Week 4: Investment Criteria, Capital Investment Decisions and Project Analysis (Ch. 8, 9, 10.3 to 10.5)

Week 4 applies discounting to the most important decision in corporate finance: which projects to invest in (capital budgeting). Chapter 8 compares six investment criteria: NPV, payback, discounted payback, average accounting return, profitability index and internal rate of return. Chapter 9 explains which cash flows belong in a project evaluation (incremental after-tax cash flows) and how to compute operating cash flow, capital spending and changes in net working capital. Chapter 10 (sections 10.3 to 10.5) covers break-even analysis and operating leverage.

Running example: you consider opening a coffee shop in Nijmegen. Initial investment €100,000 (renovation, coffee machines, furniture); expected cash inflows €30,000 in year 1, €60,000 in year 2 and €40,000 in year 3. Should you invest? Each method asks a different question: NPV (does the shop create more value than it costs?), payback (how quickly do you recover the investment?), discounted payback (the same, adjusted for time value), profitability index (return per euro invested), average accounting return (what does the accounting data say?), IRR (the project's effective percentage return).

Net present value (NPV)

Investment rule: accept if NPV is greater than or equal to zero; reject if NPV is less than zero. A positive NPV means the project is worth more than it costs, so it increases shareholder value, in line with the goal of financial management.

Strengths of NPV: (1) it uses cash flows, which are better than earnings (an accounting measure); (2) it uses all cash flows, whereas other approaches ignore cash flows beyond a certain date; (3) it discounts the cash flows and so fully incorporates the time value of money. (Book) The main difficulty is estimating future cash flows; NPV analysis is therefore also called discounted cash flow (DCF) valuation.

The payback rule

Coffee shop: cumulative cash flows are €30,000 after year 1, €90,000 after year 2 (still below €100,000) and €130,000 after year 3. In year 3 another €10,000 is needed out of €40,000, a fraction of 0.25. Payback = 2 + 10,000/40,000 = 2.25 years (about 2 years and 3 months).

Problems with the payback rule (slide example):

B never pays back; C pays back only because of a large final cash flow; D pays back twice (after year 2, again after year 4 because of a negative cash flow in year 3); E pays back after half a year but then has a catastrophic outflow the payback rule ignores.

(Book) Payback is still used by large firms as a quick screen for many small decisions, where detailed analysis would cost more than a mistake. It ignores risk differences and may accept projects with a negative NPV (a short project that pays back fast but is worth less than it costs) and reject profitable long-term projects.

The discounted payback

Ordinary versus discounted payback: initial investment 300 and cash flows of 100 per year for 5 years. Undiscounted cumulative cash flows are 100, 200, 300 (payback after 3 years). Discounted (at 12.5%) they are 89, 79, 70, 62, 55, cumulating to 89, 168, 238, 300, 355 (discounted payback after 4 years). Graphically, the discounted payback is the point where the future value of the projected cash flows catches up with the future value of the initial investment (both €481 after year 4).

Coffee shop at 6%: discounted inflows €28,302, €53,400 and €33,585; cumulative €28,302, €81,702 (still below €100,000) and €115,286. Needed in year 3: 100,000 - 81,702 = 18,298; fraction 18,298/33,585 = 0.54. Discounted payback = 2.54 years (about 2 years and 6.5 months), longer than the ordinary payback of 2.25 years.

Exercise: a project pays €50,000 per month for 12 months, requires €243,000 and the target return is 1% per month. Discounted cash flows: 49,505; 49,015; 48,530; 48,049; 47,573 (cumulative 242,672 after 5 months, €328 short of 243,000); month 6: 47,102. Fraction = 328/47,102 = 0.0069, so the discounted payback is 5.01 months.

Tutorial: a project costs €17,000 and pays €8,300 per year for 4 years at 7%. Discounted cash flows 7,757; 7,250; 6,775; 6,332; cumulative 7,757 and 15,007 after two years, so 2 + (17,000 - 15,007)/6,775 = 2.29 years. Another example: cost 7,000 with cash flows 4,200 and 5,300 at 14% (discounted 3,684 and 4,078) pays back between one and two years.

