CHAPTER 1



CHAPTER 10

Project Analysis

Answers to Problem Sets

1. a. False

b. True

c. True

 

2. a. Cash-flow forecasts overstated.

b. One project proposal may be ranked below another simply because cash

flows are based on different forecasts.

c. Project proposals may not consider strategic -alternatives.

 

3. a. Analysis of how project profitability and NPV change if different

assumptions are made about sales, cost, and other key variables.

b. Project NPV is recalculated by changing several inputs to new, but

consistent, values.

c. Determines the level of future sales at which project profitability or NPV

equals zero.

d. An extension of sensitivity analysis that explores all possible outcomes

and weights each by its probability.

e. A graphical technique for displaying possible future events and decisions

taken in response to those events.

f. Option to modify a project at a future date.

g. The additional present value created by the -option to bail out of a project,

and recover part of the initial investment, if the project performs poorly.

h. The additional present value created by the -option to invest more and

expand output, if a project performs well.

 

4. a. False

b. True

c. True

d. True

e. False

f. True

 

5. a. Describe how project cash flow depends on the underlying variables.

b. Specify probability distributions for forecast -errors for these cash flows.

c. Draw from the probability distributions to -simulate the cash flows.

 

6. a. True

b. True

c. False

d. False

 

7. Adding a fudge factor to the discount rate pushes project analysts to submit more optimistic forecasts.

8. We assume that the idea for a new obfuscator machine originates with a plant manager in the Deconstruction Division. (Keep in mind however that, in addition to bottom-up proposals, such as the obfuscator machine proposal, top-down proposals also originate with divisional managers and senior management.) Other steps in the capital budgeting process include the following:

• Many large firms begin the process with forecasts of economic variables, such as inflation and GDP growth, as well as variables of particular interest to the industry, such as prices of raw materials and industry sales projections.

• The plant manager, often in consultation with the division manager, prepares the proposal in the form of an appropriation request; the appropriation request typically includes an explanation of the need for the expenditure, detailed forecasts, discounted cash flow analysis and other supporting detail such as sensitivity analysis.

• Depending on the size of the investment, the appropriation request is reviewed and approved by the divisional manager, senior management or, in the case of major expenditures, the board of directors.

• The forecast expenditure is included as part of the annual capital budget, which is approved by top management and the board of directors.

• Major cost over-runs typically require a supplementary appropriation request, which includes an explanation of the reason why the additional expenditure was not anticipated.

• When the machine is finally up and running, most firms conduct a postaudit to identify problems and to assess forecast accuracy; the main purpose of the postaudit is to improve the process in the future.

9. a.

[pic]

= $2,584.67

[pic]$7,560

b. [pic] $2,110.19

[pic]$1,000

c. The 18% discount rate would give an approximation to the correct NPVs for projects with all (or most) of the inflows in the first year.

The present value of $1 to be received one year from now, discounted at 18% is: $0.8475

The present value of $1 × (1 – 0.08) (that is, $0.92) to be received one year from now, discounted at 10% is: $0.8364

The former calculation overstates the correct answer by approximately 1.3%. However, for cash flows five or ten years in to the future, discounting by 18% understates the correct present value by approximately 23% and 46%, respectively. The error increases substantially because the incorrect factor (i.e., 1.18) is compounded, causing the denominator of the present value calculation to be greatly overstated so that the present value is greatly understated.

10.

| |Year 0 |Years 1-10 |

|Investment |¥15 B | |

|1. Revenue | |¥44.000 B |

|2. Variable Cost | |39.600 B |

|3. Fixed Cost | |2.000 B |

|4. Depreciation | |1.500 B |

|5. Pre-tax Profit | |¥0.900 B |

|6. Tax @ 50% | |0.450 B |

|7. Net Operating Profit | |¥0.450 B |

|8. Operating Cash Flow | |¥1.950 B |

11. The spreadsheets show the following results:

| |NPV |

| |Pessimistic |Expected |Optimistic |

|Market Size |-1.17 |3.43 |8.04 |

|Market Share |-10.39 |3.43 |17.26 |

|Unit Price |-19.61 |3.43 |11.11 |

|Unit Variable Cost |-11.93 |3.43 |11.11 |

|Fixed Cost |-2.71 |3.43 |9.58 |

The principal uncertainties are market share, unit price, and unit variable cost.

