investment appraisal q&a

Investment Appraisal

PAST EXAM QUESTIONSQuestion 1

Please answer both parts.

Part I

You are the manager of a pharmaceutical company and are considering what type of laptop computers to purchase for your field salespeople. You have two, mutually exclusive, alternatives:

You can buy relatively inexpensive (and less powerful) older machines for about €500 each. These machines will be obsolete in three years and are expected to have an annual maintenance cost of €100.

Alternatively, you can buy newer and more powerful laptops for about €1,000 each. These are expected to last about five years and to have an annual maintenance cost of €50.

If your cost of capital is 10%, which course of action would you choose and why?

(15 marks)

Part II

Eugene Fama and Robert Shiller were awarded the Nobel Economic Laureate (together with Lars Peter Hansen) in 2013. In October that year, The Economist magazine wrote of the two:

In the 1960s, Mr Fama, based at the University of Chicago, showed that predicting how stock prices would change in the short run is extremely difficult. Market prices react surprisingly fast to new pieces of information, he suggested, and stock price movements are unpredictable, following a “random walk” pattern. Mr Shiller, based at Yale University, showed that what is true at very short horizons is not necessarily true over longer periods. Seminal work by Mr Shiller found that while asset prices are meant to be an aggregate of expected changes in pay-offs (like dividends in the case of stocks) dividends vary much less than stock prices. Interestingly, this makes future stock price movements easier to predict. When the price-dividend ratio is high prices tend to fall. Not only does this relationship hold for stocks, but for other assets such as bonds too.

Required

Do you believe that markets are efficient (as Fama argues) or that they can be quite inefficient (as Shiller argues)? Why?

(10 marks)

(Total 25 marks)


Answer 1

Part A

The way to convert the up-front costs into annualized equivalents is to divide the NPVs by:

{1 – (1 / [1+kc] life)} / kc

Annualized cost of inexpensive machines

= - 500 (APV, 10%, 3) - 100

= - 500 / 2.4869 - 100

= - €301

Annualized cost of expensive machines

= - 1,000 (APV, 10%, 5) - 50

= -1,000 / 3.791 - 50

= - €314

I would pick the less expensive machine. They are cheaper on an annual basis.

Part B

Eugene Fama is an advocate of the Efficient Markets Hypothesis (EMH). This argues that financial markets are "informationally efficient". In consequence of this, one cannot consistently achieve returns in excess of average market returns on a risk-adjusted basis, given the information available at the time the investment is made. There are three major versions of the hypothesis: "weak", "semi-strong", and "strong".

1. The weak-form EMH claims that prices on traded assets (e.g., stocks, bonds, or property) already reflect all past publicly available information.

2. The semi-strong-form EMH claims both that prices reflect all publicly available information and that prices instantly change to reflect new public information.

3. The strong-form EMH additionally claims that prices instantly reflect even hidden or "insider" information.

Belief in strong-form market efficiency is contradicted by legislation which penalises trading while using insider information across the developed world. So I don’t believe in the strong-form EMH. And several trends appear to contradict the semi-strong-form of the EMH. It has been found that there are several asset trading strategies which appear to outperform just a risk-adjusted form of the market return:

Investments in stocks with low price to book value ratios appear to outperform the market.

Investments in stocks with low price to sales ratios appear to outperform the market.


Shiller has found that the market over-reacts to economic news and factors and that the extent of share price volatility is not justified by the variation in discounted cash flow estimates of the shares’ underlying value. It was for this work that Shiller received his share of the Novel economics laureate.

Even Fama, together with French, argues (with his three-factor model) that expected asset returns are not simply a function of their non-diversifiable risk (as measured by their beta). Fama believes that (i) small stocks and (ii) stocks with a low price to book value do better than expected. His three-factor model expressly incorporates (other with a revised beta) these latter two factors.

But the simple reality is that – if there is a generally known method to outperform markets – market prices will adapt to incorporate the price signals sent by these methods. Another simple reality is that just because a particular strategy may have outperformed the market in the past does not necessarily mean that it must outperform again in the future. So while there may have been clear price anomalies and resulting trading opportunities in the past that doesn’t mean that, today, there is a proven method to outperform market averages other than by taking on additional risk. At this conceptual level at least, Fama may be right.


Question 2

Answer all three parts of this question.

Part A

Fresnillo plc explores and mines gold and silver in Mexico. The gold production accounts for 55 per cent of the activities of the firm, with the rest of the effort involved in silver mining. Other gold mining firms have an average beta of 0.8 and a debt to equity ratio of 1/3. Silver mining is less risky and the average beta of silver mining firms is 0.6. However, these companies tend to have more debt, with an average debt to equity ratio of ½. Fresnillo has a market capitalization of equity of £11.93 billion and it has no debt.

RequiredDetermine the expected return on the Fresnillo’s shares if the expected return on the FTSE 100 is 12 per cent and the risk free rate is 3 per cent.

(5 marks)

Part B

Fresnillo plc is considering a new three-year expansion project that requires an initial non-current asset investment of £3.9 million. The non-current asset will be depreciated using the 20 per cent reducing-balance method. At the end of three years it will be worthless. The project is estimated to generate £2,650,000 in annual sales, with costs of £840,000. The tax rate is 24% and is paid in the same year in which the tax liability arises.

Required

If you apply the cost of capital estimated in Part A above, what is the Net Present Value (NPV) of this project?

(15 marks)

Part C

Briefly explain four reasons why Net Present Value (NPV) may be superior to Internal Rate of Return (IRR) as an investment appraisal technique.

(5 marks)

(Total 25 marks)


Answer 2

Part A

Beta of Fresnillo plc: 0.55*0.8 + 0.45*0.6 = 0.71Expected Return on Shares: R = RF + β * (RΜ – RF) = 0.03 + 0.71*(0.12 – 0.03) = 0.0939 = 9.39%

Part B

Depreciation Schedule

YearBeginning

Value DepreciationEnding Book

Value

1 £3,900,000.00 £780,000.00 £3,120,000.00

2 £3,120,000.00 £624,000.00 £2,496,000.00

3 £2,496,000.00 £2,496,000.00 £0.00

Operating Cash Flows

Sales Costs Depreciation Profit Before Tax Tax OCF

1 £2,650,000 £840,000 £780,000 £1,030,000 £288,400 £1,521,600

2 £2,650,000 £840,000 £624,000 £1,186,000 £332,080 £1,477,920

3 £2,650,000 £840,000 £2,496,000 -£686,000 -£192,080 £2,002,080

NPV

Year CF DF PV0 -£3,900,000 1.0000 -£3,900,0001 £1,521,600 0.9142 £1,390,9862 £1,477,920 0.8357 £1,235,0823 £2,002,080 0.7640 £1,529,497

NPV £255,565Part C

Reasons why NPV is superior to IRR include:

1. The reinvestment rate assumption implicit in the NPV method (surplus funds generated at intermediate stages of the project are reinvested at a rate of return equal to the cost of capital) is probably more realistic than that implicit in the IRR method (surplus funds


generated at intermediate stages of the project are reinvested at a rate of return equal to the IRR).

2. In the case of mutually exclusive projects where the signals generated by the NPV and IRR methods conflict, the NPV methods offers a true signal while IRR can mislead.

3. The NPV method is fully aligned with measurements of shareholder value in a way that IRR measure are not i.e. the NPV of a project is the precise amount by which it is expected to boost shareholder value.

4. Unlike IRR, NPV never generates multiple answers for a given set of project cash flows.


Question 3

Answer both parts.

Part IYou are the new financial manager of the bed mattress firm, Fairy Tale Lullaby Ltd. The firm has always used payback period and accounting rate of return to appraise new investments. With your trusty copy of “Corporate Finance” to hand, you believe that other methods may be more appropriate for the firm. Write a report to the owners of Fairy Tale Lullaby Ltd that reviews the different methods that can be used in investment appraisal together with their strengths and weaknesses. Comment on any practical issues that Fairy Tale Lullaby may face in implementing these methods.

(15 marks)

Part IIA Solar panel production firm Soleil SA, is considering an investment in new solar production technology. The new investment would require initial funding of €4 million today and further expenditure on manufacture of €1m in each of the years 6 and 7. The net cash inflow for the years 1 to 4 is €2.34 million per year. Some equipment could be sold in the end of year 5 when the production ends and together with the cash flows from operation would produce a net cash flow of €4.85 million.

Evaluate the investment using two investment appraisal criteria. The required rate of return of Soleil SA is 12% and Soleil has been known to use a payback period of 2 years in the past. However, the firm’s managers believe that this payback period may be too short.

(15 marks)

(Total 30 marks)Answer 3Part II

€'000 Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7Investment -€4,000 -€1,000 -€1,000Cash inflow €2,340 €2,340 €2,340 €2,340 €4,850Cash flow -€4,000 €2,340 €2,340 €2,340 €2,340 €4,850 -€1,000 -€1,000Discount rate 1.000 0.893 0.797 0.712 0.636 0.567 0.507 0.452Discounted cash flow -€4,000 €2,089 €1,865 €1,666 €1,487 €2,752 -€507 -€452

NPV €4,900

PAYBACK <2 years


Question 4

Part IWeir Group plc is considering the development of a new slurry pump in its existing products. The pump is expected to improve market share for the company if it is fully integrated into its existing product line-up. With the pace of new technological developments, you expect the slurry pump to be obsolete by the end of five years. The equipment required for the project has no salvage value. The required return for projects of this type is 15 per cent, and the company has a 24 per cent tax rate. Assume that any tax due is paid one year in arrears. Assume 20 per cent reducing balance depreciation with any remaining balance fully written off in the asset’s final year.

Using the Net Present Value method to evaluate it, would you recommend this project?

Pessimistic

25% likely

Expected

50% likely

Optimistic

25% likely

Market size 1,000 1,500 1,700

Market share 15% 20% 25%

Selling price €10,000 €15,000 €20,000

Variable costs per unit 72% 70% 68%

Fixed costs per year €400,000 €450,000 €550,000

Initial investment €2,500,000 €2,500,000 €2,500,000

(32 marks)Part II

Briefly explain four reasons why Net Present Value (NPV) may be superior to Internal Rate of Return (IRR) as an investment appraisal technique.

