Risk Analysis, Real Options, and Capital

Budgeting

Student Name: Firas SuhailStudent No.: 970562

SENSITIVITY ANALYSIS AND SCENARIO ANALYSIS

Estimated cash flows are expectations of averages of possible cash flows, not exact figures (although if an exact figure were available, you would use it).

SENSITIVITY ANALYSISWhat things are likely to be wrong and what will be the effect if they are? Start with a base case – the expected cash flows – then ask “what if …?”

SENSITIVITY ANALYSISTo conduct a sensitivity analysis, hold all projections constant except one; alter that one, and see how sensitive cash flows (and NPV) are to the change – the point is to get a fix on where forecasting risk may be especially severe. You may want to use the Worst-case/Best-case idea for the item being varied

SCENARIO ANALYSISWorst-case/Best-case scenarios: putting lower and upper bounds on cash flows. Common exercises include poor revenues/high costs and high revenues/low costs. Note that a thorough scenario analysis starts with Base-case/Worst-case/Best-case .

CONTINUE The revenue estimate depend on three

assumption 1. Market share2. Size of product in market 3. Price per product

COSTS1. Variable cost Change as output change, and they are

zero when production is zero. It is common to assume that a variable

cost is constant per unit of output.For example:Direct labor and raw materials are usually variable

CONTINUE2. Fixed cost Are not dependent on the amount of

goods or services produced during the period

Fixed cost are usually measured as cost per unit of time

For example:rent per month, salaries per year

EXAMPLE

Scenario Unit sales per year

Variable cost per unit

Fixed costs per year

Base 190 $15,000 $225,000

Worst 171 $16,500 $247,500

Best 209 $13,500 $202,500

The project cost= $720,000N= 4 year lifePrice per unit= $21,000Salvage value= 0

Probably accurate to within ±10%

SOLUTION

OCF+)Where;Q: unit sale per year

Required return on the project= 15%Tax= 35%Depreciation is straight line to zero 1. Calculate operating cash flow

OCFbase = [($21,000 – 15,000)(190) – $225,000](0.65) + 0.35($720,000/4)OCFbase = $657,750

OCFworst = [($21,000 – 16,500)(171) – $247,500](0.65) +0.35($720,000/4)OCFworst = $402,300

OCFbest = [($21,000 – 13,500)(209) – $202,500](0.65) + 0.35($720,000/4)OCFbest = $950,250

CONTINUE SOLUTION2. Calculate NPV for all scenarios

NPVbase = –$720,000 + $657,750(PVIFA15%,4)NPVbase = $1,157,862.02

NPVworst = –$720,000 + $402,300(PVIFA15%,4)NPVworst = $428,557.80

NPVbest = –$720,000 + $950,250(PVIFA15%,4)NPVbest = $1,992,943.19

SENSITIVITY ANALYSIS CONTINUE• Calculate the sensitivity of the NPV to

changes in fixed costs, F cost = $230,000

New OCF:OCF = [($21,000 – 15,000)(190) – $230,000](0.65) + 0.35($720,000/4)OCF = $654,500And the NPV is:NPV = –$720,000 + $654,500(PVIFA15%,4)NPV = $1,148,583.34The sensitivity of NPV to changes in fixed costs is:ΔNPV/ΔFC = ($1,157,862.02 – 1,148,583.34)/($225,000 – 230,000)ΔNPV/ΔFC = –$1.856

For every dollar FC increase, NPV falls by $1.86.

