PLEASE SHOW WORK You are also considering another project which has a physical l

Question

PLEASE SHOW WORK

You are also considering another project which has a physical life of 3 years; that is, the machinery will be totally worn out after 3 years. However, if the project were terminated prior to the end of 3 years, the machinery would have a positive salvage value. Here are the project’s estimated cash flows:

Initial Investment    End-of-Year

And Operating       Net Salvage

Year                          Cash Flows                          Value

0                                 ($8,000)                           $8,000

1                                    3,900                                5,100

2                                    3,000                                2,500

3                                    2,550                                       0

Using the 8% cost of capital, what is the project’s NPV if it is operated for the full 3 years?

Would the NPV change if the company planned to terminate the project at the end of Year 2? At the end of Year 1?

What is the project’s optimal (economic) life?

** Please show all work! Send Excel screenshots w/ calculations **

Explanation / Answer

Solution :

NPV if project is operated for 3 years

year Cashflow Present value factor@ 8% present value of cashflow

0 ($8000) 1.00 ($8000)

1 3900 0.9259 3611

2 3000 0.8573 2572

3 2550 0.7938 2024

NPV = present value of cash inflow - initial investment

= 3611 + 2572 + 2024 - 8000

= $207   

Yes, the NPV will be definitely change is the compay planned to terminate the project at the end of 2 years or 1 years due to change in cashflows

NPV at the end of 2 year = 3611 + 2572 + 2143 (salvage value of 2500 * 0.8573) - 8000

= $326

NPV at the end of 1 year = 3611 + 4722 (salvage value of $ 5100 * 0.9259) - 8000

= $333

From the above calculation it can be seen that highest NPV is $333 which can be earned if the project will be terminated after 1 year, but to know the project's optimal (economic) life we have to calculate Equivalent net present value (EnpV) for each situation, where EPNV = NPV / present value of annuity factor

Present value of annuity factor can be calulated by using formula 1-1/(1+r)n / r

So,

ENPV if project is operated for full 3 years = $207 / 2.577 = $80.325

ENPV if project is terminated after 2 years = $ 326 / 1.7832 = $182.81

ENPV if project is terminated after 1 years = $ 333 / 0.9259 = $ 359.65

The ENPV is highest when the project is termited after 1 year, So project's optimal life is 1 year

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