(8 marks)

(Total 40 marks)

Answer 4

Part IWith a positive expected Net Present Value, I would recommend that Weir Group proceeds with this project.


Probability NPV ENPVExpected 50% €266 €132.9Pessimistic 25% -€2,069 -€517.3Optimistic 25% €3,634 €908.5

€524.1

EXPECTED Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6Investment -€2,500Sales €4,500 €4,500 €4,500 €4,500 €4,500VC -€3,150 -€3,150 -€3,150 -€3,150 -€3,150FC -€450 -€449 -€448 -€447 -€446Tax -€6 -€80 -€128 -€159 -€110WCCash flow -€2,500 €900 €895 €822 €775 €745 -€110PV factor 1 0.870 0.756 0.658 0.572 0.497 0.432PV factor -€2,500 €783 €677 €540 €443 €370 -€48

NPV €266

Sales €4,500 €4,500 €4,500 €4,500 €4,500VC -€3,150 -€3,150 -€3,150 -€3,150 -€3,150FC -€450 -€449 -€448 -€447 -€446Depreciation -€875 -€569 -€370 -€240 -€446Taxable income €25 €332 €532 €663 €458Tax rate 24% 24% 24% 24% 24%Tax charge €6 €80 €128 €159 €110

BOY €2,500 €1,625 €1,056 €687 €446Depreciation 35% -€875 -€569 -€370 -€240 -€446EOY €1,625 €1,056 €687 €446 €0


PESSIMISTIC Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6Investment -€2,500Sales €1,500 €1,500 €1,500 €1,500 €1,500VC -€1,080 -€1,080 -€1,080 -€1,080 -€1,080FC -€400 -€399 -€398 -€397 -€396Tax €205 €131 €83 €52 €101WCCash flow -€2,500 €20 €226 €153 €106 €76 €101PV factor 1 0.870 0.756 0.658 0.572 0.497 0.432PV factor -€2,500 €17 €171 €101 €61 €38 €44

NPV -€2,069

Sales €1,500 €1,500 €1,500 €1,500 €1,500VC -€1,080 -€1,080 -€1,080 -€1,080 -€1,080FC -€400 -€399 -€398 -€397 -€396Depreciation -€875 -€569 -€370 -€240 -€446Taxable income -€855 -€548 -€348 -€217 -€422Tax rate 24% 24% 24% 24% 24%Tax charge -€205 -€131 -€83 -€52 -€101



OPTIMISTIC Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Year 6Investment -€2,500Sales €8,500 €8,500 €8,500 €8,500 €8,500VC -€5,780 -€5,780 -€5,780 -€5,780 -€5,780FC -€550 -€549 -€548 -€547 -€546Tax -€311 -€385 -€433 -€464 -€415WCCash flow -€2,500 €2,170 €1,860 €1,787 €1,740 €1,710 -€415PV factor 1 0.870 0.756 0.658 0.572 0.497 0.432PV factor -€2,500 €1,887 €1,406 €1,175 €995 €850 -€179

NPV €3,634

Sales €8,500 €8,500 €8,500 €8,500 €8,500VC -€5,780 -€5,780 -€5,780 -€5,780 -€5,780FC -€550 -€549 -€548 -€547 -€546Depreciation -€875 -€569 -€370 -€240 -€446Taxable income €1,295 €1,602 €1,802 €1,933 €1,728Tax rate 24% 24% 24% 24% 24%Tax charge €311 €385 €433 €464 €415


Part II

Reasons why NPV is superior to IRR include:

1. The reinvestment rate assumption implicit in the NPV method (surplus funds generated at intermediate stages of the project are reinvested at a rate of return equal to the cost of capital) is probably more realistic than that implicit in the IRR method (surplus funds generated at intermediate stages of the project are reinvested at a rate of return equal to the IRR).

2. In the case of mutually exclusive projects where the signals generated by the NPV and IRR methods conflict, the NPV methods offers a true signal while IRR can mislead.

3. The NPV method is fully aligned with measurements of shareholder value in a way that IRR measure are not i.e. the NPV of a project is the precise amount by which it is expected to boost shareholder value.

4. Unlike IRR, NPV never generates multiple answers for a given set of project cash flows.


BASIC12. Relevant Cash Flows [LO1] Parker & Stone NV is looking at setting up a new

manufacturing plant in Rotterdam to produce garden tools. The company bought some land six years ago for €6 million in anticipation of using it as a warehouse and distribution site, but the company has since decided to rent these facilities from a competitor instead. If the land were sold today, the company would net €6.4 million. The company wants to build its new manufacturing plant on this land; the plant will cost €14.2 million to build, and the site requires €890,000 worth of grading before it is suitable for construction. What is the proper cash flow amount to use as the initial investment in non-current assets when evaluating this project? Why? Answer: €21,490,000

Explanation:The €6 million acquisition cost of the land six years ago is a sunk cost. The €6.4 million current after-tax value of the land is an opportunity cost if the land is used rather than sold off. The €14.2 million cash outlay and €890,000 grading expenses are the initial non-current asset investments needed to get the project going. Therefore, the proper year zero cash flow to use in evaluating this project is

€6,400,000 + €14,200,000 + €890,000 = €21,490,000

13. Relevant Cash Flows [LO1] Winnebagel plc. currently sells 30,000 mobile caravans per year at £53,000 each, and 12,000 luxury stationary caravans per year at £91,000 each. The company wants to introduce a new caravanette to fill out its product line; it hopes to sell 19,000 of these caravanettes per year at £13,000 each. An independent consultant has determined that if Winnebagel introduces the new caravanettes, it should boost the sales of its existing luxury stationary caravans by 4,500 units per year, and reduce the sales of its mobile caravans by 900 units per year. What is the amount to use as the annual sales figure when evaluating this project? Why?

Answer: Sales due solely to the new product line are:

19,000(£13,000) = £247,000,000

Increased sales of the caravan line occur because of the new product line introduction; thus:

4,500(£91,000) = £409,500,000

in new sales is relevant. Erosion of luxury caravan sales is also due to the new caravanettes; thus:

900(£53,000) = £47,700,000 loss in sales

is relevant. The net annual sales figure to use in evaluating the new line is thus:

£247,000,000 + £409,500,000 – £47,700,000 = £608,800,000


14. Calculating Projected Net Income [LO1] A proposed new investment has projected sales of £830,000. Variable costs are 60 per cent of sales, and fixed costs are £181,000; depreciation is £77,000. Prepare a pro forma income statement assuming a tax rate of 28 per cent. What is the projected net income?

Answer: We need to construct a basic income statement. The income statement is:

Sales £ 830,000Variable costs 498,000Fixed costs 181,000Depreciation 77,000 EBT £ 74,000Taxes@28% 20,720 Net income £ 53,280


15. Calculating OCF [LO1] Consider the following income statement:

Sales (£) 1,824,500Costs (£) 838,900Depreciation (£) 226,500Profit before taxes (£) ?

________

Taxes (28%) (£) ?________

Net income (£) ?________

Fill in the missing numbers and then calculate the OCF. What is the depreciation tax shield?

Answer: To find the OCF, we need to complete the income statement as follows:

Sales £1,824,500Costs 838,900 Depreciation 226,500Profit before Taxes £759,100Taxes@28% 212,548Net income £546,552

The OCF for the company is:

OCF = Profit Before Taxes + Depreciation – TaxesOCF = £759,100 + 226,500 – 212,548 OCF = £773,052

The depreciation tax shield is the depreciation times the tax rate, so:

Depreciation tax shield = tcDepreciationDepreciation tax shield = .28(£226,500) Depreciation tax shield = £63,420

The depreciation tax shield shows us the increase in OCF by being able to expense depreciation.


16. OCF from Several Approaches [LO1] A proposed new project has projected sales of NKr108,000, costs of NKr51,000, and depreciation of NKr6,800. The tax rate is 35 per cent. Calculate operating cash flow using the four different approaches described in the chapter, and verify that the answer is the same in each case.

Answer: To calculate the OCF, we first need to calculate net income. The income statement is:

Sales Nkr 108,000Variable costs 51,000Depreciation 6,800 EBT Nkr 50,200Taxes@35% 17,570 Net income Nkr 32,630

Using the most common financial calculation for OCF, we get:

OCF = EBT + Depreciation – Taxes OCF = Nkr50,200 + Nkr 6,800 – Nkr 17,570 OCF = Nkr39,430

The top-down approach to calculating OCF yields:

OCF = Sales – Costs – Taxes OCF = Nkr108,000 – Nkr 51,000 – Nkr 17,570 OCF = Nkr39,430

The tax-shield approach is:

OCF = (Sales – Costs)(1 – tC) + (tCDepreciation) OCF = (Nkr108,000 – Nkr 51,000)(1 – .35) + .35(Nkr 6,800) OCF = Nkr39,430

And the bottom-up approach is:

OCF = Net income + Depreciation OCF = Nkr32,630 + Nkr 6,800 OCF = Nkr39,430

All four methods of calculating OCF should always give the same answer.


17. alculating Depreciation [LO1] A piece of newly purchased industrial equipment costs €1,080,000, and is depreciated using 20 per cent reducing-balance. Calculate the annual depreciation allowances and end-of-the-year book values for this equipment.Answer: The ending book value for any year is the beginning book value minus the depreciation for the year. Remember, to find the amount of depreciation for any year, you multiply the beginning book value times the depreciation percentage for the year. The depreciation schedule for this asset for the first ten years is given below. All further years after year 10 follow the same formula:

Year Beginning Value Depreciation Ending Book Value1 €1,080,000.00 €216,000.00 €864,000.002 €864,000.00 €172,800.00 €691,200.003 €691,200.00 €138,240.00 €552,960.004 €552,960.00 €110,592.00 €442,368.005 €442,368.00 €88,473.60 €353,894.406 €353,894.40 €70,778.88 €283,115.527 €283,115.52 €56,623.10 €226,492.428 €226,492.42 €45,298.48 €181,193.939 €181,193.93 €36,238.79 €144,955.1510 €144,955.15 €28,991.03 €115,964.12

18. Calculating Salvage Value [LO1] Consider an asset that costs €548,000 and is depreciated using 20 per cent reducing-balance. The asset is to be used in a five-year project; at the end of the project, the asset can be sold for €105,000. If the relevant tax rate is 35 per cent, what is the after-tax cash flow from the sale of this asset?Answer: We want to find the BV of the asset after 5 years. With 20 per cent reducing balance depreciation, the depreciation schedule and ending book values each year will be:

Year Beginning Value Depreciation Ending Book Value1 €548,000.00 €109,600.00 €438,400.002 €438,400.00 €87,680.00 €350,720.003 €350,720.00 €70,144.00 €280,576.004 €280,576.00 €56,115.20 €224,460.805 €224,460.80 €44,892.16 €179,568.64

The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured.