The average accounting return (AAR)

Example (store in a shopping centre): investment €500,000, depreciated 100% straight-line over five years (€100,000 per year), tax 25%.

Average net income = (100,000 + 150,000 + 50,000 + 0 - 50,000)/5 = 50,000. Average book value = (500,000 + 0)/2 = 250,000 (equivalently (500k + 400k + 300k + 200k + 100k + 0)/6 = 250k; with straight-line depreciation the average is always half the initial investment). AAR = 50,000/250,000 = 20%.

Exercise (reducing balance): a machine costing 23,000 is depreciated at 20% reducing balance; book values at year end 23,000 (purchase), 18,400, 14,720, 11,776 and 9,421. It generates 4,200 net income per year on average. Average book value = (23,000 + 18,400 + 14,720 + 11,776 + 9,421)/5 = 15,463. AAR = 4,200/15,463 = 27.16%. Accept if the target return is at most 27.16%.

The profitability index (PI)

Problem of scale (Hiram Finnegan Int., 12%):

Project 2 has the higher PI, but project 1 adds more value (higher NPV). For mutually exclusive projects the PI can give the wrong ranking because it ignores scale.

The internal rate of return (IRR)

Example: an investment costs €100 and pays €60 per year for two years. NPV at 0%, 5%, 10%, 15% and 20%: 20.00, 11.56, 4.13, -2.46, -8.33. The NPV crosses zero at IRR = 13.1%. The NPV profile plots NPV against the discount rate: it starts at -100 + 60 + 60 = 20 at r = 0 and slopes downward; NPV > 0 for r below 13.1% and NPV < 0 above. For conventional projects NPV and IRR give the same accept/reject decision.

Problems with the IRR

1. Investing versus financing. Project A: -£100 at t = 0 and +£130 at t = 1; IRR 30%, NPV at 10% = +£18.2. Accept if IRR > market rate: you earn a higher rate in the project than in the market. Project B: +£100 at t = 0 and -£130 at t = 1 (financing-type cash flows, like a loan); IRR also 30%, but NPV at 10% = -£18.2 and the NPV profile slopes upward. Accept only if IRR < market rate: you pay a lower rate in the project than in the market.

2. Mixed (non-conventional) cash flows. Project C: -£100, +£230, -£132. The NPV is zero at both 10% and 20%, so there are two IRRs. The NPV is -£2 at 0%, positive between 10% and 20%, and approaches -£100 as r goes to infinity. The project is acceptable only if the market rate is above 10% but below 20%; no single IRR can be used.

3. Mutually exclusive projects. Independent projects: accepting or rejecting one does not affect the others. Mutually exclusive projects: you can accept A or B or reject both, but not accept both. Example: A = -100, 50, 40, 40, 30 (IRR 24%); B = -100, 20, 40, 50, 60 (IRR 21%). Undiscounted, B's inflows (170) exceed A's (160).

The NPV profiles cross at the crossover rate of 11.1%. Below 11.1% B has the higher NPV (although A has the higher IRR); above 11.1% A is better. Why do they differ? NPV assumes intermediate cash flows are reinvested at the discount rate (usually the cost of capital); IRR assumes reinvestment at the IRR itself, which is unrealistic if the IRR is very high. (Book) The crossover rate is the IRR of the difference in cash flows between the two projects.

4. Scale. Corporate Finance: The Motion Picture can be produced on a small budget (-€10m at date 0, +€40m at date 1: IRR 300%, NPV at 25% = €22m) or a large budget (-€25m, +€65m: IRR 160%, NPV €27m). One producer prefers the large budget (higher NPV), the other the small budget (higher IRR). NPV is right: the large budget adds €5m more value. The incremental investment (-€15m, +€25m) has an IRR of 66.7%, above 25%, so the extra money is worth spending. Rule: use net present value.

