- CFA Exams
- CFA Level I Exam
- Topic 3. Corporate Issuers
- Learning Module 5. Capital Investments and Capital Allocation
- Subject 2. Capital Allocation

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**CFA Practice Question**

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%.

B. $2,573

C. $3,290

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.

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**User Contributed Comments**
41

User |
Comment |
---|---|

kalps |
How did they get £111,500 ??? |

Gina |
could sb explain this one in detail, please? also, if you did this with a calculator. |

fels |
150'000 - (25'000 + (45'000 * 0.3)) = 111'500 |

sekib |
for further info: the 45'000 came from 100'000 - 30'000 (accum depreciation) - 25'000 (salvage value) = 45'000 |

constant |
Year 6 CF is $38750 (14000 after tax gain on sale on the new machine and 24750 saving from operation and tas shild from depreciation) where 33000 came from? |

jaan |
This question is not yet resolved can any one solve this problem, the way BA II plus works? |

examinee |
I think it should be 24750 + (50000 - 5000) - ((50000-30000) + (25000 - 5000))*0.3 = 57750. Here 50000-5000 is the net cash flow from selling asset at the end and the second term is tax dissaving which will happen because book value is lower than market value. |

synner |
Should refer to los e under replacement project. Initial Investment Outlay = Price of new machine - Cash flow from selling old machine. Cash flow from selling old machine = salvage value - (salvage value - book value)*tax rate salvage value = 25,000, book value = 70,000 from 100,000 - 30,000 (depreciation in 4 years), and tax rate = .3, so cash flow from selling old machine = 25,000 - (25,000-70,000)*.3 = 38,500. So Initial Investment Outlay = 111,500 For Operating Cash Flow from year 1-5 OCF = (Revenue - cost)(1-t) + Depreciation*t Reduced cost is 30,000 Increased depreciation is 20,000-7500. so OCF = 30,000*.7 + (20,000-7500)*.3 = 24750 In terminal period, year 6 cash flow + sell new machine. 30,000 - (30,000 - 50,000)*.3 = 36000 36000+24,750 = 60750. In TI BAII, CF0 = -111,500 C01 = 24750 F01 = 5 C02 = 60750 I = 13 CPT NPV = 4731 Different from the answer given above. I don't agree with termination cash flow being 33,000. |

synner |
btw, if Termination cash flow = 33,000+24,750 = 57750, the NPV = 3290! |

AdriGul |
FInal Cash flow is determined as follows: Calculation of CF from machine sale Sale of New Machine: 50,000 Tax Cost of Gain (a): <6,000> Calculation of Opportunity Cost (Old machine that could have been sold) Lost Sale of old machine: <5,000> Lost tax shelter on old machine (b): <6,000> Net Final Cash FLow: 33,000 (50,000 - 6,000 - 5,000 - 6,000 = 33,000 Plus operating cash flow: 24,750 Equals = 57,750 (a) Gain of 20,000 (sold for 50,000 and book value of 30,000) times 30% tax rate (b) Loss of 20,000 (sold for 5,000 and book value of 25,000) times 30% tax rate |

stefdunk |
in the terminal year cashflow, don't forget the opportunity cost of the salvage value of the original equipment. 5000 salvage value. 25000 book value, for a tax savings of 6000. new equipment salvage value 50000, book value 30000 50,000 - (50,000 - 30,000)x0.3 = 44,000 5,000 - (5,000 - 25,000)x0.3 = 11,000 44,000 - 11,000 = 33,000 |

zwer |
*-*-*-*-*-* Termination cashflow again. So we compute the "delta" for each year (e.g. difference between depreciation for new and old machine). Now, why don't we compute the difference in the cashflow from selling the new machine to the cashflow from selling the old one? Even if so, we are not given the value that the old machine can be sold for at the end of its life if we choose not to go ahead with the project! |

PhiWong |
The terminal value I got is: 68,750.00. 50,000 cash received minius 6,000 (50,000 -30,000) x0.3 taxes paid plus extra cash flow of 24,750.00. The NPV would be 8,573.37. |

Rotigga |
Cash flow from selling old machine = salvage value - (salvage value - book value) * tax rate = $25,000 - [$25,000 - ($100,000 - 4*$7,500)]*0.3 = $25,000 - ($25,000 - $70,000)*0.3 = $38,500 So, Initial cost = $150,000 - $38,500 = $111,500 OCF = EBITDA - Taxes = $30,000 - X * (0.3) = $24,750 X = (30k - $24,750)/0.3 = $17,500 is taxable income Where did the extra $7,500 come from in taxable income? OHHH, to offset the old depreciation OCF = EBITDA - Taxes = $30,000 - ($30,000 - $20,000 + $7,500) * (0.3) = $24,750 Total cash in at year 6 = $33,000 + $24,750 = $57,750 Now that we have those calculations done, use the HP-12C: 111500 [CHS][g][CFo] 24750 [g][CFj] 5 [g][Nj] 57750 [g][CFj] 13 [i] [f][NPV] = $3,289.87 That was a long problem! |

ehc0791 |
Agree with AdviGul 2004-11-15. TNOCF_new = 50000 - (50000-30000)*0.3 TNOCF_old = 5000 - (5000 - 25000)*0.3 new - old = 33000 |

ssradja |
Stefdunk did a good job to explain terminal value cash flows. Thanks! |