After-tax salvage value = €105,000 + (€179,568.64– 105,000)(0.35) After-tax salvage value = €131,099.02

To find the taxes on salvage value, remember to use the equation:

Taxes on salvage value = (BV – MV)tc

This equation will always give the correct sign for a tax inflow (refund) or outflow (payment).


19. Calculating Salvage Value [LO4] An asset used in a four-year project is to be depreciated using the 18 per cent reducing-balance method. The asset has an acquisition cost of £7,900,000 and will be sold for £1,400,000 at the end of the project. If the tax rate is 23 per cent, what is the after-tax salvage value of the asset? Answer: To find the BV at the end of four years, we need to find the accumulated depreciation for the first four years.

Year Beginning Value Depreciation Ending Book Value1 £7,900,000 £1,422,000 £6,478,0002 £6,478,000 £1,166,040 £5,311,9603 £5,311,960 £956,153 £4,355,8074 £4,355,807 £784,045 £3,571,762

The asset is sold at a loss to book value, so the depreciation tax shield of the loss is recaptured.

After-tax salvage value = £1,400,000 + ((£3,571,762 – 1,400,000) (0.23))After-tax salvage value = £1,899,505

20. Calculating Project OCF [LO1] Summer Tyme plc. is considering a new three-year expansion project that requires an initial non-current asset investment of £3.9 million. The non-current asset will be depreciated using the 20 per cent reducing-balance method. At the end of three years it will be worthless. The project is estimated to generate £2,650,000 in annual sales, with costs of £840,000. If the tax rate is 28 per cent, what is the OCF for each year of this project? Answer: First calculate the depreciation schedule.

YearBeginning


Value1 £3,900,000.00 £780,000.00 £3,120,000.002 £3,120,000.00 £624,000.00 £2,496,000.00

3 £2,496,000.00£2,496,000.0

0 £0.00

The operating cash flow for each year is calculated as follows:

Sales Costs Depreciation Profit Before Tax Tax OCF1 £2,650,000 £840,000 £780,000 £1,030,000 £288,400 £1,521,6002 £2,650,000 £840,000 £624,000 £1,186,000 £332,080 £1,477,9203 £2,650,000 £840,000 £2,496,000 -£686,000 -£192,080 £2,002,080


21. Calculating Project NPV [LO1] In the previous problem, suppose the required return on the project is 12 per cent. What is the project’s NPV?

Answer: Since we have the OCF for each year, it is easy to calculate the NPV

Year CF PV(CF)0 -£3,900,000 -£3,900,0001 £1,521,600 £1,358,5712 £1,477,920 £1,178,1893 £2,002,080 £1,425,041

NPV = £61,801

22. Calculating Project Cash Flow from Assets [LO1] In the previous problem, suppose the project requires an initial investment in net working capital of £300,000, and the non-current asset will have a market value of £210,000 at the end of the project. What is the project’s year 0 net cash flow? Year 1? Year 2? Year 3? What is the new NPV?Answer: The cash outflow at the beginning of the project will increase because of the spending on NWC. At the end of the project, the company will recover the NWC, so it will be a cash inflow. The sale of the equipment will result in a cash inflow, but we also must account for the taxes which will be paid on this sale. So, the cash flows for each year of the project will be:

Year Cash Flow0 –£4,200,000 = –£3,900,000 – 300,0001 £1,521,6002 £1,477,9203 £2,453,280 = £2,002,080 + 300,000 + 210,000 + (0 – 210,000)(.28)

And the NPV of the project is:

NPV = £82,956


23. NPV and Straight-Line Depreciation [LO1] In the previous problem, suppose the non-current asset actually is depreciated straight-line to zero over the three years of the project. All the other facts are the same. What is the project’s year 1 net cash flow now? Year 2? Year 3? What is the new NPV?

Answer: First we will calculate the annual depreciation and book value for the equipment necessary for the project. The depreciation amount each year will be the cost of the non-current asset divided by the life of the project (3 years). Note that in the final year we adjust the depreciation amount to reflect the sale of the non-current asset:

Year Beginning Value DepreciationEnding Book

Value1 £3,900,000 £1,300,000 £2,600,0002 £2,600,000 £1,300,000 £1,300,0003 £1,300,000 £1,300,000 £0

We now calculate the operating cash flow (OCF).

Sales Costs Depreciation Profit Before Tax Tax OCF1 £2,650,000 £840,000 £1,300,000 £510,000 £142,800 £1,667,2002 £2,650,000 £840,000 £1,300,000 £510,000 £142,800 £1,667,2003 £2,650,000 £840,000 £1,300,000 £510,000 £142,800 £1,667,200

Finally, the net cash flows must be calculated.

OCF Investment NWC NCF PV(NCF)0 -£3,900,000 -£300,000 -£4,200,000 -£4,200,0001 £1,667,200 £1,667,200 £1,488,5712 £1,667,200 £1,667,200 £1,329,0823 £1,667,200 £300,000 £2,118,400 £1,507,835

NCF3=£1,667,200+£300,000+£210,000+(£0-£210,000)*0.28= £2,118,400

Remember to include the NWC cost in Year 0, and the recovery of the NWC at the end of the project. The NPV of the project with these assumptions is:

NPV = £125,488


24. Project Evaluation [LO1] Dog Up! Franks is looking at a new sausage system with an installed cost of €390,000. This cost will be depreciated straight-line to zero over the project’s five-year life, at the end of which the sausage system can be scrapped for €60,000. The sausage system will save the firm €120,000 per year in pre-tax operating costs, and the system requires an initial investment in net working capital of €28,000. If the tax rate is 30 per cent and the discount rate is 10 per cent, what is the NPV of this project?

Answer: First, we will calculate the annual depreciation of the new equipment. It will be:

Annual depreciation = €390,000/5 Annual depreciation = €78,000

Now, we calculate the after-tax salvage value. The after-tax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:

After-tax salvage value = MV + (BV – MV)tcVery often, the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the after-tax salvage value becomes:

After-tax salvage value = MV + (0 – MV)tc After-tax salvage value = MV(1 – tc)

We will use this equation to find the after-tax salvage value since we know the book value is zero. So, the salvage value is:

After-tax salvage value = €60,000(1 – 0.34) After-tax salvage value = €39,600

Using the tax shield approach, we find the OCF for the project is:

OCF = €120,000(1 – 0.34) + 0.34(€78,000) OCF = €105,720

Now we can find the project NPV. Notice that we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the salvage value.

NPV = –€390,000 – €28,000 + €105,720(PVIFA10%,5) + [(€39,600 + €28,000) / 1.15] NPV = €24,736.26


25. Bid Price [LO3] Blue Operations plc. needs someone to supply it with 150,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid on the contract. It will cost you £780,000 to install the equipment necessary to start production; you’ll depreciate this cost using 18 percent reducing balances over the project’s life. You estimate that in five years this equipment can be salvaged for £50,000. Your fixed production costs will be £240,000 per year, and your variable production costs should be £8.50 per carton. You also need an initial investment in net working capital of £75,000. If your tax rate is 23 percent and you require a 16 percent return on your investment, what bid price should you submit? Answer: For this project, you will need to use a spreadsheet and trial and error or solver. Solver is an exceptionally useful add-on in Excel that allows you to quickly solve these types of problems. The approach in this question is similar to all capital budgeting decisions. First, determine the depreciation schedule, then estimate the operating cash flows, and finally undertake the cash flow analysis.

Determine the depreciation schedule of the investment asset.

Year 1 2 3 4 5

(a) Starting Value £780,000

£639,600

£524,472

£430,067

£352,655

(b) Depreciation 18% £140,400

£115,128

£94,405 £77,412 £302,655

(c) Accumulated Depreciation

£140,400

£255,528

£349,933

£427,345

£730,000

(d) Residual Value £639,600

£524,472

£430,067

£352,655

£50,000

Estimate the operating cash flows and carry out the cash flow analysis. Using Solver, the minimum bid price that is found to make the project feasible is £11.93. The spreadsheet with cash flows pertaining to this amount is presented below. Notice that the IRR is 16.00%, which would be expected given that the discount rate is 16%.

