Finance Week 7

IPCOR421 FinanceAlex Kane 1

CLASS NOTES

WEEK VII

READING ASSIGNMENT

BMA 6


Objectives of the Chapter

A. Correct use of NPV, as applied to taxable corporations -- using accounting data

B. Equivalent annual cost (EAC) andreplacement decisions

C. Cost of excess capacity

D. Examples of project interactions (as in mutual exclusivity): Optimal timing of investments and fluctuating load factors


Correct use of NPV

1. Use CF, not accounting net income2. Use incremental CF, including all incidental

effects3. Include opportunity costs (an incidental in 2.)4. Include WC requirements5. Ignore sunk cost6. Treat inflation and foreign currencies consistently7. Account for depreciation correctly, that is, only via

tax effects


Accounting and CF• Two types of accounting reports: Flow (income statement,

sources and uses of funds) and Stock (balance sheet)• The income statement excludes capital costs (investment

CF) and includes depreciation (not a CF)• WC is an investment. Amortization is usually 0 (for cash)

or small (account receivables, inventory)• Must estimate CF on after-tax basis• Accounting is accrual based, CF is on cash basis• Assess incremental not average CF, leads to difference of

NPV with and without the project. Examples:Land used in project (available both before and after the project)Introduction of new products: must account for CF lost on old

products


More on incremental CF

• Sunk cost are painful but must be ignored

• Overhead cost cannot be allocated as in A/C

• Separate investment from financing decisions– compute NPV based on all equity financing– Add any NPV from financing decisions

• WC needs must be assessed and accounted for -- both when the investment takes place and in terminal value


A simple income statement• Gross margin = Sales – cost of goods sold• Operating expenses

Promotion, sellingwarehousing + shipping G&A (general and administration)R&D + process improvementDepreciation (not a cash item)

• Operating Income = Gross margin – Operating expenses• Extraordinary items and loss from discontinuous operations• EBIT = op. income – extraordinary items

Interest on various debt• EBT• Taxes• NI = EBT – Taxes


The depreciation tax shield• CF = NI + depreciation• How is it that airlines, when awash in red ink, can still

purchase new planes?• Because large depreciation charges can swamp negative NI• Denote: EBITDA = EBIT before dep and amortization• Assume no debt (equity financing)• NI = (EBITDA – Dep)*(1 – taxrate) = =

EBITDA*(1–taxrate) – Dep + Dep*taxrate• CF = NI + Dep = EBITDA*(1–taxrate) + dep*taxrate• Tax shied (TS) = Dep*taxrate• Depreciation contributes to CF by reducing the corp tax

(TS)


NPV and depreciation tax shield

• NPV= PV(–capital expenditures +terminal value) + PV[EBITDA*(1 – taxrate)] + PV(dep*taxrate=TS)NPV= PV(after-tax CF) + PVTS

• PVTS = present value of tax shield

• Accelerated depreciation results in higher PVTS and higher NPV (see Table 6.4 for illustration)

• Exercise: Compute the NPV of each alternative in 6.4 at 15%, per $1 of capital expenditure


Equivalent Annual Cost (EAC)• Toyota wants to offer a 4-year lease on a $20k Camry. The

residual value is estimated at $10k. How much should Toyota charge customers?Ignore taxes and assume monthly payments at end of months

The required APR on such lease is 9% (monthly rate=0.0075)

Notice: The effective annual rate is greater than 9% (compute)

Denote the monthly leasing charge by L

20,000 = PV (0.0075, 48, PMT=L, Car value=10,000)

L=PMT(0.0075,48, 20000,–10,000) = $323.85

(can easily fix when payments are at beginning of month)

• L=323.85 is the EAC (monthly) of a Camry over its first 4 years -- assuming we agree on the residual value !


