Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company's current truck (not the least of which is that it runs). The new truck would cost $54,750. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $7,500. At the end of 8 years, the company will sell the truck for an estimated $27,300. Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company's cost of capital is 8%.

Compute the Net present value and the cash payback period?

Question

Mathematics

Kasey Pearson

7 February, 17:03

Linkin Corporation is considering purchasing a new delivery truck. The truck has many advantages over the company's current truck (not the least of which is that it runs). The new truck would cost $54,750. Because of the increased capacity, reduced maintenance costs, and increased fuel economy, the new truck is expected to generate cost savings of $7,500. At the end of 8 years, the company will sell the truck for an estimated $27,300. Traditionally the company has used a rule of thumb that a proposal should not be accepted unless it has a payback period that is less than 50% of the asset's estimated useful life. Larry Newton, a new manager, has suggested that the company should not rely solely on the payback approach, but should also employ the net present value method when evaluating new projects. The company's cost of capital is 8%.

Compute the Net present value and the cash payback period?

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Answers (1)

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Dante Zhang · Answer 1

Payback is 7.3 years

NPV $3,099

Step-by-step explanation:

The formula for payback period period=initial investment/annual cost savings

The initial investment is the amount of cash outflow that would be required to purchase the new delivery truck, which is $54,750, while on the other hand the annual cost savings is $7,500

cash payback period=$54,750/$7,500=7.3 years

Ordinarily, the expected payback is 1/2 of 8 years=4 years.

The net present is the present worth of the future cost savings as well as the scrap value of the truck in year 8, calculated by multiplying the cash flows with the discounted factors for relevant years as below:

Years cash flow DCF at 8% Present values

0 - $54,750 1 - $54,750

1-7 years $7500 5.2064 $39,048

8 $34,800 0.54027 $18,801

NPV $3,099

Note that the $34,800 = $7500+$27300

The year 1-7 factor is annuity factor for 8% 7 years