0 (£) 1 (£) 2 (£) 3 (£) 4 (£) 5 (£)Sales 150,000 150,000 150,000 150,000 150,000

Revenues 1,789,108 1,789,108 1,789,108 1,789,108 1,789,108Variable Costs 1,275,000 1,275,000 1,275,000 1,275,000 1,275,000Fixed Costs 240,000 240,000 240,000 240,000 240,000Depreciation 18% 140,400 115,128 94,405 77,412 302,655EBT 133,708 158,980 179,703 196,696 -28,547Tax 30,753 36,565 41,332 45,240 -6,566Net Income 102,955 122,415 138,371 151,456 -21,981Operating Cash Flow 243,355 237,543 232,776 228,868 280,674

- 1 2 3 4 5


Operating Cash Flow 243,355 237,543 232,776 228,868 280,674Net Working Capital -75,000 75,000Investment -780,000 50,000Net Cash Flow -855,000 243,355 237,543 232,776 228,868 405,674PV Cash Flows @ 16% -855,000 209,789 176,533 149,130 126,402 193,147NPV -0IRR 16.00%


26. Project Evaluation [LO1] Your firm is contemplating the purchase of a new £925,000 computer-based order entry system. The system will be depreciated using the 20 per cent reducing-balance method over its five-year life. It will be worth £90,000 at the end of that time. You will save £360,000 before taxes per year in order-processing costs, and you will be able to reduce working capital by £125,000 (this is a onetime reduction). If the tax rate is 28 per cent, what is the IRR?Answer: First, we will calculate the annual depreciation of the new equipment. It will be:

Year 1 2 3 4 5(a) Starting Value £925,000 £740,000 £592,000 £473,600 £378,880(b)

Depreciation 20% 20%*(a) £185,000 £148,000 £118,400 £94,720 £288,880

(c) Accumulated Depreciation £185,000 £333,000 £451,400 £546,120 £835,000(d)

Residual Value (a)-(c) £740,000 £592,000 £473,600 £378,880 £90,000

Notice that in the last year of the project, we calculated the annual depreciation figure as £288,880. This comprises two components. The first component is the 20% depreciation charge on the year 5 starting value of £378,880, which is equal to £75,776. This leaves a residual value of £303,104. The second component is the tax loss that the company experiences from selling the system for £90,000. This is equal to £303,104 - £90,000 = £213,104. Combined, they equal £288,880. Next we calculate the operating cash flows from the project:

1 2 3 4 5Cash Savings 360,000 360,000 360,000 360,000 360,000Depreciation £185,00

0£148,000 £118,400 £94,720 £288,880

Pre-Tax Savings £175,000

£212,000 £241,600 £265,280 £71,120

Tax @ 28% £49,000 £59,360 £67,648 £74,278 £19,914After Tax Savings

£126,000

£152,640 £173,952 £191,002 £51,206

OCF £311,000

£300,640 £292,352 £285,722 £340,086

Now we can find the project IRR. There is an unusual feature that is a part of this project. Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the salvage value at the end of the project (the tax effects have already been incorporated into the analysis). The cash flows arising from the project are:

0 1 2 3 4 5Investment -£925,000 £90,000NWC £125,000 -£125,000OCF £311,000 £300,640 £292,352 £285,722 £340,086Net Cash Flow -£800,000 £311,000 £300,640 £292,352 £285,722 £305,086

2 3 4 5

£311,000 £300,640 £292,352 £285,722 £305,0860 £800,000

(1 ) (1 ) (1 ) (1 ) (1 )NPV

IRR IRR IRR IRR IRR


IRR = 25.49%27. Calculating EAC [LO4] A five-year project has an initial fixed non-current asset

investment of £270,000, an initial NWC investment of £25,000, and an annual OCF of £42,000. The non-current asset is depreciated 20 per cent reducing-balance over the life of the project, and has no salvage value. If the required return is 11 per cent, what is this project’s equivalent annual cost, or EAC?Answer: To calculate the EAC of the project, we first need the NPV of the project.

Sales Investment NWC NCF PV(NCF)0 -£270,000 -£25,000 -£295,000 -£295,0001 -£42,000 -£42,000 -£37,8382 -£42,000 -£42,000 -£34,0883 -£42,000 -£42,000 -£30,7104 -£42,000 -£42,000 -£27,6675 -£42,000 £25,000 -£17,000 -£10,089

NPV = –£435,391.39

Now we can find the EAC of the project. The EAC is:

EAC = –£435,391.39 / (PVIFA11%,5) = –£117,803.98


28. Calculating EAC [LO4] You are evaluating two different silicon wafer milling machines. The Techron I costs €210,000, has a three-year life, and has pre-tax operating costs of €34,000 per year. The Techron II costs €320,000, has a five-year life, and has pre-tax operating costs of €23,000 per year. For both milling machines, use 20 per cent reducing-balance depreciation over the project’s life and assume a salvage value of €20,000. If your tax rate is 35 per cent and your discount rate is 14 per cent, compute the EAC for both machines. Which do you prefer? Why?

Answer: We need to first calculate the NPV of each machine. Focusing on the Techron I first, the depreciation schedule of the machine is given below:

Year 1 2 3(a) Starting Value €210,000 €168,000 €134,400(b) Depreciation 20% 20%*(a) €42,000 €33,600 €114,400(c) Accumulated Depreciation €42,000 €75,600 €190,000(d) Residual Value (a)-(b) €168,000 €134,400 €20,000

We now calculate the income statement for the Techron I1 2 3

Pre-Tax Operating Costs -€ 34,000 -€ 34,000 -€ 34,000Depreciation -€42,000 -€33,600 -€114,400EBT -€76,000 -€67,600 -€148,400Tax -€26,600 -€23,660 -€51,940Net Income -€49,400 -€43,940 -€96,460

This allows us to calculate the Operating Cash Flow of the Techron I.1 2 3

Net Income -€49,400 -€43,940 -€96,460Depreciation €42,000 €33,600 €114,400Operating Cash Flow -€7,400 -€10,340 €17,940

Now we can estimate the NPV of the Techron I.0 1 2 3

Investment -€210,000 €20,000Operating Cash Flow -€7,400 -€10,340 €17,940Cash Flows -€210,000 -€7,400 -€10,340 €37,940PV Cash Flows -€210,000 -€6,491 -€7,956 €25,608

The NPV of Techron I is thus -€198,839.

The equivalent annual cost of the Techron I is

-€198,839 = EAC(PVIFA14%,3)EAC = –€85,646

We now do the same with the Techron II. First the depreciation schedule:

Year 1 2 3 4 5

(a) Starting Value €320,00 €256,00 €204,80 €163,84 €131,07


0 0 0 0 2(b)

Depreciation 20% 20%*(a) €64,000 €51,200 €40,960 €32,768 €111,072


€64,000 €115,200

€156,160

€188,928

€300,000

(d)

Residual Value (a)-(b) €256,000

€204,800

€163,840

€131,072

€20,000

Then the income statement:

1 2 3 4 5Pre-Tax Operating Costs -€ 23,000 -€ 23,000 -€ 23,000 -€ 23,000 -€ 23,000Depreciation -€64,000 -€51,200 -€40,960 -€32,768 -€111,072EBT -€87,000 -€74,200 -€63,960 -€55,768 -€134,072Tax -€30,450 -€25,970 -€22,386 -€19,519 -€46,925Net Income -€56,550 -€48,230 -€41,574 -€36,249 -€87,147

This allows us to calculate operating cash flow:

1 2 3 4 5Net Income -€56,550 -€48,230 -€41,574 -€36,249 -€87,147Depreciation €64,000 €51,200 €40,960 €32,768 €111,072Operating Cash Flow €7,450 €2,970 -€614 -€3,481 €23,925

Now we can estimate the Net Present Value of the Techron II:

0 1 2 3 4 5Investment -€320,000 €20,000Operating Cash Flow €7,450 €2,970 -€614 -€3,481 €23,925Cash Flows -€320,000 €7,450 €2,970 -€614 -€3,481 €43,925PV Cash Flows -€320,000 €6,535 €2,285 -€414 -€2,061 €22,813

The Net Present Value of the Techron II is -€290,842 and the equivalent annual cost is:

-€290,842 = EAC(PVIFA14%,5)EAC = –€84,717

Comparing the EAC of the Techron I (€85,646) with the EAC of the Techron II (€84,717) leads us to go with the Techron II.


29. Calculating a Bid Price [LO3] Alson Enterprises needs someone to supply it with 185,000 cartons of machine screws per year to support its manufacturing needs over the next five years, and you’ve decided to bid for the contract. It will cost you £940,000 to install the equipment necessary to start production; you’ll depreciate this cost straight-line to zero over the project’s life. You estimate that, in five years, this equipment can be salvaged for £70,000. Your fixed production costs will be £305,000 per year, and your variable production costs should be £9.25 per carton. You also need an initial investment in net working capital of £75,000. If your tax rate is 23 per cent and you require a 12 per cent return on your investment, what bid price should you submit?

Answer:

To find the bid price, we need to calculate all other cash flows for the project, and then solve for the bid price. The after-tax salvage value of the equipment is:After-tax salvage value = £70,000 (1 – 0.23) = £53,900Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the NPV of the project is:NPV = 0 = –£940,000 – £75,000 + £OCF(PVIFA12%,5) + [(£75,000 + £53,900 ) / 1.125]Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:OCF = £941,858.68 / PVIFA12%,5 = £261,280.76The easiest way to calculate the bid price is the tax shield approach, so:OCF = £261,280.76 = [(P – v)Q – FC ](1 – tc) + tcD£261,280.76 = [(P – £9.25)(185,000) – £305,000 ](1 – 0.23) + 0.23(£940,000/5)P = £9.13


INTERMEDIATE 30. Cost-Cutting Proposals [LO2] Geary Machine Shop is considering a four-year

project to improve its production efficiency. Buying a new machine press for £560,000 is estimated to result in £210,000 in annual pretax cost savings. The press is depreciated using the 20 per cent reducing-balance method, and it will have a salvage value at the end of the project of £80,000. The press also requires an initial investment in spare parts inventory of £20,000, along with an additional £3,000 in inventory for each succeeding year of the project. If the shop’s tax rate is 28 per cent and its discount rate is 9 per cent, should the company buy and install the machine press?

Answer: First, we will calculate the depreciation each year, which will be:

Year Beginning Value DepreciationEnding Book

Value1 £560,000.00 £112,000.00 £448,000.002 £448,000.00 £89,600.00 £358,400.003 £358,400.00 £71,680.00 £286,720.004 £286,720.00 £206,720.00 £80,000.00

So, the OCF for each year will be:

Year SavingsDepreciatio

n Profit before Tax Tax OCF

1 £210,000 £112,000.00 £98,000.00 £27,440.00£182,560.0

0

2 £210,000 £89,600.00 £120,400.00 £33,712.00£176,288.0

0

3 £210,000 £71,680.00 £138,320.00 £38,729.60£171,270.4

0

4 £210,000 £206,720.00 £3,280.00 £918.40£209,081.6

0

Now we have all the necessary information to calculate the project NPV. We need to be careful with the NWC in this project. Notice the project requires £20,000 of NWC at the beginning, and £3,000 more in NWC each successive year. We will subtract the £20,000 from the initial cash flow, and subtract £3,000 each year from the OCF to account for this spending. In Year 4, we will add back the total spent on NWC, which is £29,000. The £3,000 spent on NWC capital during Year 4 is irrelevant. Why? Well, during this year the project required an additional £3,000, but we would get the money back immediately. So, the net cash flow for additional NWC would be zero. With all this, the equation for the NPV of the project is:

Year OCF Investment NWC NCF PV(NCF)0 -£560,000 -£20,000 -£580,000 -£580,000.001 £182,560.00 -£3,000 £179,560 £164,733.942 £176,288.00 -£3,000 £173,288 £145,853.04


3 £171,270.40 -£3,000 £168,270 £129,935.624 £209,081.60 £80,000 £29,000 £318,082 £225,337.02

NPV = £85,859.64

Yes, the company should buy and install the machine press.