(Book) The IRR remains popular because managers like to talk in rates of return and because it can be computed without knowing the discount rate. The modified IRR (MIRR) first adjusts cash flows (discounting negative ones or compounding positive ones at the required return) so that only one IRR remains.

Capital budgeting in practice

A survey of European and US firms (Brounen, De Jong and Koedijk, 2006) shows the percentage of CFOs that always or almost always use each technique: in the US, IRR (75.6%) and NPV (74.9%) dominate; in the UK the payback period is most popular (69.2%); in the Netherlands NPV (70.0%) comes first, followed by payback (64.7%) and IRR (56.0%); in Germany payback is most used (50.0%); in France real options (53.1%). Venture capital funds are commonly ranked by IRR.

Making capital investment decisions: relevant cash flows

The key elements are incremental cash flows that are after tax (not accounting values), that ignore sunk costs, include opportunity costs and side effects, and exclude financing costs.

(Book) The stand-alone principle: once the incremental cash flows are identified, the project can be evaluated as a kind of 'mini-firm' with its own revenues, costs, assets and cash flows.

• Sunk costs: a sunk cost is a cash flow that has already occurred. Rule: ignore all sunk costs. Example: General Milk paid a consultant £100,000 last year for a test marketing analysis of chocolate milk; this is irrelevant for the decision now, because it cannot be recovered whatever is decided.
• Opportunity costs: lost revenues you forgo as a result of making the investment. Rule: incorporate opportunity costs. Example: Gonzales Trading's empty warehouse in Salamanca could be sold or rented out; using it for a new line of pinball machines has a cost.
• Side effects: classified as erosion (a new product reduces the cash flows of existing products, also called cannibalism) or synergy (a new project increases the cash flows of existing projects). Rule: incorporate side effects. Example: only the sales of Innovative Motors' new convertible that do not reduce sales of its hard-top sports car are incremental. A racing team costing £35 million that raises cash flows elsewhere in the firm by a PV of £65 million has an incremental value of +£30 million, not -£35 million.
• Financing costs: interest, dividends and repayments are not included; the project is evaluated as if all-equity financed, because financing is reflected in the discount rate.
• After-tax cash flows are used, measured when they actually occur; net working capital is a real investment that is usually recovered at the end.

Tutorial (Winnebagel): a new caravanette line sells 19,000 units at £13,000 (£247m); it raises luxury caravan sales by 4,500 units at £91,000 (+£409.5m, synergy) and reduces mobile caravan sales by 900 units at £53,000 (-£47.7m, erosion). Relevant annual sales = 247 + 409.5 - 47.7 = £608.8 million.

Project's total (free) cash flow

• Free cash flow: cash left after operating costs, taxes, investments in fixed assets and changes in working capital; how much cash the company can give to investors without harming operations. It shows whether a firm finances its growth itself or needs external capital. Netflix long had high OCF but negative FCF because of heavy content spending.
• Operating cash flow: cash from day-to-day operations, reflecting the ability to generate cash from the core business; unlike accounting profit it contains no accruals. Amazon collects cash from customers long before it pays suppliers.
• CapEx: cash spent on acquiring or upgrading long-term assets; maintenance CapEx keeps capacity, growth CapEx expands it. High CapEx lowers FCF today but should raise future OCF (Tesla's Gigafactories). Software firms with low CapEx often have high FCF.
• Change in NWC: an increase ties up cash (more inventory, slower-paying customers); a decrease releases cash (better terms with suppliers). Even profitable firms can run into liquidity problems if too much cash is stuck in working capital (retailers build inventory before Christmas).

Understanding the components answers: is cash generation sustainable, does growth create or destroy value, how much cash is really available for shareholders and debtholders? Profits may be 'paper profits'; FCF shows the real economic value.

Four definitions of operating cash flow

Example: sales 50,000 units at £4 = £200,000; variable costs £2.50 per unit = £125,000; fixed costs £12,000; depreciation £90,000/3 = £30,000; EBIT = £33,000; taxes 34% = £11,220; net income £21,780.

