How to Analyze Investment Projects

Instructor’s ManualChapter 6 Page 1

CHAPTER 6

HOW TO ANALYZE INVESTMENT PROJECTS

Objectives

To show how to use discounted cash flow analysis to make investment decisions such as:

Whether to enter a new line of business
Whether to invest in equipment to reduce operating costs

Outline

6.1The Nature of Project Analysis

6.2Where Do Investment Ideas Come From?

6.3The Net Present Value Investment Rule

6.4Estimating a Project’s Cash Flows

6.5Cost of Capital

6.6Sensitivity Analysis Using Spreadsheets

6.7Analyzing Cost-Reducing Projects

6.8Projects with Different Lives

6.9Ranking Mutually Exclusive Projects

6.10Inflation and Capital Budgeting

Summary

The unit of analysis in capital budgeting is the investment project. From a finance perspective, investment projects are best thought of as consisting of a series of contingent cash flows over time, whose amount and timing are partially under the control of management.

The objective of capital budgeting procedures is to assure that only projects which increase shareholder value (or at least do not reduce it) are undertaken.

Most investment projects requiring capital expenditures fall into three categories: new products, cost reduction, and replacement. Ideas for investment projects can come from customers and competitors, or from within the firm’s own R&D or production departments.

Projects are often evaluated using a discounted cash flow procedure wherein the incremental cash flows associated with the project are estimated and their NPV is calculated using a risk-adjusted discount rate which should reflect the risk of the project.

If the project happens to be a “mini-replica” of the assets currently held by the firm, then management should use the firm’s cost of capital in computing the project’s net present value. However, sometimes it may be necessary to use a discount rate which is totally unrelated to the cost of capital of the firm’s current operations. The correct cost of capital is the one applicable to firms in the same industry as the new project.

It is always important to check whether cash flow forecasts have been properly adjusted to take account of inflation over a project’s life. There are two correct ways to make the adjustment:

Use the nominal cost of capital to discount nominal cash flows.
Use the real cost of capital to discount real cash flows.

Solutions to Problems at End of Chapter

1.Your firm is considering two investment projects with the following patterns of expected future net after-tax cash flows:

Year / Project A / Project B
1 / $1 million / $5 million
2 / 2 million / 4 million
3 / 3 million / 3 million
4 / 4 million / 2 million
5 / 5 million / 1 million

The appropriate cost of capital for both projects is 10%.

If both projects require an initial outlay of $10 million, what would you recommend and why?

SOLUTION:

Year / Project A / Present Values of A @ 10% / Project B / Present Values of B@ 10%
1 / $1 million / 909,091 / $5 million / 4,545,454
2 / 2 million / 1,652,893 / 4 million / 3,305,785
3 / 3 million / 2,253,944 / 3 million / 2,253,944
4 / 4 million / 2,732,054 / 2 million / 1,366,027
5 / 5 million / 3,104,607 / 1 million / 620,921
Total PV / 10,652,589 / 12,092,132
NPV / 652,589 / 2,092,132

Project B is better than A because it has a higher NPV, a result of paying cash earlier.

Investing in Cost-Reducing Equipment

2.A firm is considering investing $10 million in equipment which is expected to have a useful life of four years and is expected to reduce the firm’s labor costs by $4 million per year. Assume the firm pays a 40% tax rate on accounting profits and uses the straight line depreciation method. What is the after-tax cash flow from the investment in years 1 through 4? If the firm’s hurdle rate for this investment is 15% per year, is it worthwhile? What are the investment’s IRR and NPV?

SOLUTION:

We have to find the incremental cash flows resulting from this investment. There are two methods that we can use to find the after tax cash flow.

1. Find the (incremental) net income, then add (incremental) depreciation. Hence:

Annual depreciation (using straight-line method) = $10MM/4 = $2.5MM

Pretax income increases by: $4MM - $2.5MM = $1.5MM

Net income increase by : 1.5x(1-0.4) = $0.9MM

Adding back depreciation (non cash expense): OCF = 0.9 + 2.5 = $3.4MM

2. Add the depreciation tax shield to the after-tax incremental cost saving. Hence, the yearly OCF from year 1 to 4 is: 4x(1-0.4) + 2.5x0.4 = $3.4MM

Year / CFI
0 / -$10MM
1 / +$3.4MM
2 / +$3.4MM
3 / +$3.4MM
4 / +$3.4MM

At 15% discount rate:

NPV = -$293,073MM. The NPV is negative, hence the investment is not worthwhile taking.

IRR = 13.54%. The IRR is less than the cost of capital (15%) of the project. Again, don’t take the project.

