Reading 32 - Calculating NPV

CFA Level I Corporate Finance
#1

Hi,

This is a rather long problem, can anyone please help to calculate NPV?

HC Ltd. purchased a machine 4 years ago at a cost of $100,000. The machine had an expected life of 10 years at the time of the purchase and an expected market value of $5,000 at the end of the 10 years. It is being depreciated by the straight-line method toward a salvage value of $25,000; that is, depreciation is $7,500 per year. The machine can be sold now for $25,000. A new machine can be purchased for $150,000 including installation costs. During its 6-year life, it will reduce pre-tax cash operating expenses by $30,000 per year. Sales are not expected to change. At the end of its useful life, this machine is estimated to be worth $50,000. Straight-line depreciation will be used to depreciate the machine to a salvage value of $30,000; that is depreciation is $20,000 per year. The firm’s tax rate is 30%. The appropriate discount rate is 13%.

What is the NPV of the investment?

A. $1,892
B. $2,573
C. $3,290

Correct Answer: C

The initial investment outlay is $111,500. The net operating cash flows are $24,750 (years 1-6) and the total termination cash flow is $33,000 in year 6. The NPV of these cash flows discounted at 13% is $3,290.

#2

You stated the solution here, so why you are asking about how to calculate the NPV? I presume you can punch the numbers into your financial calculator to get the NPV.

Or are you asking about how to calculate the initial outlay, or net operating cash flows, terminal cash flow etc…

#3

I copied the solution and I want to understand how to calculate the initial outlay, net operating cash flows etc…

Much appreciated your help!

#4

For replacements of assets, you will have to compare the cash flows with replacement and cash flows without replacement, then calculate the NPV based on the difference in cash flows.

INITIAL OUTLAY:

With replacement:
Disposal of Old Machine:
Net book value of old machine
= Historical ~cost - Accumulated ~depreciation
= 100,000 - (4 \times 7,500) = 70,000

After-tax ~sales ~proceeds
= Sales ~proceeds - Tax ~rate \times (Sales proceeds - Net book value)
= 25,000 - 30\% \times (25,000 - 70,000)
= 25,000 - (-13,500)
= 38,500

Without replacement:
Initial outlay of old machine = 0 (No changes are made, so no outlay)

Initial outlay of new replacement
= New machine cost - After tax sales proceeds of old machine - Initial outlay of old machine
= 150,000 - 38,500 - 0
= 111,500

AFTER-TAX OPERATING CASH FLOW (Year 1-6)

With replacement:
After-tax operating cash flow (Year 1-6)
= (Incremental sales - Incremental operating expenses - Incremental depreciation) x (1 - Tax rate) + Incremental Depreciation
= (0 - (-30,000) - 20,000) x (1 - 0.30) + 20,000
= 27,000

Without replacement

After-tax operating cash flow (Year 1-6)
= (Incremental sales - Incremental operating expenses - Incremental depreciation) x (1 - Tax rate) + Incremental Depreciation
= (0 - 0 - 7,500) x (1 - 0.30) + 7,500
= 2,250

Difference in after-tax operating cash flow (Year 1-6)
= 27,000 - 2,250
= 24,750

TERMINAL AFTER-TAX CASH FLOW

With replacement:
Terminal after-tax cash flow (Year 6) for selling NEW MACHINE
= Sales proceeds - Tax rate x (Sales proceeds - Net Book Value)
= 50,000 - 30% x (50,000 - 30,000)
= 44,000

Without replacement:
Terminal after-tax cash flow (Year 6) for selling OLD MACHINE
= Sales proceeds - Tax rate x (Sales proceeds - Net Book Value)
= 5,000 - 30% x (5,000 - 25,000)
= 11,000

Different in terminal after-tax cash flow in Year 6
= 44,000 - 11,000
= 33,000

For the rest, just punch the numbers into your financial calculator and you should get the NPV in option C.

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#5

wow, thanks so much for taking the time to explain the problem. I very much appreciated!

Happy Sunday.

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#7

Could you explain this part please? I think i just got bugged out. I think something went wrong.

截屏2020-07-26 上午1.45.40
截屏2020-07-26 上午1.45.401032×252 15.3 KB

#8

Should be:

= 25,000 - 30 \% \times (25,000 - 70,000)
= 25,000 - (-13,500)
= 38,500

#9

Thank you very much! Appreciated your effort!

1 Like