BREAK-EVEN ANALYSIS Break-even analysis is a widely used

technique for analyzing sales volume and profitability. More to the point, it determines the sales volume necessary to cover costs

BREAK-EVEN ANALYSIS There are three common break-even

measures1. Accounting break-even: sales volume

at which net income = 02. Cash break-even: sales volume at

which operating cash flow = 03. Financial break-even: sales volume at

which net present value = 0

ACCOUNTING BREAK-EVEN Net income = Sales – Costs – Taxes NI = [Q*P – FC – Q*v – D](1 – T) = 0

EXAMPLE Calculate the quantity (Q) necessary for

accounting break-even. Using the following information:

FC = $40,000; Depreciation = $4,000; Price per unit = $3; VC per unit = $0.30

Q = (FC + D) / (P – v) Q = ($40,000 + $4,000) / ($3 - $.3) = 16,296 units

BREAK EVEN POINT USING ACCOUNTING NUMBERS

𝑇 𝑟

𝑇 𝑐

𝑣𝑐

𝐹 𝑐

profit

loss

P

Q 16,296

CASH BREAK-EVEN POINT

Cash break-even point =(Fixed costs - depreciation) / CM UnitThe cash breakeven point indicates the minimum amount of sales required to contribute to a positive cash flow.

A small coal mine can produce a max of 100,000 tons per month. The coalsells for $30.00 per ton and the contribution is around 75%. TFC per month is $1,850,000. How many tons of coal the mine has to produce in order to break even?Total revenue = n P = 100,000 x $30.00 = $3,000,000.Total contribution = 0.75 x 3,000,000 = $2,250,000B (% capacity) =FC / Contribution =1850000 /2250000 = 82.22%It requires 100,000 tons x 82.22% = 82,222 tons to break even.

Example 1

Example 2

If VC is 60% of sales; with unit price at $10/each and FC = $40,000. What is the cash break even point?Sales @ BEP = a (Sales @ the BEP) + TFCX = .60(X) + $40,000X = $100,000To find break-even in units:$100,000/$10.00 = 10,000

FINANCIAL BREAK-EVEN In financial break even point it takes in

consideration the economic opportunity costs

Financial break even point higher than accounting break even point

Companies that break even on an accounting basis are really losing money. They are losing the opportunity costs of the initial investment

CONTINUE FINANCIAL BREAK EVEN POINT

𝑄 𝑓=𝐸𝐴𝐶+ 𝑓𝑖𝑥𝑒𝑑𝑐𝑜𝑠𝑡 𝑥(1−𝑡 𝑐)−𝐷𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 𝑥 𝑡𝑐

(𝑆𝑎𝑙𝑒𝑠𝑝𝑟𝑖𝑐𝑒𝑝𝑒𝑟𝑢𝑛𝑖𝑡−𝑉𝑎𝑟𝑖𝑎𝑏𝑙𝑒𝑐𝑜𝑠𝑡 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 )𝑥 (1−𝑡 𝑐)

Where;

EAC: equivalent annual cost

∑1

𝑛 1(1+𝑟 )𝑛

EXAMPLE

5967

𝑄𝑓= 40000+5967

(3−0 . 3)=17025𝑢𝑛𝑖𝑡

The price is $3 per unit and the variable costs are $0.30 per unit. The fixed costs are $40,000. The initial investment is $20,000. The project lasts five years and has a discount rate of 15%. Assume no taxes, no depreciation

BREAK EVEN POINT USING FINANCIAL NUMBERS

𝑇 𝑟

𝑇 𝑐

𝑣𝑐

𝐹 𝑐

profit

loss

P

Q17,025

MONTE CARLO SIMULATION

MONTE CARLO SIMULATION When the assumptions underlying the capital

budgeting are complex, it becomes difficult to find the expected value of the NPV.

For such a case, Monte Carlo Simulation can help find the expected value of the project.

MONTE CARLO SIMULATION Moreover, you can visualize the

distribution of NPV easily by using Monte Carlo Simulation.

In the following slides, we will use an example to illustrate how a Monte Carlo Simulation can be used.

MONTE CARLO SIMULATION Backyard Barbeque Inc (BBI) is considering

an project to produce a new grill that cooks with compressed hydrogen.

For simplicity, let us assume that the lifetime of the project is 2 years. The discount rate is 10%

The company came up with the following assumptions for the purpose of capital budgeting.