Investing in a New Product

3.Tax-Less Software Corporation is considering an investment of $400,000 in equipment for producing a new tax preparation software package. The equipment has an expected life of 4 years. Sales are expected to be 60,000 units per year at a price of $20 per unit. Fixed costs excluding depreciation of the equipment are $200,000 per year, and variable costs are $12 per unit. The equipment will be depreciated over 4 years using the straight line method with a zero salvage value. Working capital requirements are assumed to be 1/12 of annual sales. The market capitalization rate for the project is 15% per year, and the corporation pays income tax at the rate of 34%. What is the project’s NPV? What is the breakeven volume?

SOLUTION:

Sales revenue will be: $20 per unit x 60,000 units per year = $1,200,000 per year

Investment in working capital = 1/12 x $1,200,000 = $100,000

The total investment is $500,000: $400,000 for the equipment and $100,000 in working capital.

Depreciation = $400,000/4 = $100,000 per year

Total annual operating costs = $12 per unit x 60,000 units per year + $300,000 = $1,020,000 per year

The expected annual net cash flow can be derived using the formula:

CF = net income + depreciation

= (1 - tax rate)(Revenue - total operating costs) + depreciation

= .66 x ($1,200,000 - $1,020,000) + $100,000

= $218,800 per year

Year / CFI
0 / -500,000
1 / +218,800
2 / +218,800
3 / +218,800
4 / +318,800

At a 15% hurdle rate: NPV = $181,845

In order for the NPV to be 0, what must the cash flow from operations be?

n / I / PV / FV / PMT / Result
4 / 15 / –500,000 / 100,000 / ? / PMT = $155,106

Now we must find the number of units per year (Q), that corresponds to an operating cash flow of this amount. A little algebra reveals that the breakeven level of Q is units per year:

CASH FLOW = NET PROFIT + DEPRECIATION

= .66(8Q – 300,000) + 100,000 = 155,106

= .66(8Q – 300,000) = 55,106

8Q – 300,000 = 55,106/.66 = 83,493.94

Q = 383,493.94 = 47,937 units per year

Note that computing the accounting breakeven quantity gives:

Breakeven quantity = fixed costs/contribution margin

QB = F

P - V

QB = $300,000 per year = 37,500 units per year

$8 per unit

Investing in a New Product

4.Healthy Hopes Hospital Supply Corporation is considering an investment of $500,000 in a new plant for producing disposable diapers. The plant has an expected life of 4 years. Sales are expected to be 600,000 units per year at a price of $2 per unit. Fixed costs excluding depreciation of the plant are $200,000 per year, and variable costs are $1.20 per unit. The plant will be depreciated over 4 years using the straight line method with a zero salvage value. The hurdle rate for the project is 15% per year, and the corporation pays income tax at the rate of 34%.

Find:

a.The level of sales that would give a zero accounting profit.

b.The level of sales that would give a 15% after-tax accounting rate of return on the $500,000 investment.

The IRR, NPV, and payback period (both conventional and discounted) if expected sales are 600,000 units per year.
The level of sales that would give an NPV of zero.

SOLUTION:

The initial investment is $500,000.

Depreciation = $500,000/4 = $125,000 per year

Total annual fixed costs = $200,000 + $125,000 per year = $325,000 per year

a.To find the accounting breakeven quantity apply the breakeven formula:

Breakeven quantity = fixed costs/contribution margin

QB = F

P - V

QB = $325,000 per year = 406,250 units per year

$.80 per unit

b.To earn a 15% accounting ROI, the after tax profit (net income) has to be:.15 x $500,000 = $75,000

That means before-tax profit has to be $75,000/.66 = $113,636.

To earn this additional profit, the new breakeven quantity must increase by:

142,045 units per year (required profit before taxes/ contribution margin = $113,636/$.80) to a total of 548,295 per year.

c.If 600,000 units per year can be sold, then the expected annual net cash flow can be derived using the formula:

CF = net income + depreciation

= (1 - tax rate)(Revenue - total operating costs) + depreciation

= .66 x ($1,200,000 - $720,000 - $325,000) + $125,000

= $227,300 per year

n / i / PV / FV / PMT / Result
4 / 15 / ? / 0 / 227,300 / PV = $648,937
4 / ? / -500,000 / 0 / 227,300 / IRR = 29.09%
? / 15 / -500,000 / 0 / 227,300 / n = 2.87 years

NPV =$648,937 - $500,000 = $148,937

Conventional payback period = $500,000/$227,300 per year = 2.2years

d.In order for the NPV to be 0, what must the cash flow from operations be?

n / i / PV / FV / PMT / Result
4 / 15 / –500,000 / 0 / ? / PMT = $175,133

Now we must find the number of units per year (Q), that corresponds to an operating cash flow of this amount. A little algebra reveals that the breakeven level of Q is units per year:

