Corporate Finance, Module 9, Analyzing Corporate Projects

Homework Assignment

(The attached PDF file has better formatting.)

A project has an 8 year life and requires an investment of $40 million.

    Pessimistic    Expected     Optimistic
Market Size    120,000    200,000    250,000
Market Share (%)    20%    25%    30%
Unit Price    $700    $800    $900
Unit Cost    $500    $400    $350
Fixed Cost (Millions)    $10 MM    $8 MM    $6 MM


The marginal tax rate is 35%, the opportunity cost of capital is 14%, and the firm uses straight-line depreciation for tax purposes.

A.    What is the net present value of this project in the expected scenario?
B.    What is the net present value in the pessimistic scenario?
C.    What is the net present value in the optimistic scenario?

Solution Format:

Part A: We show the format for computing the net present value. Fill in the column labeled values for the expected scenario, and make similar tables for the optimistic and pessimistic scenarios.

Description    Calculation Procedure    Value ($000,000)
1. Revenues    200,000 × 25% × $800    
2. Variable cost    200,000 × 25% × $400    
3. Fixed cost    $8,000,000    
4. Depreciation    $40,000,000 / 8    
5. Pretax profit    (1) – (2 + 3 + 4)    
6. Tax    (5) × 0.35    
7. Net profit    (5) – (6)    
8. Net cash flow    (7) + (4)    


Question: Why do we consider depreciation? Depreciation is an accounting item; don’t we focus on cash flows?

Answer: We are not concerned with GAAP (book) depreciation; we are concerned with tax depreciation. We remove the straight line depreciation to compute the pre-tax profit and the federal income taxes; we then add back the depreciation to compute the cash flows.

Question: What is a depreciation tax credit? Don’t we add back only the depreciation times the tax rate?

Answer: For taxable income, we subtract tax depreciation; call this D. The tax liability is taxable income times the tax rate τ; the tax liability is a cash outflow. We add back tax depreciation to get the cash flows. The net effect on cash flows is –D – (–D × τ) + D = + D × τ. The depreciation tax credit is D × τ.

Later modules cover this subject in more detail. Two errors are common: (i) subtracting (instead of adding) the depreciation tax credit and (ii) using D × (1 – τ) as the tax credit.

At 14%, the present value of an 8 year annuity is 4.639. We multiply the net cash flow on the last line of the table by the 4.639 annuity factor and subtract the original investment of $40 million to get the net present value of the project. In practice, the cash flows are rarely the same in all eight years, and we must form a complete spreadsheet with eight years.

Question: How would a financial analyst use this analysis? Why not use expected values for all entries?

Answer: Sales personnel are optimistic; it’s hard to succeed in sales if one isn’t optimistic. The sales department estimates are a mix of optimistic scenarios and average scenarios. The financial analyst must be sure to include the pessimistic scenarios.

Question: Isn’t more important to know net present value analysis than to learn methods of projecting cash flows? For our cash flows analyses, we ask underwriters and agents for best estimates of cash flows; the actuaries work out the net present values.

Answer: We focus in this course on capitalization rates, betas, tax shields, and options. But these are not the major reasons that financial analysts make poor decisions; the major problem is that we can not easily project cash flows.

Instead of just asking the firm about the expected cash flows, the analyst should break up the question into its parts:

●    What are the annual expected sales of the product?
●    How many firms are competing in this industry?
●    What market share do we expect for our firm?
●    What is the anticipated price of the product?
●    What are our variable costs to produce the product?
●    What are our fixed costs to produce the product?

For each of these questions, the analyst takes optimistic and pessimistic values. If expected industry sales are 200,000 units, the analyst may look at values ranging from 150,000 units to 250,000 units. If the firm’s expected market share is 25%, the analyst may look at values ranging from 20% to 30%.

The analyst also examines the sensitivity of the net present value to the values in each line. The analyst may ask: if our market share is 10% lower or higher than expected, what is the effect on the net present value?

Question: Are the cash flow projections for insurance products any different?

Answer: For other products, higher costs are associated with lower market share. If a firm makes cellular phones and can produce them for 20% less than its competitors, it will probably have a higher market share. For auto insurance, costs occur after the policies are sold. Higher than expected loss costs generally mean inadequate premiums. We assume that competitors are charging adequate premiums, so higher than expected loss costs often mean higher market share. Lower than expected loss costs often mean redundant premiums and lower market share. Insurance cash flows projections require a keen understanding of the relation between premium adequacy and market share.

Corpfin, Mod 9: Taxes

Jacob: If income is negative, is the tax liability zero or negative?

Rachel: When we evaluate a project, negative income offsets positive income. Suppose an insurer sells 1,000 personal auto insurance policies. Ten policies have losses of $5,000 apiece and the other 90 policies have gains of $1,000 apiece. The after-tax income is

10 × (–$5,000) × (1 – 35%) + 90 × (+$1,000) × (1 – 35%) = $26,000

Jacob: Does this apply to cohorts as well?