12. a.

| |Year 0 |Years 1-10 |

|Investment |¥30 B | |

|1. Revenue | |¥37.500 B |

|2. Variable Cost | |26.000 |

|3. Fixed Cost | |3.000 |

|4. Depreciation | |3.000 |

|5. Pre-tax Profit (1-2-3-4) | |¥5.500 |

|6. Tax | |2.750 |

|7. Net Operating Profit (5-6) | |¥2.750 |

|8. Operating Cash Flow (4+7) | |5.750 |

|NPV = |+ ¥5.33 B |

b.

| |Inflows |Outflows | | | |

|Unit Sales |Revenues |Investment |V. Costs |F. Cost |Taxes |PV |PV |NPV |

|(000’s) |Yrs 1-10 |Yr 0 |Yr 1-10 |Yr 1-10 |Yr 1-10 |Inflows |Outflows | |

|0 |0.00 |30.00 |0.00 |3.00 |-3.00 |0.00 |-30.00 |-30.00 |

|100 |37.50 |30.00 |26.00 |3.00 |2.75 |230.42 |-225.09 |5.33 |

|200 |75.00 |30.00 |52.00 |3.00 |8.50 |460.84 |-420.18 |40.66 |

Note that the break-even point can be found algebraically as follows:

NPV = -Investment + [(PVA10/10%) ( (t ( Depreciation)] +

[Quantity ( (Price – V.Cost) – F.Cost]((1 – t)((PVA10/10%)

Set NPV equal to zero and solve for Q:

|Proof: | | |

|1. Revenue | |¥31.84 B |

|2. Variable Cost | |22.08 |

|3. Fixed Cost | |3.00 |

|4. Depreciation | |3.00 |

|5. Pre-tax Profit | |¥3.76 B |

|6. Tax | |1.88 |

|7. Net Profit | |¥1.88 |

|8. Operating Cash Flow | |¥4.88 |

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c. The break-even point is the point where the present value of the cash flows, including the opportunity cost of capital, yields a zero NPV.

d. To find the level of costs at which the project would earn zero profit, write the equation for net profit, set net profit equal to zero, and solve for variable costs:

Net Profit = (R – VC – FC - D) ( (1 – t)

0 = (37.5 – VC – 3.0 – 1.5) ( 0.50

VC = 33.0

This will yield zero profit.

Next, find the level of costs at which the project would have zero NPV. Using the data in Table 11.1, the equivalent annual cash flow yielding a zero NPV would be:

¥15 B/PVA10/10% = ¥2.4412 B

If we rewrite the cash flow equation and solve for the variable cost:

NCF = [(R – VC – FC – D) ( (1 – t)] + D

2.4412 = [(37.5 – VC – 3.0 – 1.5) ( 0.50] + 1.5

VC = 31.12

This will yield NPV = 0, assuming the tax credits can be used elsewhere in the company.

e. DOL = 1 + (fixed costs / profit)

Fixed costs rise 1.5 due to additional depreciation of the 15 billion yen investment. Profits increase by 0.4 reflecting the lower variable costs.

This gives us a DOL = 1 + ((3 + 1.5 + 1.5) / 3.4) = 2.76

13. If Rustic replaces now rather than in one year, several things happen:

i. It incurs the equivalent annual cost of the $9 million capital investment.

ii. It reduces manufacturing costs.

For example, for the “Expected” case, analyzing “Sales” we have (all dollar figures in millions):

i. The economic life of the new machine is expected to be 10 years, so the equivalent annual cost of the new machine is:

$9/5.6502 = $1.59

ii. The reduction in manufacturing costs is:

0.5 ( $4 = $2.00

Thus, the equivalent annual cost savings is:

–$1.59 + $2.00 = $0.41

Continuing the analysis for the other cases, we find:

| | |Equivalent Annual Cost Savings (Millions) |

| | |Pessimistic | |Expected | |Optimistic |

|Sales | |0.01 | |0.41 | |1.21 |

|Manufacturing Cost | |-0.59 | |0.41 | |0.91 |

|Economic Life | |0.03 | |0.41 | |0.60 |

14. [pic]

Operating profits are unchanged in all scenarios, as we have just shifted the nature of the costs.

