Question

The US Post Office is considering outsourcing their overnight priority mail service out of their Miami office region. However, the number of letters that delivered each year varies. The outsources service would cost $2.50 per letter. If the post office is to continue to deliver the service, it must upgrade its current equipment at a cost of $50,000 and it would cost them $1.00 per letter for the US Post Office to provide the service. The useful life of the equipment is 5 years and the outcome agreement would be for 5 years. The salvage value of the equipment would be $10,000 at the end of 5 years. How many letters must be delivered overnight priority annually to make it immaterial as to whether they should outsource the service or continue doing it themselves? (MARR is 10%)

Answer 1

Answer:

Let the number of letters to be delivered every year for 5 years be x

Given MARR = 0.1

Let us now find the NPV of each outcome

If the service is outsourced,

NPV₁ = -2.5x - 2.5x/1.1 - 2.5x/1.1² - 2.5x/1.1³ - 2.5x/1.1⁴

If the service is not outsourced,

NPV₂ = -50000 - x - x/1.1 - x/1.1² - x/1.1³ - x/1.1⁴ + 10000/1.1⁴

To make it immaterial to outsource or do it on their own, cost of outsourcing = cost of doing it on own => NPV₁ = NPV₂

=> -2.5x - 2.5x/1.1 - 2.5x/1.1² - 2.5x/1.1³ - 2.5x/1.1⁴ = -50000 - x - x/1.1 - x/1.1² - x/1.1³ - x/1.1⁴ + 10000/1.1⁴

=> x = 43169.865/6.254 = 6902.76

Hence, Annual Delivery = 6903