Rachel: Yes. An insurer expects to lose money the first year on a cohort of new business and to recoup the loss in renewal years. The first year loss on one cohort offsets gains on other cohorts.

Jacob: What if the insurer loses money in total? For example, what it Hurricane Katrina causes a net loss for the insurer?

Rachel: The loss may be carried back to the previous two years to offset taxable income in those years; the IRS gives a tax refund.

Jacob: What if the insurer lost money in the previous two years as well?

Rachel: The loss is carried forward and can offset income in future years. One shows a deferred tax asset in GAAP or statutory accounting statements.

Corpfin, Mod 9: Depreciation Tax Credit

Jacob: What is a depreciation tax credit?

Rachel: Suppose a firm buys machinery for $40 million, which last 4 years. It expect to earn $14.5 million a year from the machinery, and its cost of capital is 12% per annum.

If the tax rate is zero, the net present value (in $000,000) is

–40 + 14.5 / 1.12 + 14.5 / 1.12² + 14.5 / 1.12³ + 14.5 / 1.12⁴ = $4.04

If the tax rate is 35% and all cash flows are taxable income (either positive or negative), the net present value is

(1 – 35%) × (–40 + 14.5 / 1.12 + 14.5 / 1.12² + 14.5 / 1.12³ + 14.5 / 1.12⁴) = $2.63

If the tax rate is 35% and the machinery is depreciated 25% each year, the net present value is

–40 + (14.5 / 1.12 + 14.5 / 1.12² + 14.5 / 1.12³ + 14.5 / 1.12⁴) × (1 – 35%)

+ (10 / 1.12 + 10 / 1.12² + 10 / 1.12³ + 10 / 1.12⁴) × 35% = ($0.74)

If the tax rate is 35% and the machinery is depreciated 50% each of the first two year, the net present value is

–40 + (14.5 / 1.12 + 14.5 / 1.12² + 14.5 / 1.12³ + 14.5 / 1.12⁴) × (1 – 35%)

+ (20 / 1.12 + 20 / 1.12²) × 35% = $0.46

The depreciation tax credit is the present value of the tax refunds created by the $10 million or $20 million tax depreciation.

Jacob: Why is this a tax credit? The net present value is greater with no taxes or with all cash flows taxed when they occur.

Rachel: Think of the net present value as no tax offset for buying the machinery and a tax on each year’s income. This gives a low (negative) present value. The tax credit is the savings from depreciation.

If your pretax profit is negative, is the tax zero or is it still 35% (i.e. a tax refund)?

[NEAS: Taxes are paid on corporate income.  Suppose a firm has two projects:

Project A earns $1,000.

Project B earns -$1,000.

The corporate earnings are zero, and the tax liability is zero.  The tax liability on Project A is $350, and the tax liability on Project B is -$350.

If a firm has negative income in total, it has a tax carryback to recover taxes paid in the past two years.  If its negative income exceeds taxes paid in the past two years, it can carry forward the operating loss for the next five years.

The tax laws are complex; they are not needed for this course.  Assume that negative income in a project leads to a tax refund.]

I'm confused about the timing for these figures.  I assume that they are all annual figures for each of the eight years.  Therefore, the fixed cost (Description 3) is annual for each of the eight years.  If so, then the depreciation (4) is 1/8 the first year, 2/8 the second year, and so forth, since a new annual fixed cost is incurred each year.  Is the "Solution Format" provided only meant to calculate the net cash flow (8) for the first year?

Alternatively, if the fixed cost is meant to cover the entire 8 year period, then is the pretax profit (5) meant to cover the 8 years?  If so, then the depreciation should equal the entire fixed cost (1/8 per year times 8 years).

 

The 'solution' gives you the cash flow for each of the eight years.  Assume that everything is constant for each year and that the fixed cost given is for one year (not a total for all years).

What does it mean when it says that the project has an 8 year life? Does it mean that the firm is locked into all 8 years of paying the fixed cost by some contract or similar situation? Or does it mean that the $40 million investment can apply for 8 years in the best-case scenario, and the firm can abandon the project after a bad year and avoid paying either the fixed or unit costs in following years?

[NEAS: The firm expects the project to last eight years, because the equipment lasts eight years or the market for the product lasts eight years. The eight years is an estimate, of course, but firms must make estimates to evaluate profitability. This homework assignment does not involve the real option to abandon a project; it uses present values of future cash flows.]

I get

A. 4.3 million

B. - 47.56 million

C. 74.4 million

Any comments? 

I don't like my answer for B.  After reading Mr. NEAS's reply about negative pre-tax profits, I am still not sure how to compute the tax.  For this homework, is it 0 or is it a refund of 0.35*(negative profit)?

[NEAS: For a single project in a large firm, negative profits offset positive profits in other projects, so negative projects get a 35% tax refund.]

I also have 4.3MM for A, and 74.4MM for C.  Can somebody confirm these answers so that I know that I'm doing these correctly before I try to tackle B.  Thanks

All three of brian's answers are correct in my book.