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The Speedy-Delivery Company has two options for its delivery truck. The first option is to purchase a new truck for $14,000. The new truck will have a useful life of 6 years and a residual value of $2000. Operating costs for the new truck will be $200. The second option is to overhaul its existing truck. The cost of the overhaul will be $8000. The overhauled truck will have a useful life of 6 years and a residual value of $0. Operating costs for the overhauled truck will be $800. Using Speedy's discount rate of 4%, which option is better and by what amount

Sagot :

Parrain

Answer: Overhauling is a better option as it is cheaper by $1,273

Explanation:

Total cost of the new truck:

= Cost to purchase + Present value of operating costs - Present value of residual value

= 14,000 + (200 * present value of annuity factor, 4%, 6 years) - 2,000 / (1 + 4%)⁶

= 14,000 + (200 * 5.2421) - 1,581

= $13,467

Total cost of Overhauling truck:

= 8,000 + (800 * present value of annuity factor, 4%, 6 years)

= 8,000 + (800 * 5.2421)

= $12,194

Overhauling is a better option as it is cheaper by:

= 13,467 - 12,194

= $1,273

View image Parrain

The better option will be overhauling the truck as it is cheaper by $1,273.

Based on the information given, the total cost of the new truck will be:

= Cost to purchase + Present value of operating costs - Present value of residual value

= 14,000 + (200 × PV of annuity factor, 4%, 6) - 2,000 / (1 + 4%)⁶

= 14,000 + (200 * 5.2421) - 1,581

= $13,467

The total cost of overhauling the truck will be:

= 8,000 + (800 × present value of annuity factor, 4%, 6)

= 8,000 + (800 × 5.2421)

= $12,194

Therefore, the difference between the two options will be:

= $13,467 - $12,194

= $1,273

Therefore, the better option will be overhauling the truck as it is cheaper by $1,273.

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