Consider two machines; identical output• Machine A Machine B• Purchase 500 1600• Life (years) 4 8• Ann.op.cost 300 150• Residual 0 0• Required rate 12 12• $ cost over 8years 3400 2800• Cash outflows of an 8-year replacement chain:• A: 500, 300, 300, 300, 800, 300, 300, 300, 300• B: 1600, 150, 150, 150, 150, 150, 150, 150, 150


Solution• You can construct equivalent-length chains, compute PV

of each chain and compare (brute force) • The insightful and efficient method is to calculate the EAC

of each machine• EAC = PMT(rate, life, PV(CF, including residual))• EAC(A) = 464.62 EAC(B) = 472.08• Note that, in general, required rate could be different for

the two machines (but not so common) because:– Newer (less tested) technology makes B riskier– Unexpected inflation makes A riskier (need to replace sooner)– The inflation consideration can be done either by calculation with

real CFs and a real discount rate, nominal CF with nominal r


Maintenance and repairs (M&R) over time

• Reconsider the case of a Machine like A– In all probability it could be operated beyond Year 4– In general, M&R costs will grow over time, at some

point at an increasing rate• Suppose a realistic forecast is this:

– Cost 800– M&R = 250, 300, 400, 550, 700, 1000

• How long should this machine be operated?• Notice that how long we operate the machine determines

its EAC, because of difference in PV(CF)


The replacement decision (r=12%)• The choice to operate the machine over different lives makes for

mutually exclusive “projects”

• Years to operate next year’s M&R EAC

1 PMT(12,1, 800+PV(250)) 300 1146

2 PMT(12,2,800 + PV(250,300)) 400 746.94

3 PMT(12,3,800 + PV(250,300,400)) 550 644.13

4 PMT(12,4,800 + PV(250,300,400,550)) 700 624.43

5 PMT(12,5,800 + PV(250,300,400,550,700)) 1000 636.33

– Minimum EAC is achieved at 4 years

– Lengthening life by 1 year costs more in maintenance than the EAC, hence must replace


Fluctuating demand• Consider a power plant with two generators

• One works constantly, the other during peak hours

• There is a choice of two types of turbines– Expensive -- saves fuel– Cheap -- gas guzzler

• It is plausible that optimal choice will be: – Use the expensive turbine to work constantly– Use the cheap turbine for peak demand


Excess capacity

• The principle of optimal replacement is more general than choice and life of machines

• Building excess capacity of a production process is equivalent to lengthening its life -- less stress on equipment and can handle growing demand

• Hence, decision of optimal capacity is inseparable from a decision of the economic life of the project


Project interactions• This means you cannot decide on the project

based on its data (NPV) alone• Mutual exclusive projects (common) implies

decision on one project depends on other(s)• A common example is timing of a project, also

known as the “value of waiting to invest”• A project planned to start on date t, must also be

evaluated if it were to start at date t+h for various values of h

• Waiting has a large value (more info, less risk), must have good reason to start immediately !


Forestry: example of timing

• Suppose you own a tree whose current market value (net of cost of cutting) is W

• The value of the lumber grows at the rate g and the cost of capital is r

• When should you cut the tree?

• At time t, the value of the tree is W(1+g)^t

• At this point, if we cut the tree, sell it, and invest for one period, we will have:

• (1+r)W(1+g)^t


Forestry continued

• If we wait one more period, the value of lumber will be: (1+g)W(1+g)^t

• Harvest if value of cutting now is greater than from waiting

• (1+r)W(1+g)^t > (1+g)W(1+g)^t => r>g• Conclusion: When r>g we’ll cut immediately,

since the gain from waiting one period (g) is smaller than harvest and invest for one period (r)

• If g>r, we’ll never cut the tree. But: it is impossible that anything grows forever at g>r


Fixed cost affects optimal cutting time• In reality, there are fixed cost (F) associated with

cutting (getting the heavy equipment in place etc.)• Now, waiting has additional gain: postponing F • If we wait one period we’ll have

(1+g)W(1+g)^t–F

• If we cut and invest for one period we’ll have (1+r)[W(1+g)^t – F]

• Break even:(1+g)W(1+g)^t – F = (1+r)[W(1+g)^t – F]

Must solve for break even t. Looks hard but isn’t


Solution• Solution to the equation in the previous slide: • t = ln[(F/W) * r/(r–g)] / ln(1+g)• If F/W significant, t>0 even if r>g• t goes up when g or F/W goes up • t goes down when r goes up• Replace ‘tree’ with ‘oil well’. W is value of oil in well

at current price, g is the growth (inflation) in price of oil. The calculation shows how supply of oil interacts with demand (oil inflation, g, is not perfectly correlated with i of CPI)

• If all producers optimize in a competitive market, price of oil will rise at the rate r !! (one of Hotelling’s laws)

Finance Week 7

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