31. Comparing Mutually Exclusive Projects [LO1] Hagar Industrial Systems Company (HISC) is trying to decide between two different conveyor belt systems. System A costs 430,000 Norwegian kroner (NKr), has a four-year life, and requires NKr120,000 in pre-tax annual operating costs. System B costs NKr540,000, has a six-year life, and requires NKr80,000 in pre-tax annual operating costs. Both systems are to be depreciated using the reducing-balance method of 50 per cent per annum, and will have zero salvage value at the end of their life. Whichever system is chosen, it will not be replaced when it wears out. If the tax rate is 28 per cent and the discount rate is 20 per cent, which system should the firm choose?Answer: In this question, the two machines cannot be compared using the equivalent annual cost method because once one machine runs out, it will not be replaced. In addition, with this type of question, it is important to know the relative income streams arising from each conveyor belt. This is because the longer lasting conveyer belt will provide income beyond the lifetime of the conveyor belt that breaks down first. This information isn’t provided by the question and so, it is impossible to compare each machine.


32. Comparing Mutually Exclusive Projects [LO4] Suppose in the previous problem that HISC always needs a conveyor belt system; when one wears out, it must be replaced. Which project should the firm choose now?

Answer: If the conveyor belt can be replaced, we can use the EAC method. We calculate the EAC of System A by first determining its depreciation schedule.

Year 1 2 3 4(a) Starting Value NKr430,000 NKr215,000 NKr107,500 NKr53,750(b) Depreciation 50% 50% NKr215,000 NKr107,500 NKr53,750 NKr53,750(c) Accumulated Depreciation NKr215,000 NKr322,500 NKr376,250 NKr430,000(d) Residual Value (a)-(b) NKr215,000 NKr107,500 NKr53,750 NKr0

We now calculate net income from System A.

1 2 3 4Pre-Tax Operating Costs -Kr 120,000 -Kr120,000 -Kr 120,000 -Kr 120,000Depreciation -Kr215,000 -Kr107,500 -Kr53,750 -Kr53,750EBT -Kr335,000 -Kr227,500 -Kr173,750 -Kr173,750Tax 28% -Kr93,800 -Kr63,700 -Kr48,650 -Kr48,650Net Income -Kr241,200 -Kr163,800 -Kr125,100 -Kr125,100

Operating Cash Flow is:

1 2 3 4Net Income -NKr241,200 -Kr163,800 -Kr125,100 -Kr125,100Depreciation Kr215,000 Kr107,500 Kr53,750 Kr53,750Operating Cash Flow -Kr26,200 -Kr56,300 -Kr71,350 -Kr71,350

PV of cash flows:

0 1 2 3 4Investment -Kr430,000Operating Cash Flow -Kr26,200 -Kr56,300 -Kr71,350 -Kr71,350Cash Flows -Kr430,000 -Kr26,200 -Kr56,300 -Kr71,350 -Kr71,350PV Cash Flows -Kr430,000 -Kr21,833 -Kr39,097 -Kr41,291 -Kr34,409

The NPV of System A is -NKr566,630 and the EAC is: -NKr566,630= EAC(PVIFA20%,4)EAC = –Kr218,883

Now for System B. The same series of tables will be presented.

Depreciation Schedule:

Year 1 2 3 4 5 6Starting Value Kr540,000 Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875Depreciation 50% Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875 Kr16,875Accumulated Depreciation Kr270,000 Kr405,000 Kr472,500 Kr506,250 Kr523,125 Kr540,000


Residual Value Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875 Kr0

Income Statement:1 2 3 4 5 6

Pre-Tax Operating Costs -Kr 80,000 -Kr 80,000 -Kr 80,000 -Kr 80,000 -Kr 80,000 -Kr 80,000Depreciation -Kr270,000 -Kr135,000 -Kr67,500 -Kr33,750 -Kr16,875 -Kr16,875EBT -Kr350,000 -Kr215,000 -Kr147,500 -Kr113,750 -Kr96,875 -Kr96,875Tax -Kr98,000 -Kr60,200 -Kr41,300 -Kr31,850 -Kr27,125 -Kr27,125Net Income -Kr252,000 -Kr154,800 -Kr106,200 -Kr81,900 -Kr69,750 -Kr69,750

Operating Cash Flow:1 2 3 4 5 6

Net Income -Kr252,000 -Kr154,800 -Kr106,200 -Kr81,900 -Kr69,750 -Kr69,750Depreciation Kr270,000 Kr135,000 Kr67,500 Kr33,750 Kr16,875 Kr16,875Operating Cash Flow Kr18,000 -Kr19,800 -Kr38,700 -Kr48,150 -Kr52,875 -Kr52,875

PV of cash flows:0 1 2 3 4 5 6

Investment -Kr540,000Operating

Cash Flow

Kr18,000 -Kr19,800 -Kr38,700 -Kr48,150 -Kr52,875 -Kr52,875

Cash Flows -Kr540,000 Kr18,000 -Kr19,800 -Kr38,700 -Kr48,150 -Kr52,875 -Kr52,875PV Cash

Flows-Kr540,000 Kr15,000 -Kr13,750 -Kr22,396 -Kr23,220 -Kr21,249 -Kr17,708

The Net Present Value of System B is -Kr623,323 and the equivalent annual cost is: -Kr623,323 = EAC(PVIFA20%,6)

EAC = –Kr187,437

The equivalent annual cost of System B is significantly smaller than that of System A and so System B should be chosen.


33. Calculating a Bid Price [LO3] Consider a project to supply 100 million postage stamps per year to the Royal Mail for the next five years. You have an idle parcel of land available that cost £2,400,000 five years ago; if the land were sold today, it would net you £2,700,000 after tax. In five years the land can be sold for £3,200,000 after tax. You will need to install £4.1 million in new manufacturing plant and equipment to actually produce the stamps: this plant and equipment will be depreciated straight-line to zero over the project’s five-year life. The equipment can be sold for £540,000 at the end of the project. You will also need £600,000 in initial net working capital for the project, and an additional investment of £50,000 in every year thereafter. Your production costs are 0.5 pence per stamp, and you have fixed costs of £950,000 per year. If your tax rate is 34 per cent and your required return on this project is 12 per cent, what bid price should you submit on the contract?Answer: To find the bid price, we need to calculate all other cash flows for the project, and then solve for the bid price. The after-tax salvage value of the equipment is:

After-tax salvage value = £540,000(1 – 0.34) After-tax salvage value = £356,400

Now we can solve for the necessary OCF that will give the project a zero NPV. The current after-tax value of the land is an opportunity cost, but we also need to include the after-tax value of the land in five years since we can sell the land at that time. The equation for the NPV of the project is:

NPV = 0 = –£4,100,000 – 2,700,000 – 600,000 + OCF(PVIFA12%,5) – £50,000(PVIFA12%,4) + {(£356,400 + 600,000 + 4(50,000) + 3,200,000] / 1.125}

Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:

OCF = £5,079,929.11 / PVIFA12%,5 OCF = £1,409,221.77

The easiest way to calculate the bid price is the tax shield approach, so:

OCF = £1,409,221.77 = [(P – v)Q – FC ](1 – tC) + tcD£1,409,221.77 = [(P – £0.005)(100,000,000) – £950,000](1 – 0.34) + 0.34(£4,100,000/5) P = £0.03163

34. Interpreting a Bid Price [LO3] In the previous problem, suppose you could keep working capital investments down to only £25,000 per year. How would this new information affect your calculated bid price?Answer: At a given price, taking accelerated depreciation compared to straight-line depreciation causes the NPV to be higher; similarly, at a given price, lower net working capital investment requirements will cause the NPV to be higher. Thus, NPV would be zero at a lower price in this situation. In the case of a bid price, you could submit a lower price and still break-even, or submit the higher price and make a positive NPV.


35. Comparing Mutually Exclusive Projects [LO4] Vandalay Industries is considering the purchase of a new machine for the production of latex. Machine A costs £2,900,000 and will last for six years. Variable costs are 35 per cent of sales, and fixed costs are £170,000 per year. Machine B costs £5,100,000 and will last for nine years. Variable costs for this machine are 30 per cent of sales, and fixed costs are £130,000 per year. The sales for each machine will be £10 million per year. The required return is 10 per cent, and the tax rate is 35 per cent. Both machines will be depreciated on a straight-line basis. If the company plans to replace the machine when it wears out on a perpetual basis, which machine should you choose?

Answer: Since we need to calculate the EAC for each machine, sales are irrelevant. EAC only uses the costs of operating the equipment, not the sales. Using the bottom up approach, or net income plus depreciation, method to calculate OCF, we get:

Machine A Machine BVariable costs –£3,500,000 –£3,000,000Fixed costs –170,000 –130,000Depreciation –483,333 –566,667EBT –£4,153,333 –£3,696,667Tax 1,453,667 1,293,833Net income –£2,699,667 –£2,402,833+ Depreciation 483,333 566,667OCF –£2,216,333 –£1,836,167

The NPV and EAC for Machine A is:

NPVA = –£2,900,000 – £2,216,333(PVIFA10%,6) NPVA = –£12,552,709.46

EACA = – £12,552.709.46 / (PVIFA10%,6) EACA = –£2,882,194.74

And the NPV and EAC for Machine B is:

NPVB = –£5,100,000 – 1,836,167(PVIFA10%,9) NPVB = –£15,674,527.56

EACB = – £15,674,527.56 / (PVIFA10%,9) EACB = –£2,721,733.42

You should choose Machine B since it has smaller EAC (absolute value).


