁵-50,000/(1+0.1)⁵=105x/(1+0.1)+105x/(1+0.1)²+105x/(1+0.1)³+105x/(1+0.1)⁴+105x/(1+0.1)⁵

5x/(1+0.1)+5x/(1+0.1)²+5x/(1+0.1)³+5x/(1+0.1)⁴+5x/(1+0.1)⁵=100,000-50,000/(1+0.1)⁵=68,953.93395

5x(1/(1+0.1)+1/(1+0.1)²+1/(1+0.1)³+1/(1+0.1)⁴+1/(1+0.1)⁵=68,953.93395

5x*3.79=68,953.93395

x= 68,953.93395/18.95=3638.73

Therefore the answer is c. 3650 (perhaps after rounding off everywhere)

Hope it helps. Do ask for any clarifications required.

Rahul Sunny answered 1 month ago

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