MONTE CARLO SIMULATION EXAMPLE

Assumptions 1

The revenue from the new grill will be given by

Number of grill sold by entire industry

xmarket share of BBI hydrogen grill (in percent)

price per hydrogen grill

x

CONTINUE Assumption 2The operating cost per year will be

Fixed manufacturing costs

+Variable manufacturing costs

+ Marketing costs Selling costs+

Assumption 3The initial cost is estimated to be $50 million

Cost of patent +Test marketing costs

+Cost of production facility

Fixed cost is estimated to be $5 million per year. Variable cost is estimated to be 40% of the revenue

CONTINUE Assumption 4The probability distribution of the next year’s industry wide unit sales of grills is given by

prob

abili

ty

Next years industry wide unit sales (in million)

CONTINUE

prob

abili

ty

The market share of BBI hydrogen grill next year

Assumption 5 Distribution of the market share of BBI in

each year is given by

CONTINUE Assumption 6 The price of the

grill per unit for each year is given by

Price= $190 +$1×(Industry wide unit sales in million) +(random component)

Where (random component)=$3 with probability 50% and ‒$3 with probability 50%

204

200

198

201

203

197

200.5

Positive random drawing (50% probability)

Expected

Negative random drawing (50% probability)

Nex

t yea

rs p

rice

per h

ydro

gen

grill

Next years industry wide unit sales (in million)

CONTINUE Assumption 7

Growth rate of industry wide unit sale is also assumed to be a random number. The distribution of the growth rate for each year is given by

MONTE CARLO SIMULATION Assumption 8: There is no tax.

This is just an assumption to make the computation easy.

CONTINUE Open “Monte Carlo example”

Ex 1: Compute the NPV for the following condition.

Year 1market wide unit sale =10millionYear 1 market share =2%Year 1 price error component is $3Growth rate of the market unit sales is 3%Year 2 market share =1%Year 2 price error component =‒$3

MONTE CARLO SIMULATION Ex 2Generate each variable 500 times (Monte Carlo Simulation with 500 repetitions). Then compute the expected net present value of the project. Also make a histogram to show the distribution of the net present value of the project.

MONTE CARLO SIMULATION

The result of Monte Carlo simulation (500 random draws) shows that the probability that the project will have negative net present value is very small. The expected value of NPV is about $14.5 million dollars. This would give the company confidence about the project.

REAL OPTIONSReal options provide the right to buy or sell real assets. These options often apply in capital budgeting situations and can be very valuable.

REAL OPTIONSThe

Option to Expand

The Option to

Delay

The Option to

Abandon

THE OPTION TO EXPAND EXAMPLE Mr. willing liked the idea of hotel made of ice

more than anything else. Conrad estimate the annual cash flow from a single ice hotel to be $2 million, based on an initial investment of $12 million. He felt that 20% was appropriate discount rate, giving the risk of this new venture. Believing that the cash flows would be perpetual, Mr. willing determined the NPV of the project to be:-$12x10^6+$2x10^6/0.2= -$2 million

CONTINUE THE OPTION TO EXPAND EXAMPLE

Most entrepreneurs would have rejected this venture, given it negative NPV. But Conrad he was pretty sure that initial investment would cost $12 million per year actually reflected his belief that there was a 50% probability that annual cash flow will be $3 million and 50% probability that annual cash flows will be $1 million

The NPV calculation for the two forecast are given here:

Optimistic forecast: -$12x10^6+$3x10^6/0.2=$3 millionPessimistic forecast: -$12x10^6+$1x10^6/0.2= -$7 million

CONTINUE THE OPTION TO EXPAND EXAMPLE

However, if the optimistic forecast turns out to be correct, Mr. Willing would want to expand. An average of two forecast yield an NPV for the project of:$ 3𝑚𝑖𝑙𝑙𝑖𝑜𝑛+(−$7𝑚𝑖𝑙𝑙𝑖𝑜𝑛)