36. Equivalent Annual Cost [LO4] Compact fluorescent lamps (CFLs) have become more popular in recent years, but do they make financial sense? Suppose a typical 60 watt incandescent light bulb costs £0.50 and lasts 1,000 hours. A 15 watt CFL, which provides the same light, costs £3.50 and lasts for 12,000 hours. A kilowatt-hour of electricity costs £0.101, which is about the national average. A kilowatt-hour is 1,000 watts for 1 hour. If you require a 10 per cent return and use a light fixture for 500 hours per year, what is the equivalent annual cost of each light bulb?Answer: A kilowatt hour is 1,000 watts for 1 hour. A 60-watt bulb burning for 500 hours per year uses

30,000 watt hours, or 30 kilowatt hours. Since the cost of a kilowatt hour is £0.101, the cost per year is:

Cost per year = 30(£0.101)Cost per year = £3.03

The 60-watt bulb will last for 1,000 hours, which is 2 years of use at 500 hours per year. So, the NPV of the 60-watt bulb is:

NPV = –£0.50 – £3.03(PVIFA10%,2)NPV = –£5.76

And the EAC is:

EAC = –£5.83 / (PVIFA10%,2) EAC = –£3.32

Now we can find the EAC for the 15-watt CFL. A 15-watt bulb burning for 500 hours per year uses 7,500 watts, or 7.5 kilowatts. And, since the cost of a kilowatt hour is £0.101, the cost per year is:

Cost per year = 7.5(£0.101)Cost per year = £0.7575

The 15-watt CFL will last for 12,000 hours, which is 24 years of use at 500 hours per year. So, the NPV of the CFL is:

NPV = –£3.50 – £0.7575(PVIFA10%,24)NPV = –£10.31

And the EAC is:

EAC = –£10.85 / (PVIFA10%,24) EAC = –£1.15

Thus, the CFL is much cheaper. But see our next two questions.


37. Break-Even Cost [LO2] The previous problem suggests that using CFLs instead of incandescent bulbs is a no-brainer. However, electricity costs actually vary quite a bit, depending on location and user type (you can get information on your rates from your local power company). An industrial user in the Scottish Highlands might pay £0.04 per kilowatt-hour, whereas a residential user in Essex might pay £0.25. What’s the break-even cost per kilowatt-hour in Problem 36?Answer: To solve the EAC algebraically for each bulb, we can set up the variables as follows:

W = light bulb wattageC = cost per kilowatt hourH = hours burned per yearP = price the light bulb

The number of watts use by the bulb per hour is:

WPH = W / 1,000

And the kilowatt hours used per year is:

KPY = WPH × H

The electricity cost per year is therefore:

ECY = KPY × C

The NPV of the decision to but the light bulb is:

NPV = – P – ECY(PVIFAR%,t)

And the EAC is:

EAC = NPV / (PVIFAR%,t)

Substituting, we get:

EAC = [–P – (W / 1,000 × H × C)PVIFAR%,t] / PFIVAR%,t

We need to set the EAC of the two light bulbs equal to each other and solve for C, the cost per kilowatt hour. Doing so, we find:

[–£0.50 – (60 / 1,000 × 500 × C)PVIFA10%,2] / PVIFA10%,2 = [–£3.50 – (15 / 1,000 × 500 × C)PVIFA10%,24] / PVIFA10%,24

C = £0.004509

So, unless the cost per kilowatt hour is extremely low, it makes sense to use the CFL. But when should you replace the incandescent bulb? See the next question.


38. Break-Even Replacement [LO2] The previous two problems suggest that using CFLs is a good idea from a purely financial perspective unless you live in an area where power is relatively inexpensive, but there is another wrinkle. Suppose you have a residence with a lot of incandescent bulbs that are used on average for 500 hours a year. The average bulb will be about halfway through its life, so it will have 500 hours remaining (and you can’t tell which bulbs are older or newer). At what cost per kilowatt-hour does it make sense to replace your incandescent bulbs today?Answer: We are again solving for the break-even kilowatt hour cost, but now the incandescent bulb has only 500 hours of useful life. In this case, the incandescent bulb has only one year of life left. The break-even electricity cost under these circumstances is:

[–£0.50 – (60 / 1,000 × 500 × C)PVIFA10%,1] / PVIFA10%,1 = [–£3.50 – (15 / 1,000 × 500 × C)PVIFA10%,24] / PVIFA10%,24

C = –£0.007131

Unless the electricity cost is negative (Not very likely!), it does not make financial sense to replace the incandescent bulb until it burns out.


39. Issues in Capital Budgeting [LO1] The debate regarding CFLs versus incandescent bulbs (see Problems 36–38) has even more wrinkles. In no particular order:

• Incandescent bulbs generate a lot more heat than CFLs.• CFL prices will probably decline relative to incandescent bulbs.• CFLs unavoidably contain small amounts of mercury, a significant environmental

hazard, and special precautions must be taken in disposing of burned-out units (and also in cleaning up a broken lamp). Currently, there is no agreed-upon way to recycle a CFL. Incandescent bulbs pose no disposal/breakage hazards.

• Depending on a light’s location (or the number of lights), there can be a non-trivial cost to change bulbs (i.e., labour cost in a business).

• Coal-fired power generation accounts for a substantial portion of the mercury emissions in Europe, though the emissions will drop sharply in the relatively near future.

• Power generation accounts for a substantial portion of CO2 emissions in Europe.• CFLs are more energy and material intensive to manufacture. On-site mercury

contamination and worker safety are issues.• If you install a CFL in a permanent lighting fixture in a building, you will probably

move long before the CFL burns out.• Another lighting technology based on light-emitting diodes (LEDs) exists, and is

improving. LEDs are currently much more expensive than CFLs, but costs are coming down. LEDs last much longer than CFLs, and use even less power. Also, LEDs don’t contain mercury.

Qualitatively, how do these issues affect your position in the CFL versus incandescent light bulb debate? Australia recently proposed banning the sale of incandescent bulbs altogether, as have several European countries. Does your analysis suggest such a move is wise? Are there other regulations, short of an outright ban, that make sense to you?

Answer: The debate between incandescent bulbs and CFLs is not just a financial debate, but an environmental one as well. The numbers below correspond to the numbered items in the question:

1. The extra heat generated by an incandescent bulb is waste, but not necessarily in a heated structure, especially in northern climates.

2. Since CFLs last so long, from a financial viewpoint, it might make sense to wait if prices are declining.

3. Because of the nontrivial health and disposal issues, CFLs are not as attractive as our previous analysis suggests.

4. From a company’s perspective, the cost of replacing working incandescent bulbs may outweigh the financial benefit. However, since CFLs last longer, the cost of replacing the bulbs will be lower in the long run.

5. Because incandescent bulbs use more power, more coal has to be burned, which generates more mercury in the environment, potentially offsetting the mercury concern with CFLs.

6. As in the previous question, if CO2 production is an environmental concern, the lower power consumption from CFLs is a benefit.


7. CFLs require more energy to make, potentially offsetting (at least partially) the energy savings from their use. Worker safety and site contamination are also negatives for CFLs.

8. This fact favors the incandescent bulb because the purchasers will only receive part of the benefit from the CFL.

9. This fact favours waiting for new technology.

While there is always a “best” answer, this question shows that the analysis of the “best” answer is not always easy and may not be possible because of incomplete data. As for how to better legislate the use of CFLs, our analysis suggests that requiring them in new construction might make sense. Rental properties in general should probably be required to use CFLs (why rentals?).

Another piece of legislation that makes sense is requiring the producers of CFLs to supply a disposal kit and proper disposal instructions with each one sold. Finally, we need much better research on the hazards associated with broken bulbs in the home and workplace and proper procedures for dealing with broken bulbs.


40. Replacement Decisions [LO2] Your small remodelling business has two hydrogen-battery/petrol hybrid eco-vehicles. One is a small passenger car used for jobsite visits and for other general business purposes. The other is a heavy truck used to haul equipment. The car gets 50 miles per litre. The truck gets 20 miles per litre. You want to improve petrol mileage to save money, and you have enough money to upgrade one vehicle. The upgrade cost will be the same for both vehicles. An upgraded car will get 80 miles per litre; an upgraded truck will get 25 miles per litre. The cost of petrol is £1.09 per litre. Assuming an upgrade is a good idea in the first place, which one should you upgrade? Both vehicles are driven 12,000 miles per year.

Answer: Surprise! You should definitely upgrade the truck. Here’s why. At 20 mpl, the truck burns 12,000 / 20 = 600 litres of petrol per year. The new truck will burn 12,000 / 25 = 480 litres of petrol per year, a savings of 120 litres per year. The car burns 12,000 / 50 = 240 litres of petrol per year, while the new car will burn 12,000 / 80 = 150 litres of petrol per year, a savings of 90 litres per year, so it’s not even close.

This answer may strike you as counterintuitive, so let’s consider an extreme case. Suppose the car gets 6,000 mpl, and you could upgrade to 12,000 mpl. Should you upgrade? Probably not since you would only save one litre of petrol per year. So, the reason you should upgrade the truck is that it uses so much more petrol in the first place.

Notice that the answer doesn’t depend on the cost of petrol, meaning that if you upgrade, you should always upgrade the truck. In fact, it doesn’t depend on the miles driven, as long as the miles driven are the same.


41. Replacement Decisions [LO2] In the previous problem, suppose you drive the truck x miles per year. How many miles would you have to drive the car before upgrading the car would be the better choice? (Hint: Look at the relative petrol savings.)