All four methods always give the same answer. The tax-shield approach shows that depreciation has value only because it reduces taxes: the depreciation tax shield equals depreciation x tax rate. Tutorial: sales Nkr108,000, variable costs 51,000, depreciation 6,800, tax 35%: EBT 50,200, taxes 17,570, net income 32,630; OCF = 50,200 + 6,800 - 17,570 = 32,630 + 6,800 = (108,000 - 51,000) x 0.65 + 0.35 x 6,800 = Nkr39,430. Another: sales £830,000, variable costs 60% (£498,000), fixed costs £181,000, depreciation £77,000, tax 28%: EBT 74,000, tax 20,720, net income 53,280, OCF = 53,280 + 77,000 = £130,280.

Depreciation methods and taxes

Straight-line depreciation writes off the same amount each year (for example 20% of the original cost each year, so the asset is fully written off after five years). Reducing balance depreciation applies a fixed percentage to the remaining book value each year, so the charges fall over time and the asset is never fully written off; the remaining book value is compared with the salvage value.

With straight-line depreciation to zero, the whole salvage value is a taxable gain: after-tax salvage = salvage x (1 - T). Tutorial: salvage €60,000 at 34% gives 60,000 x 0.66 = €39,600.

Net working capital in project cash flows

An investment in NWC is a cash outflow; recovering it is a cash inflow. Example: NWC of £20,000 is needed from year 0 to year 3. The change in NWC is +20,000 in year 0, 0 in years 1 and 2 and -20,000 in year 3, so the effect on cash flow (x -1) is -20,000 at the start and +20,000 at the end. Total project cash flow with OCF of 51,780 per year and CapEx of 90,000: year 0: -20,000 - 90,000 = -110,000; years 1 and 2: 51,780; year 3: 51,780 + 20,000 = 71,780.

Worked example: Whair Balls Ltd

A leading producer of sports balls considers brightly coloured bowling balls. A marketing survey (cost £250,000, already paid) suggests a market share of 10% to 15%. The decision: carry out a full capital budgeting analysis. Data (in £'000): investment 10,000, depreciated at 25% reducing balance, salvage value 1,000 after 4 years; marginal tax rate 28%; sales 7,000 and operating costs 2,000 per year; NWC at the end of years 0 to 4: 200, 450, 750, 950 and 100 (all recovered at the end); the project uses empty office space that could be sold at any time for 500 after tax; discount rate 12%.

NPV = £3,083 thousand, so the project should be accepted. Points to note: the survey is sunk and ignored; the office space is an opportunity cost (-500 now, recovered as +500 at the end, as assumed on the slide); the tax saving on the loss on sale (the book value 3,164 exceeds the salvage value 1,000) is included through the extra deduction in year 4; NWC changes are the year-to-year differences, and in year 4 the decrease from 950 to 100 (850) plus the recovery of the remaining 100 flow back.

Tutorial (Dog Up! Franks): a sausage system costs €390,000, straight-line to zero over 5 years (depreciation 78,000), salvage €60,000 (after tax 39,600), pre-tax cost savings €120,000 per year, NWC €28,000 at the start (recovered at the end), tax 34%, discount rate 10%. OCF = 120,000 x 0.66 + 78,000 x 0.34 = 105,720. NPV = -390,000 - 28,000 + 105,720 x A(10%, 5) + (39,600 + 28,000)/1.1^5 = €24,736.

Tutorial (Yuvhadit cemetery): €800,000 investment, net cash inflow €80,000 next year growing 6% forever, required return 12%: PV = 80,000/(0.12 - 0.06) = €1,333,333; NPV = €533,333, accept. The growth rate at which NPV = 0: 800,000 = 80,000/(0.12 - g), so g = 2%.

(Book, 9.6) Special cases of DCF analysis: evaluating cost-cutting proposals, setting a bid price (the lowest price with NPV = 0) and comparing equipment with different lives using the equivalent annual cost (the PV of costs converted to an annuity).

