# Comparing alternatives: Buy a truck vs rent a truck

Date of Exam

Subject

**Problem**

A contractor can buy a dump trucks for P800,000 each (surplus) or rent them for P1,189 per truck per day. The truck has salvage value of P100,000 at the end of its useful life of 5 years. Annual cost of maintenance is P20,000. If money is worth 14% per annum, determine the number of days per year that a truck must be used to warrant the purchase of the truck.

A. 200 | C. 198 |

B. 199 | D. 197 |

**Answer Key**

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[ A ]

**Solution**

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**Purchase a truck**

Annual Cost = Annual interest on investment + Annual operation and maintenance cost + Annual depreciation using sinking fund method

$AC = (FC)i + OM + \dfrac{(FC - SV)i}{(1 + i)^n - 1}$

$AC = (800,000)(0.14) + 20,000 + \dfrac{(800,000 - 100,000)(0.14)}{(1 + 0.14)^5 - 1}$

$AC = \text{P}237,898.48$

**Rent a truck**

Let *N* = the required number of days per year

$\text{Cost of renting} = \text{Annual Cost}$

$1,189N = 237,898.48$

$N = 200 \text{ days}$ ← *answer*

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