Answer: We can begin by calculating the litres saved by purchasing the new truck. The current and new litre usage when driving x miles per year are:

Current truck litres = x / 20New truck litres = x / 25

So the litres saved by purchasing the new truck are:

Truck litres saved = x / 20 – x / 25

If we let y equal the increased mileage for the car, the litres used by the current car, the new car, and the savings by purchasing the new car are:

Current car litres = (x + y) / 50New car litres = (x + y) / 80Car litres saved = (x + y) / 50 – (x + y) / 80

We need to set the litre savings from the new truck purchase equal to the litre savings from the new car purchase equal to each other, so:

x / 20 – x / 25 = (x + y) / 50 – (x + y) / 80

From this equation you can see again that the cost per litre is irrelevant. Each term would be multiplied by the cost per litre, which would cancel out since each term is multiplied by the same amount. To add and subtract fractions, we need to get the same denominator. In this case, we will choose a denominator of 1,000 since all four of the current denominators are multiples of 1,000. Doing so, we get:

50x / 1,000 – 40x / 1,000 = 20(x + y) / 1,000 – 12.5(x + y) / 1,00010x / 1,000 = 7.5(x + y) / 1,00010x = 7.5x + 7.5y2.5x = 7.5yy = x/3

The difference in the mileage should be 1/3 of the miles driven by the truck. So, if the truck is driven 12,000 miles, the breakeven car mileage is 16,000 miles (12,000 + 12,000/3).


CHALLENGE

42. Calculating Project NPV [LO1] You have been hired as a consultant for Pristine Urban-Tech Zither plc. (PUTZ), manufacturers of fine zithers. The market for zithers is growing quickly. The company bought some land three years ago for £1.4 million in anticipation of using it as a toxic waste dump site, but has recently hired another company to handle all toxic materials. Based on a recent appraisal, the company believes it could sell the land for £1.5 million on an after-tax basis. In four years the land could be sold for £1.6 million after taxes. The company also hired a marketing firm to analyse the zither market, at a cost of £125,000. An excerpt of the marketing report is as follows: The zither industry will have a rapid expansion in the next four years. With the brand name recognition that PUTZ brings to bear, we feel that the company will be able to sell 3,200, 4,300, 3,900 and 2,800 units each year for the next four years, respectively. Again, capitalizing on the name recognition of PUTZ, we feel that a premium price of £780 can be charged for each zither. Because zithers appear to be a fad, we feel that, at the end of the four-year period, sales should be discontinued.

PUTZ believes that fixed costs for the project will be £425,000 per year, and variable costs are 15 per cent of sales. The equipment necessary for production will cost £4.2 million, and will be depreciated according to the 20 per cent reducing-balance method. At the end of the project the equipment can be scrapped for £400,000. Net working capital of £125,000 will be required immediately. PUTZ has a 28 per cent tax rate, and the required return on the project is 13 per cent. What is the NPV of the project? Assume the company has other profitable projects.

Answer: We will begin by calculating the depreciation schedule of the investment.

YearBeginning


Value1 £4,200,000.00 £840,000.00 £3,360,000.002 £3,360,000.00 £672,000.00 £2,688,000.003 £2,688,000.00 £537,600.00 £2,150,400.00

4 £2,150,400.00£1,750,400.0

0 £400,000.00

Now we need to calculate the operating cash flow each year. Revenues first:

Year unit sales Unit Price Revenues1 3,200 £780 £2,496,0002 4,300 £780 £3,354,0003 3,900 £780 £3,042,0004 2,800 £780 £2,184,000


Now the operating cash flow:

Year Revenues Fixed CostsVariable

Costs DepreciationProfit Before

Taxes Taxes OCF1 £2,496,000 £425,000 £374,400 £840,000 £856,600 £239,848 £1,456,7522 £3,354,000 £425,000 £503,100 £672,000 £1,753,900 £491,092 £1,934,8083 £3,042,000 £425,000 £456,300 £537,600 £1,623,100 £454,468 £1,706,2324 £2,184,000 £425,000 £327,600 £1,750,400 -£319,000 -£89,320 £1,520,720

Now calculate the net cash flows:

Year OCF Land Investment NWC NCF PV(NCF)0 -£1,500,000 -£4,200,000 -£125,000 -£5,825,000 -£5,825,000.001 £1,456,752 £1,456,752 £1,289,161.062 £1,934,808 £1,934,808 £1,515,238.473 £1,706,232 £1,706,232 £1,182,504.364 £1,520,720 £1,600,000 £400,000 £125,000 £3,645,720 £2,235,988.35

Notice the calculation of the cash flow at time 0. The capital spending on equipment and investment in net working capital are cash outflows are both cash outflows. The after-tax selling price of the land is also a cash outflow. Even though no cash is actually spent on the land because the company already owns it, the after-tax cash flow from selling the land is an opportunity cost, so we need to include it in the analysis. The company can sell the land at the end of the project, so we need to include that value as well. With all the project cash flows, we can calculate the NPV, which is:

NPV = £397,892.25

The company should accept the new product line.


43. Project Evaluation [LO1] Aguilera Acoustics (AA) projects unit sales for a new seven-octave voice emulation implant as follows:

Year Unit sales1 85,0002 98,0003 106,0004 114,0005 93,000

Production of the implants will require €1,500,000 in net working capital to start, and additional net working capital investments each year equal to 15 per cent of the projected sales for the following year. Total fixed costs are €900,000 per year, variable production costs are €240 per unit, and the units are priced at €325 each. The equipment needed to begin production has an installed cost of €21,000,000. Because the implants are intended for professional singers, this equipment is considered industrial machinery, and is thus depreciated by the reducing-balance method at 20 per cent per annum. In five years this equipment can be sold for about 20 per cent of its acquisition cost. AA is in the 35 per cent marginal tax bracket, and has a required return on all its projects of 18 per cent. Based on these preliminary project estimates, what is the NPV of the project? What is the IRR?

Answer: This is an in-depth capital budgeting problem. Probably the easiest OCF calculation for this problem is the bottom up approach, so we will construct an income statement for each year. Beginning with the initial cash flow at time zero, the project will require an investment in equipment.

To start off, we determine the depreciation schedule. The salvage value is 20% of the installed cost, which is 20%*€21,000,000 = €4,200,000.00

Year 1 2 3 4 5(a) Starting Value £21,000,000.00 £16,800,000.00 £13,440,000.00 £10,752,000.0

0£ 8,601,600.00

(b) Depreciation 20% £ 4,200,000.00 £ 3,360,000.00 £ 2,688,000.00 £ 2,150,400.00

£ 4,401,600.00


£ 4,200,000.00 £ 7,560,000.00 £10,248,000.00 £12,398,400.00

£16,800,000.00

(d) Residual Value £16,800,000.00 £13,440,000.00 £10,752,000.00 £ 8,601,600.00

£ 4,200,000.00

The Income Statement is next in line.

1 2 3 4 5Sales (in units) 85,000 98,000 106,000 114,000 93,000


Revenues €27,625,000.00 €31,850,000.00 €34,450,000.00 €37,050,000.00 €30,225,000.00Variable Costs €20,400,000.00 €23,520,000.00 €25,440,000.00 €27,360,000.00 €22,320,000.00Fixed Costs € 900,000.00 € 900,000.00 € 900,000.00 € 900,000.00 € 900,000.00Depreciation 20% € 4,200,000.00 € 3,360,000.00 € 2,688,000.00 € 2,150,400.00 € 4,401,600.00EBT € 2,125,000.00 € 4,070,000.00 € 5,422,000.00 € 6,639,600.00 € 2,603,400.00Tax € 743,750.00 € 1,424,500.00 € 1,897,700.00 € 2,323,860.00 € 911,190.00Net Income € 1,381,250.00 € 2,645,500.00 € 3,524,300.00 € 4,315,740.00 € 1,692,210.00Operating Cash Flow € 5,581,250.00 € 6,005,500.00 € 6,212,300.00 € 6,466,140.00 € 6,093,810.00

Net Working Capital is a function of next year’s sales and so we can now calculate how much net working capital is required each year.

0 1 2 3 4 5

Revenues €27,625,000.00

€31,850,000.00

€34,450,000.00

€37,050,000.00

€30,225,000.00

Net Working Capital

€1,500,000.00* € 4,777,500.00 € 5,167,500.00 € 5,557,500.00 € 4,533,750.00 € 0.00

*As per the question data “£1,500,000” of NWC is required at the beginning (year zero) of the project and additional net working capital investments each year equal to 15 per cent of the projected sales for the following year. Here, we should not be confused and consider an additional 15% NWC of sales in the beginning (year zero), rather it is required starting from year 1.

The Cash Flow analysis can now be carried out.

0 1 2 3 4 5Investment -€21,000,000.00 €4,200,000.00Operating Cash Flows €5,581,250.00 €6,005,500.0

0€6,212,300.0

0€6,466,140.0

0€6,093,810.00

Change in NWC -€ 1,500,000.00 -€3,277,500.00 -€390,000.00 -€390,000.00 €1,023,750.00

€4,533,750.00

Net Cash Flow -€22,500,000.00 € 2,303,750.00 €5,615,500.00

€5,822,300.00

€7,489,890.00

€14,827,560.00

PV Cash Flows @ 18% -€22,500,000.00 € 1,952,330.51 €4,032,964.67

€3,543,631.53

€3,863,201.94

€6,481,263.13

The NPV of the investment:= -€22,500,000.00 + €1,952,330.51 + €4,032,964.67 + €3,543,631.53 + €3,863,201.94 + €6,481,263.13= -€2,626,608.23

Using a spreadsheet, solver or trial and error, the IRR is 13.87%


44. Calculating Required Savings [LO2] A proposed cost-saving device has an installed cost of £480,000. The device will be used in a five-year project, and will be depreciated using the reducing-balance method at 20 per cent per annum. The required initial net working capital investment is £40,000, the marginal tax rate is 28 per cent, and the project discount rate is 12 per cent. The device has an estimated year 5 salvage value of £45,000. What level of pre-tax cost savings do we require for this project to be profitable?

Answer: As with every capital budgeting decision that involves reducing balance depreciation, the schedule must first be estimated.

Year 1 2 3 4 5(a) Starting Value £480,000 £384,000 £307,200 £245,760 £196,608(b) Depreciation 20% £96,000 £76,800 £61,440 £49,152 £151,608(c) Accumulated Depreciation £96,000 £172,800 £234,240 £283,392 £435,000(d) Residual Value £384,000 £307,200 £245,760 £196,608 £45,000

Then the income statement is calculated. In this type of problem, you need to calculate the break-even cost savings. For an analyst, the best approach is to use a spreadsheet and then trial and error or Solver.

Using this technique, a cost savings of £148,548 leads to a net present value of zero.