CASH FLOW = NET PROFIT + DEPRECIATION

= .66(.8Q – 325,000) + 125,000 = 175,133

= .66(.8Q – 325,000) = 50,133

.8Q – 325,000 =50,133/.66 = 75,959

Q =400,959 = 501,199 units per year

Replacement Decision

5.Pepe’s Ski Shop is contemplating replacing its ski boot foam injection equipment with a new machine. The old machine has been completely depreciated but has a current market value of $2000. The new machine will cost $25,000 and have a life of ten years and have no value after this time. The new machine will be depreciated on a straight-line basis assuming no salvage value. The new machine will increase annual revenues by $10,000 and increase annual nondepreciation expenses by $3000.

a.What is the additional after-tax net cash flow realized by replacing the old machine with the new machine? (Assume a 50% tax rate for all income, i.e. the capital gains tax rate on the sale of the old machine is also 50%. Draw a time line.)

b.What is the IRR of this project?

c.At a cost of capital of 12%, what is the net present value of this cash flow stream?

d.At a cost of capital of 12%, is this project worthwhile?

SOLUTION:

a. t ATNCF

0-24,000 = -25,000 + 2000 x (1-0.5)

1,2,...,10 4,750 = (10,000  3,000  2,500)(1  0.5) + 2,500

b.IRR =14.82%

c.NPV = $2,838.56

d. This project is worthwhile because its NPV is positive. Also, its IRR is higher than its cost of capital.

6.PCs Forever is a company that produces personal computers. It has been in operation for two years and is at capacity. It is considering an investment project to expand its production capacity. The project requires an initial outlay of $1,000,000: $800,000 for new equipment with an expected life of four years and $200,000 for additional working capital. The selling price of its PCs is $1,800 per unit, and annual sales are expected to increase by 1,000 units as a result of the proposed expansion. Annual fixed costs (excluding depreciation of the new equipment) will increase by $100,000, and variable costs are $1,400 per unit. The new equipment will be depreciated over four years using the straight line method with a zero salvage value. The hurdle rate for the project is 12% per year, and the company pays income tax at the rate of 40%.

a.What is the accounting break-even point for this project?

b.What is the project’s NPV?

c.At what volume of sales would the NPV be zero?

SOLUTION:

a.To find the accounting break-even quantity, apply the break-even formula:

Break-even quantity = total fixed costs/contribution margin

Total fixed costs = fixed costs (cash) + depreciation

The additional fixed costs due to the expansion project are $300,000 (fixed costs + depreciation) per year and the contribution margin is $400 per unit. So the accounting breakeven quantity is 750additional units per year.

b.Increase in Sales Revenue

(1,000 units at a price of $1,800)$1,800,000 per year

Increase in Total Variable Costs

(1,000 units at $1,400) per unit)$1,400,000 per year

Increase in fixed costs excluding depreciation$100,000 per year

Increase in depreciation$200,000 per year

Increase in Total Fixed Costs $300,000 per year

Increase in Annual Operating Profit $100,000 per year

Taxes @ 40% $40,000 per year

Increase in After-tax Operating Profit $60,000 per year

Increase in Net Cash Flow from Operations: 60,000+200,000= $260,000 per year

The initial investment $1,000,000: $800,000 for the equipment and $200,000 for working capital. Using a financial calculator to find the NPV we find:

n / i / PV / FV / PMT
4 / 12 / ? / 200,000 / 260,000

PV=916,814

NPV = PV – $1,000,000

= $916,814 – $1,000,000

= –$83,186

The NPV is negative, hence the project is not worth taking.

c.To find the NPV breakeven value for the incremental cash flow from operations we do the following calculation:

n / i / PV / FV / PMT
4 / 12 / –1,000,000 / 200,000 / ?

PMT = $287,387.55

(Note that the $200,000 terminal value in year 4 is the investment in working capital.)

Now we must find the incremental number of units per year ( Q), that corresponds to an incremental operating cash flow of this amount.

Incremental Cash Flow = Increase in net profit + increase in depreciation

= (1-0.4)x(400 Q – 300,000) + 200,000 = $287,387.55

Q = $445,646 = 1,114.1, the smallest rounded number is 1,115 units per year

400

So the expansion must result in at least 1,115 additional units per year in order to justify the capital outlay.

Inflation and Capital Budgeting

7.Patriots Foundry (PF) is considering getting into a new line of business: producing souvenir statues of Paul Revere. This will require purchasing a machine for $40,000. The new machine will have a life of two years (both actual and for tax purposes) and will have no value after two years. PF will depreciate the machine on a straight-line basis. The firm thinks it will sell 3,000 statues per year at a price of $10 each, variable costs will be $1 per statue and fixed expenses (not including depreciation) will be $2,000 per year. PF’s cost of capital is 10%. All of the foregoing figures assume that there will be no inflation. The tax rate is 40%.

a.What is the series of expected future cash flows?

b.What is the expected net present value of this project? Is the project worth undertaking?

c.What is the NPV breakeven quantity?