2=−$ 2𝑚𝑖𝑙𝑙𝑖𝑜𝑛

If he believes that there are 10 location in the country that can support an ice hotel, the turn NPV of the venture would be:

$ 3𝑚𝑖𝑙𝑙𝑖𝑜𝑛𝑥 10+(−$7𝑚𝑖𝑙𝑙𝑖𝑜𝑛)2

=$11 .5𝑚𝑖𝑙𝑙𝑖𝑜𝑛

THE OPTION TO ABANDON EXAMPLE The same example of the ice hotel, which illustrated

the option to expand, can also illustrate the option to abandon.Imagine that Mr. willing now believes that there is a 50% probability that annual cash flows will be $6 million, and a 50% probability ability that annual cash flows will be -$2 million. The NPV calculation under the two forecast become:

Optimistic forecast: -$12x10^6+$6x10^6/0.2= $18 million Pessimistic forecast: -$12x10^6 - $2x10^6/0.2= -$22 million

CONTINUE THE OPTION TO ABANDON EXAMPLE

Yielding an NPV for the project of:

Now imagine that Mr. Willing wants to own, at most just one ice hotel, implying that there is no option to expand, because the NPV is negative, it looks as if he will not build the hotel.

THE OPTION TO DELAY: EXAMPLE

Consider the above project, which can be undertaken in any of the next 4 years. The discount rate is 10 percent. The present value of the benefits at the time the project is launched remains constant at $25,000, but since costs are declining, the NPV at the time of launch steadily rises.

The best time to launch the project is in year 2—this schedule yields the highest NPV when judged today.

Year Cost PV NPV t

0 20,000$ 25,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 2 17,100$ 25,000$ 7,900$ 3 16,929$ 25,000$ 8,071$ 4 16,760$ 25,000$ 8,240$

2)10.1(900,7$529,6$

Year Cost PV NPV t NPV 0

0 20,000$ 25,000$ 5,000$ 5,000$ 1 18,000$ 25,000$ 7,000$ 6,364$ 2 17,100$ 25,000$ 7,900$ 6,529$ 3 16,929$ 25,000$ 8,071$ 6,064$ 4 16,760$ 25,000$ 8,240$ 5,628$

Decision Tree

DECISION TREES Decision trees are a convenient way to

represent sequential decisions over time. Such decisions often arise when the uncertainty surrounding an investment can be reduced by some initial information-gathering such as test marketing a new product or preparing a feasibility study .

EXAMPLE OF A DECISION TREE

Do not study

Study finance

Squares represent decisions to be made.Circles represent receipt of information, e.g., a test score.

The lines leading away from the squares represent the options

“C”

“A”

“B”

“F”

“D”

DECISION TREES

B&B has new baby powder ready to market, if the firm goes directly to the market with the product, there is only a 55% percent chance of success, however, the firm can conduct customer segment research which will take a year and cost $1 million by going through research, B&B will be able to better target potential customer and will increase the probability 70 percent. If successful, the present value payoff is only profit(at time of initial selling) of $30 million. If unsuccessful, the present payoff is only $3 million. Should the firm conduct customer segment research or go directly to market? The appropriate discount rate is 15 percent

Example

DECISION TREES

NPV= C0 + {[CSuccess (Prob. of Success)] + [CFailure (Prob. of Failure)]} / (1 + R)^tNPV = –$1,000,000 + {[$30,000,000 (0.70)] + [$3,000,000 (0.30)]} / 1.15NPV = $18,043,478.26

Make the research

NPV = CSuccess (Prob. of Success) + CFailure (Prob. of Failure)NPV = $30,000,000(.55) + $3,000,000(.45)NPV = $17,850,000.00

Don’t Make the research

No Research

DECISION TREES

ResearchFailure

Success

Failure

Success

$18.0435 million at t = 0

$17.85 million at t = 0

Thank you