0 1 2 3 4 5Pre-Tax Cost Savings £148,548 £148,548 £148,548 £148,548 £148,548Depreciation 20% £96,000 £76,800 £61,440 £49,152 £151,608EBT £52,548 £71,748 £87,108 £99,396 -£3,060Tax £14,713 £20,089 £24,390 £27,831 -£857Net Income £37,835 £51,659 £62,718 £71,565 -£2,203Operating Cash Flow £133,835 £128,459 £124,158 £120,717 £149,405

0 1 2 3 4 5Investment -£480,000 £45,000Operating Cash Flows £133,835 £128,459 £124,158 £120,717 £149,405Net Working Capital -£40,000 £40,000Net Cash Flow -£520,000 £133,835 £128,459 £124,158 £120,717 £234,405PV Cash Flows @ 12% -£520,000 £119,495 £102,406 £88,373 £76,718 £133,008NPV 0IRR 12.00%


45. Calculating a Bid Price [LO3] Your company has been approached to bid on a contract to sell 10,000 voice recognition (VR) computer keyboards a year for four years. Because of technological improvements, beyond that time they will be outdated, and no sales will be possible. The equipment necessary for the production will cost £2.4 million and will be depreciated on a reducing-balance (20 per cent) method. Production will require an investment in net working capital of £75,000 to be returned at the end of the project, and the equipment can be sold for £200,000 at the end of production. Fixed costs are £500,000 per year, and variable costs are £165 per unit. In addition to the contract, you feel your company can sell 3,000, 6,000, 8,000 and 5,000 additional units to companies in other countries over the next four years, respectively, at a price of £275. This price is fixed. The tax rate is 28 per cent, and the required return is 13 per cent. Additionally, the managing director of the company will undertake the project only if it has an NPV of £100,000. What bid price should you set for the contract?

Answer: We start our analysis by first determining the depreciation schedule of the investment.

Year 1 2 3 4(a) Starting Value £2,400,000 £1,920,000 £1,536,000 £1,228,800(b) Depreciation 20% £480,000 £384,000 £307,200 £1,028,800(c) Accumulated Depreciation £480,000 £864,000 £1,171,200 £2,200,000(d) Residual Value £1,920,000 £1,536,000 £1,228,800 £200,000

There are two parts to this analysis. The first part is the original contract for 10,000 units. From the spreadsheet below, it can be seen that the investment on its own would not be worthwhile if the bid price was set at £275.

0 1 2 3 4Sales 10,000 10,000 10,000 10,000

Revenues £2,750,000 £2,750,000 £2,750,000 £2,750,000Variable Costs £1,650,000 £1,650,000 £1,650,000 £1,650,000Fixed Costs £500,000 £500,000 £500,000 £500,000Depreciation 20% £480,000 £384,000 £307,200 £1,028,800EBT £120,000 £216,000 £292,800 -£428,800Tax £33,600 £60,480 £81,984 -£120,064Net Income £86,400 £155,520 £210,816 -£308,736Operating Cash Flow £566,400 £539,520 £518,016 £720,064

0 1 2 3 4Operating Cash Flow £566,400 £539,520 £518,016 £720,064Net Working Capital -£75,000 £75,000Investment -£2,400,000 £200,000Net Cash Flow -£2,475,000 £566,400 £539,520 £518,016 £995,064PV Cash Flows @ 13% -£2,475,000 £501,239 £422,523 £359,011 £610,291NPV -£581,935IRR 2.10%


However, your company feels that it can also sell additional units to other countries at £275 per unit. Since these cash flows are additional to the core cash flows, fixed costs and depreciation become irrelevant cash flows.

The Cash Flow Analysis for this expansion is given below:

0 1 2 3 4Sales 3,000 6,000 8,000 5,000

Revenues £825,000 £1,650,000 £2,200,000 £1,375,000Variable Costs £495,000 £990,000 £1,320,000 £825,000EBT £330,000 £660,000 £880,000 £550,000Tax £92,400 £184,800 £246,400 £154,000Net Income £237,600 £475,200 £633,600 £396,000Operating Cash Flow £237,600 £475,200 £633,600 £396,000

0 1 2 3 4Operating Cash Flow £237,600 £475,200 £633,600 £396,000Net Cash Flow £0 £237,600 £475,200 £633,600 £396,000PV Cash Flows @ 13% £0 £210,265 £372,151 £439,117 £242,874NPV £1,264,408

Since the NPV of this expansion is positive at £1,264,408, we can add this to the original analysis and arrive at a bid price that gives the project an NPV of £100,000. This can be done easily in Solver and the spreadsheet is presented below. The bid price that gives a £100,000 NPV is equal to £247.80.

0 1 2 3 4Sales 10,000 10,000 10,000 10,000

Revenues £2,478,022.5 £2,478,022.5

£2,478,022.5 £2,478,022.5

Variable Costs £1,650,000 £1,650,000 £1,650,000 £1,650,000Fixed Costs £500,000 £500,000 £500,000 £500,000Depreciation 20% £480,000 £384,000 £307,200 £1,028,800EBT £151,977.5 £55,977.5 £20,822.5 -£700,777.5

Tax -£42,553.7 -£15,673.7 £5,830.3 -£196,217.7

Net Income -£109,423.8 -£40,303.8 £14,992.2 -£504,559.8

Operating Cash Flow £370,576.2 £343,696.2 £322,192.2 £524,240.2

0 1 2 3 4

Operating Cash Flow £ 608,176.20 £ 818,896.20 £ 955,792.20 £ 920,240.20

Net Working Capital -£75,000 £75,000

Investment -£2,400,000 £200,000


Net Cash Flow -£2,475,000 £ 608,176.20 £ 818,896.20 £ 955,792.20 £ 1,195,240.20

PV Cash Flows @ 13% -£2,475,000 £ 538,209.02 £ 641,315.84 £ 662,411.94 £ 733,063.20

NPV £100,000


46. Replacement Decisions [LO2] Suppose we are thinking about replacing an old computer with a new one. The old one cost us €650,000; the new one will cost €780,000. The new machine will be depreciated straight-line to zero over its five-year life. It will probably be worth about €150,000 after five years.The old computer is being depreciated straight-line at a rate of €130,000 per year. It

will be completely written off in three years. If we don’t replace it now, we shall have to replace it in two years. We can sell it now for €210,000; in two years, it will probably be worth €60,000. The new machine will save us €145,000 per year in operating costs. The tax rate is 38 per cent, and the discount rate is 12 per cent.

(a) Suppose we recognize that, if we don’t replace the computer now, we shall be replacing it in two years. Should we replace now or should we wait? (Hint: What we effectively have here is a decision either to ‘invest’ in the old computer (by not selling it) or to invest in the new one. Notice that the two investments have unequal lives.)

(b) Suppose we consider only whether we should replace the old computer now without worrying about what’s going to happen in two years. What are the relevant cash flows? Should we replace it or not? (Hint: Consider the net change in the firm’s after-tax cash flows if we do the replacement.)

Answer: a. Since the two computers have unequal lives, the correct method to analyze the decision is

the EAC. We will begin with the EAC of the new computer. Using the depreciation tax shield approach, the OCF for the new computer system is:

OCF = (€145,000)(1 – .38) + (€780,000 / 5)(.38) = €149,180

Notice that the costs are positive, which represents a cash inflow. The costs are positive in this case since the new computer will generate a cost savings. The only initial cash flow for the new computer is cost of €780,000. We next need to calculate the after-tax salvage value, which is:

After-tax salvage value = €150,000(1 – .38) = €93,000

Now we can calculate the NPV of the new computer as:

NPV = –€780,000 + €149,180(PVIFA12%,5) + €93,000 / 1.125

NPV = –€189,468.79

And the EAC of the new computer is:

EAC = –€189,468.79 / (PVIFA12%,5) = –€52,560.49

Analyzing the old computer, the only OCF is the depreciation tax shield, so:

OCF = €130,000(.38) = €49,400

The initial cost of the old computer is a little trickier. You might assume that since we already own the old computer there is no initial cost, but we can sell the old computer, so there is an opportunity cost. We need to account for this opportunity cost. To do so, we will calculate the after-tax salvage value of the old computer today. We need the book

49


value of the old computer to do so. The book value is not given directly, but we are told that the old computer has depreciation of €130,000 per year for the next three years, so we can assume the book value is the total amount of depreciation over the remaining life of the system, or €390,000. So, the after-tax salvage value of the old computer is:

After-tax salvage value = €210,000 + (€390,000 – €210,000)(.38) = €278,400

This is the initial cost of the old computer system today because we are forgoing the opportunity to sell it today. We next need to calculate the after-tax salvage value of the computer system in two years since we are ‘buying’ it today. The after-tax salvage value in two years is:

After-tax salvage value = €60,000 + (€130,000 – €60,000)(.38) = €86,600

Now we can calculate the NPV of the old computer as:

NPV = –€278,400 + €49,400 / 1.12 + (€49,400 + €86,600) / 1.122

NPV = –€125,874.49

And the EAC of the old computer is:

EAC = –€125,874.49 / (PVIFA12%,2) = –€74,479.70

Even if we are going to replace the system in two years no matter what our decision today, we should replace it today since the EAC for a new computer is less.

b. If we are only concerned with whether or not to replace the machine now, and are not worrying about what will happen in two years, the correct analysis is NPV. To calculate the NPV of the decision on the computer system now, we need the difference in the total cash flows of the old computer system and the new computer system. From our previous calculations, we can say the cash flows for each computer system are:

t New computer Old computer Difference0 –€780,000 –€278,400 –€501,6001 €149,180 €49,400 €99,7802 €149,180 €136,000 €13,1803 €149,180 0 €149,1804 €149,180 0 €149,1805 €242,180 0 €242,180

Since we are only concerned with marginal cash flows, the cash flows of the decision to replace the old computer system with the new computer system are the differential cash flows. The NPV of the decision to replace, ignoring what will happen in two years is:

NPV = –€501,600 + €99,780/1.12 + €13,180/1.122 + €149,180/1.123 + €149,180/1.124 + €242,180/1.125

NPV = -€63,594.30

If we are not concerned with what will happen in two years, we should not replace the old computer system as it gives us a negative NPV.

50


51

investment appraisal q&a

Documents