With $33 million in variable costs, DOL [pic]

With $33 million in fixed costs, DOL [pic]

15. a. [pic]

For a 1% increase in sales, from 100,000 units to 101,000 units:

[pic]

b. [pic]

[pic]

c. [pic]

For a 1% increase in sales, from 200,000 units to 202,000 units:

[pic]

16.

17. Problem requires use of Excel program; answers will vary.

18. a. Timing option

b. Expansion option

c. Abandonment option

d. Production option

19. Working from right to left, the following spreadsheet calculates a weighted average NPV of 119 at the start of Phase 3 trials.

|Weighted NPV |Prob. of |NPV with abandonment |Resulting NPV with|Phase III results |PV if successful|Probability of |

| |outcome | |130 investment; r | | |Phase III success|

| | | |= 9.6% | | | |

|39 |5% |781 |781 |Blockbuster |1500 |80% |

|59 |20% |295 |295 |Above average |700 |80% |

|21 |40% |52 |52 |Average |300 |80% |

|0 |25% |0 |-69 |Below Average |100 |80% |

|0 |10% |0 |-106 |Dog |40 |80% |

|119 | | | | | | |

We can calculate the NPV at the initial investment decision as follows:

[pic]

So the investment remains positive.

20. Working from right to left, the following spreadsheet shows that the weighted average NPV at the start of the Phase 3 trials increases to $146 million with the higher upside PV.

|Weighted NPV |Prob. of |NPV with abandonment |Resulting NPV with|Phase III results |PV if successful|Probability of |

| |outcome | |130 investment; r | | |Phase III success|

| | | |= 9.6% | | | |

|119 |25% |478 |478 |Upside |1000 |80% |

|26 |50% |52 |52 |Most likely |300 |80% |

|0 |25% |0 |-69 |downside |100 |80% |

|146 | | | | | | |

We can calculate the NPV at the initial investment decision as follows:

[pic]

The project is still positive but NPV has fallen, showing that the extra $20 million investment is not worthwhile. Decreasing the probability of phase III success to 75% results in the following calculations:

|Weighted NPV |Prob. of |NPV with abandonment |Resulting NPV with|Phase III results |PV if successful|Probability of |

| |outcome | |130 investment; r | | |Phase III success|

| | | |= 9.6% | | | |

|110 |25% |440 |440 |Upside |1000 |75% |

|20 |50% |41 |41 |Most likely |300 |75% |

|0 |25% |0 |-73 |downside |100 |75% |

|130 | | | | | | |

[pic]

So the R&D proposal is still not worthwhile.

21.

a.

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b. Analyze the decision tree by working backwards. If we purchase the piston plane and demand is high:

• The NPV at t = 1 of the ‘Expand’ branch is:

• The NPV at t = 1 of the ‘Continue’ branch is:

Thus, if we purchase the piston plane and demand is high, we should expand further at t = 1. This branch has the highest NPV.

c. Continuing the analysis, if we purchase the piston plane and demand is low:

• The NPV of the ‘Continue’ branch is:

• We can now use these results to calculate the NPV of the ‘Piston’ branch at t = 0:

• Similarly for the ‘Turbo’ branch, if demand is high, the expected cash flow at t = 1 is:

(0.8 ( 960) + (0.2 ( 220) = $812

• If demand is low, the expected cash flow is:

(0.4 ( 930) + (0.6 ( 140) = $456

• So, for the ‘Turbo’ branch, the combined NPV is:

[pic]

Therefore, the company should buy the Piston-engine plane today.

d. To determine the value of the option to expand, we first compute the NPV without the option to expand:

[pic]

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Therefore, the value of the option to expand is: $117 – $52 = $65

22. Problem requires use of Crystal Ball software simulation; answers will vary.

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Pilot production and market tests

Observe demand

Low demand (50% probability)

Stop:

NPV = $0

[ For full-scale production:

NPV = -1000 + (75/0.10)

= -$250 ]

High demand (50% probability)

Invest in full-scale production:

NPV = -1000 + (250/0.10)

= +$1,500

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