Narsi |
Initial cash flow calculations include cash from selling the old asset. When it is the case how can we take into account opportunity cost of selling the old machine in year 10. It amounts to selling the old machine twice. |

vi2009 |
Accumulated Depreciation for old machine = 4*7,500 = $30,000 Book value = 100,000-30,000 = 70,000 Selling price = $25,000 Loss=70,000-25,000=(45,000) Tax credit = 0.3*45,000 = 13,500 CF from sale of old equipment = 25,000+13,500=38,500 Nett $ need to put up for new machine = 150,000-38,500 = 111,500 |

vi2009 |
CF for YR1 to 6: 30,000 * (1-T) = 21,000 difference in depreciation = 20,000 - 7500 = 12,500 Tax benefit from depreciation = 0.3*12,500 = 3750 Therefore, CF = 21,000 + 3750 = 24,750 Terminal value = Difference in terminal value (New - Old) Old equipment: SV = 25,000; MV = 5,000 therefore tax credit = 20,000*0.3 = 6000. CF = 5000+6000=11,000 new equipment: SV = 30,000; MV = 50,000 therefore tax = 20,000*0.3 = 6000. CF = 50,000-6000 = 44,000 Difference = New = Old = 33,000 CF: Y0 = 111,500 Y1 to 5 = 24,750 Y6 = 24,750 + 33,000 = 57,750 interest = 13% NPV = 3290 |

creativemny |
The old machine is a sunk cost, therefore the loss is not part of initial value. However, the tax savings from the timing of the sale reduces initial cost. |

ptyson |
great question |

miiyeung |
long ass question, better not be on exam... |

lortola |
for me terminal value is 44,000, ie: Mket value = 50,000 bk value (at the end of year 6) 30,000 50,000 - (50,000 - 30,000)x0.3 = 44,000 the old machine had been sold at the beginning of the deal, we don't need to take it into account for the calculation of final CF |

chantal |
accounting losses on the disposition of the asset is not and should not be included in operating cash flows for capital budgeting. A terminal loss of 45000$ will give rise to a tax saving of 13500$ (ie cash inflow) only if it was the LAST asset in ITS class...which it wont since it is being replaced. What am i missing ? |

VenkatB |
thanks stefdunk |

bablig |
Follow Adri Gul. |

REITboy |
Did someone answer Narsi's question? |

Nando1 |
I have the same question as Narsi and Reitboy: why do we double count the selling of the old machine - once upfront and then again at the end? The AnalystNotes for this section say for replacement projects the selling of the old machine should be used to offset the initial investment outlay. Even the example doesn't take into account the old machine during the terminal year CF calc. Is this example wrong or am I missing something? |

DS12 |
I still do not understand where the year six cash flows of 33,000 came from |

Paulvw |
Scary, very good question. |

BryonBUI |
Rottiga is right. For DS12 question Terminal cash flow = TNOCF = Delta Salvage - tax(Delta Salvage - Delta Book value)=(50,000-5,000)-0.3 x ((50,000 - 5,000) - (30,000 - 25,000)) = 33,000. Since this is replacement project, all CF are incremental. There is tax saving in the initial outlay assuming the lost can be used to offset the gain somewhere else within the company |

NIKKIZ |
First calculate the cash flows as if the replacement project was never undertaken: 5 cashflows of 2.25k (equivalent to the annual tax benefit from the old machine 7.5k x 30% tax) and a final terminal value of 13.25k (tax benefit of 2.25k + 5k cash sale + 6k tax credit due to loss on sale vs book value). Next calculate the cashflows from the replacement project: Cash Outlay = -150k + 25k cash inflow from sale of machine + 13.5k tax credit from loss on sale of machine Annual cashflows are 27k per year 30k - (30-20*30%) Terminal year cashflow is 27k + 50k cash inflow - 6k taxes due on sale = 71k terminal value. Finally - take the differences on a year-by-year basis; CF0 -111.5k Yrs 1 to year 5 = 2.25k 27k = 24.75k difference Yr 6 = 13.25k and 71k = 57.75k These are your inputs into the BA2 calculator. |

johntan1979 |
If I see this kind of question in the exam, I will skip it and guess the answer because: 1. Reading and understanding the whole damn question alone takes more than 1 minute 2. I might not even know how to answer it after wasting my time reading it. 3. Even if I get it, I might get it wrong. |

gulfa99 |
U don't have sufficient time to solve these types of question during exam.. I didn't survive the last and fist attempt and never came across such type of questions |

SKIA |
I agree with Johntan1979 and Gulfa99 -- Skip it, skip it, it's the very best thing of all, there's a counter on this clock! (hopefully someone else gets the skip it theme song in their head) |

daverco |
The formula in the book adds the two terms that must be subtracted from the new-machine cost. As in: salvage + T (salvage - book). In this example they are subtracted, and it is correct to do it this way. Is this because book value is greater than salvage value in this case? |

daverco |
Never mind, I was confused. It's simple match logic. |

ashish100 |
lmao johntan1979 this guy's logic is pretty funny but realistic |

kseeba17 |
way too much effort for a single mark. Waste my time 2017, ill take the L. |

MathLoser |
*The final boss of this level appears* |

khalifa92 |
Good practice question Initial outlay = FCinv + NWCinv - Salt + T(Salt-BVt) Initial outlay = 150 + 0 - 25 + 0.3 (25-70) Initial outlay = 111.5 CF1-6= (S-C-D)(1-t)+D CF1-6= [(0-0)-(-30-0)-(20-7.5)](1-0.3)+(20-7.5) CF1-6= 24.75 TNOCF = Salt + NWCinv - T(Salt-BVt) TNOCF= (50-5) + (0-0) - [ 0.3(50-30) - 0.3(5-25)] TNOCF= 45 - 0 - [ 6 - (-6)] TNOCF= 33 |