Now assume instead that there will be inflation of 6% per year during each of the next two years and that both revenues and nondepreciation expenses increase at that rate. Assume that the real cost of capital remains at 10%.

d.What is the series of expected nominal cash flows?

e.What is the net present value of this project, and is this project worth undertaking now?

f.Why does the NPV of the investment project go down when the inflation rate goes up?

SOLUTION:

a.The expected future net cash flows are:

CF = (1 - tax rate) (revenue - cash expenses) + tax rate x depreciation

CF = .6 x ($30,000 - $3,000 -$2,000) + .4 x $20,000

CF = .6 x $25,000 + .4 x $20,000 = $23,000 in each of the next two years

N / i / PV / FV / PMT / Result
2 / 10 / ? / 0 / 23,000 / 39,917.36

NPV = $39,917.36 - $40,000 = -$82.64

So the project is not worthwhile.

To find the NPV breakeven value for the incremental cash flow from operations we do the following calculation:

N / i / PV / FV / PMT / Result
2 / 10 / -40,000 / 0 / ? / 23,047.62

Now we must find the number of units per year (Q), that corresponds to a net cash flow of this amount.

CF = (1 - tax rate) (Revenue - Cash expenses) + tax rate x Depreciation

= .6(9Q – 5,000) + 20,000x0.4= $23,047.62

9Q – 5,000 = 15,047.62/.6 = 25,079.37

Q = 30,079.37/9 = 3,342.1, the smallest rounded number is 3.343 statues per year

d.Now assume that there will be inflation of 6% per year during each of the next two years and that both revenues and nondepreciation expenses increase at that rate.

CF = .6 x (Revenue - Cash expenses) + .4 x Depreciation

In year 1:

CF1 = .6 x $25,000 x 1.06 + .4 x $20,000 = .6 x $26,500 + .4 x $20,000 = $23,900

In year 2:

CF2 = .6 x $25,000 x 1.062 + .4 x $20,000 = .6 x $28,090 + .4 x $20,000 = $24,854

e.To find the NPV we discount the nominal cash flows at the nominal cost of capital. First we must find the nominal cost of capital:

Nominal cost of capital = (1.06)(1.1) - 1 = .166 or 16.6% per year

The NPV is -40,000 + 23,900/1.166 + 24,854/1.1662 = -$1,221.60

The project is not worthwhile.

f.If all components of the net cash flow increased at the rate of inflation of 6% per year, then the NPV would be unaffected by inflation. But in this case, the depreciation is fixed in dollar terms, so that the depreciation tax saving loses value the higher the rate of inflation.

Understanding incremental cash flows

8.Determine which of the following cash flows are incremental cash flows that should be incorporated into a NPV calculation.

The sale of an old machine, when a company is replacing property, plant, and equipment for a new product launch.
The cost of research and development for a new product concept that was conducted over the past year that is now being put into production.
Potential rental income that was forgone from a previously unused warehouse owned by the company, which is now being used as part of a new product launch.
New equipment purchased for a project.
The annual depreciation expense on new equipment purchased for a project.
Net working capital expenditures of $10 million in year 0, $12 million in year 1 and $5million in year 2.
A dividend payment that was funded in part by a given project’s contribution to the net income for that year.

SOLUTION:

Yes, the sale of the machine is part of the project initiative. Therefore, the proceeds from the sale of the equipment should be counted.
No, the R&D expenditure is a sunk cost that should not be included in the project evaluation. The cost occurred over the past year and must be borne by the company regardless of whether the project is undertaken or not. Sunk costs should never be considered when evaluating a future decision.
Yes, this is an opportunity cost that is being borne by the company. If the warehouse would have remained unused and could have produced rental income then it must be considered as a cost.
Yes, capital expenditures must be incorporated in an NPV analysis.
Yes, annual depreciation is part of incremental cash flows. However, it is the “depreciation tax shield” that is the incremental cash flow and not the actual depreciation expense.
Yes, net working capital is factored into the incremental cash flow. However, it is the “change” in net working capital that is taken into consideration. Therefore, year 0 would have -$10 million that must be added to the operating cash flow for that year. Year 1 would have -$2 million that would need to be added to operating cash flow for that year. Finally, year 3 would show a +$7 million that would need to be added. Remember that in the final year of the project the net working capital figure must be reversed.
No, dividend payments are not incremental cash flows. Whether or not to pay a dividend is the decision of the overall firm and not a cost of an individual project.

9.You have taken a product management position within a major consumer goods firm after graduation. The contract is for four years and your compensation package is as follows:

$5,000 relocation expense
$55,000
$10,000 bonus if annual goals are met
$15,000 additional bonus at the end of four years if your team achieves a given market share

You are confident in your abilities and assume there is a 65% chance in receiving each annual bonus and a 75% chance in receiving the fourth year additional bonus. The effective annual interest rate is 8.5%. What is the net present value of your compensation package.