Break-even analysis: main elements

Example: fixed costs €8,000 and variable costs €3 per unit give total costs of €8,000 at 0 units, €11,000 at 1,000, €23,000 at 5,000 and €38,000 at 10,000 units. (Book) Marginal (incremental) cost is the change in costs from producing one more unit; average cost falls as fixed costs are spread over more units.

Example (Wettway Yachts, Margo-class yacht): price £40,000 per boat, variable cost £20,000, fixed costs £500,000 per year, initial investment £3,500,000 depreciated straight-line to zero over 5 years (£700,000 per year), no salvage, no working capital, required return 20%.

• Cash break-even: Q = 500,000/(40,000 - 20,000) = 25 boats. At this level OCF = 0: the project never recovers its investment.
• Accounting break-even: Q = (500,000 + 700,000)/20,000 = 60 boats. OCF equals depreciation (£700,000), so net income is zero and the investment is recovered, but without any return on it (the payback equals the project life).
• Financial break-even: step 1: find the OCF that gives NPV = 0 as an ordinary annuity: 3,500,000 = OCF* x A(20%, 5) = OCF* x 2.9906, so OCF* = £1,170,000. Step 2: Q = (500,000 + 1,170,000)/20,000 = 83.5, so Wettway needs to sell about 84 boats. At this level the project earns exactly the required 20%.

Always: cash break-even < accounting break-even < financial break-even (for a project with a positive required return). Lockheed L-1011 TriStar (1970): Lockheed calculated a break-even of about 200 aircraft but ignored the opportunity cost of the roughly $1 billion invested; the financial break-even was about 500 aircraft. By 1984 only 250 TriStars had been sold, and in 1971 Lockheed faced bankruptcy. The accounting break-even is misleading because it ignores the cost of capital.

Tutorial: price €80, variable costs 50% (€40), fixed costs €1,000 per year, investment €7,000 over 5 years, 10% required return. OCF* = 7,000/A(10%, 5) = 7,000/3.7908 = €1,846.6; Q = (1,000 + 1,846.6)/40 = 71.2, so at least 72 units. At 20% the financial break-even rises to (1,000 + 2,340.6)/40 = 83.5 units, while the accounting break-even ((1,000 + 1,400)/40 = 60 units) does not depend on the discount rate. Tutorial (two cases): price Nkr3,020, v 2,275, F 14,000,000, D 6,500,000: cash break-even 18,792 units and accounting break-even 27,517 units; price 38, v 27, F 73,000, D 150,000: cash 6,636 and accounting 20,273 units.

Operating leverage

Example (Dog Style Ltd): gourmet dog food sells for $1.20 per can, variable cost $0.80, fixed costs $360,000 per year, depreciation $60,000. Accounting break-even: Q = (360,000 + 60,000)/0.40 = 1,050,000 cans. At this level OCF = D = $60,000, so DOL = 1 + 360,000/60,000 = 7. A 10% increase in quantity raises OCF by 7 x 10% = 70%. Check: new OCF = 60,000 + 0.40 x 105,000 = $102,000, an increase of 42,000/60,000 = 70%. If fixed costs were only $120,000: break-even = 180,000/0.40 = 450,000 cans, DOL = 1 + 120,000/60,000 = 3 and a 10% increase in quantity raises OCF by 30% (60,000 to 78,000).

Tutorial: at 100,000 units the DOL is 3.40. If output falls to 80,000 units (-20%), OCF changes by 3.4 x (-20%) = -68%. If fixed costs are £130,000: 3.40 = 1 + 130,000/OCF gives OCF = £54,167; at 58,000 units (-42%) OCF changes by 3.40 x (-42%) = -142.8%, so OCF = 54,167 x (1 - 1.428) = -£23,183. (Book) High operating leverage magnifies forecasting risk: small errors in sales forecasts lead to large errors in cash flow and NPV. Firms can keep flexibility by, for example, outsourcing or leasing instead of investing in fixed assets. DOL is highest near the cash break-even and declines as output grows.