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Discounted Cash Flow Techniques

Chapter Seven

Higgins, Analysis for Financial Management, 12e

Capital Budgeting

The future of a company lies in the investments it makes today.

Weigh outlay today vs. expected future benefits

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Higgins, Analysis for Financial Management, 12e

DCF

Discounted cash flow analysis is the backbone of modern finance.

DCF is used to evaluate cash flow streams whose costs and/or benefits extend beyond the current year.

Why DCF techniques are important

Many corporate activities involve costs and benefits extending over time.

Adjustments for the time value of money are critical.

Allow for a measurement of shareholder value creation

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Higgins, Analysis for Financial Management, 12e

Figures of Merit

Three-step procedure:

Estimate the relevant cash flows.

Calculate a figure of merit for the investment, summarizing the investment’s economic worth.

Compare the figure of merit to an acceptance criterion.

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Higgins, Analysis for Financial Management, 12e

Estimating Cash Flows

The first step is challenging.

Doing it well requires a thorough understanding of the company’s markets, competitive position, and long-run intentions.

Potential estimation difficulties relate depreciation, financing costs, working capital investments, shared resources, excess capacity, and contingent opportunities.

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Higgins, Analysis for Financial Management, 12e

A Simple Example

We will return to the issue of estimating cash flows later.

To begin, let’s consider a simple example where the cash flows are given.

We will consider various possible figures of merit for this investment.

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Higgins, Analysis for Financial Management, 12e

TABLE/FIGURE 7.1 Cash Flows for Container-Loading Pier ($ millions)

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Higgins, Analysis for Financial Management, 12e

Payback Period and Accounting Rate of Return

The payback period is the amount of time the company must wait before recouping its original investment.

The pier’s payback period: 40/7.5 = 5⅓

The accounting rate of return is the ratio of annual average cash flow to total cash outflow.

The pier’s accounting rate of return: [(7.5 × 9 + 17)/10]/40 = 21.1%

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Higgins, Analysis for Financial Management, 12e

Problems with These Figures of Merit

The payback period ignores cash flows after payback, and also ignores the time value of money.

The payback period is sometimes useful as a rough guide to project risk.

The accounting rate of return ignores the timing of cash flows.

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Higgins, Analysis for Financial Management, 12e

Time Value of Money

Reasons why a dollar today can be worth more than a dollar in the future:

Inflation

Uncertainty

Opportunity cost

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Higgins, Analysis for Financial Management, 12e

Compounding and Discounting

Future value received in a year from $1 invested today at 10% is $1.10.

Present value of $1.10 to be paid in a year when the interest rate is 10% is $1.

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Higgins, Analysis for Financial Management, 12e

Two Years

With compounding, future value received in 2 years from $1 invested today at 10% is

$1.21 = 1 × 1.1 × 1.1

In reverse, the present value of $1.21 to be paid in two years when the interest rate is 10% is obtained by

1.21/1.12 = 1

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Higgins, Analysis for Financial Management, 12e

By Extension to t Years

By extension from 2 years to t years.

Divide by 1.1t in the present value formula.

Or, more generally, divide by (1+r)t, where r is the discount rate

Multiply by 1.1t in the future value formula.

Or, more generally, multiple by (1+r)t, where r is the discount rate

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Higgins, Analysis for Financial Management, 12e

Ch. 5 14

You try it. Compounding and discounting cash flows.

Your employer promises you a bonus of $10,000 in 3 years. If your discount rate is 6%, what is the present value of this bonus?

You invest $5,000 in a savings account that pays 3% annually. How much will you have in the account in 10 years?

Higgins, Analysis for Financial Management, 12e

10,000/1.063 = $8,396.19

5,000 × 1.0310 = $6.719.58

Interpretation of Discount Rate

If a company has cash on hand, the discount rate reflects the company’s opportunity cost of capital.

If a company raises the cash externally, the discount rate measures the investor’s opportunity cost of capital.

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Higgins, Analysis for Financial Management, 12e

PMT

4 … n

…

Solving Present Value Problems with Calculators or Spreadsheets

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Higgins, Analysis for Financial Management, 12e

Using a calculator to find the future value of a $100 in 22 years, at an interest rate of 7%

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Why is the answer negative?

Higgins, Analysis for Financial Management, 12e

Using a spreadsheet to find the future value of a $100 in 22 years, at an interest rate of 7%

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Why are there brackets around these variables?

Higgins, Analysis for Financial Management, 12e

Ch. 5 19

You try it. Find the present value of an annuity.

What is the present value of $1,000 to be received at the end of each the next 20 years if the discount rate is 12%?

Higgins, Analysis for Financial Management, 12e

=PV(0.12,20,1000) = -7,469.44

N=20, I/YR=12, PMT=1,000, FV=0, answer is PV=-7,469.44

Equivalence

Two cash flow streams with the same present value can be transformed into each other.

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Higgins, Analysis for Financial Management, 12e

Example of Equivalence

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A contract that pays $2 million per year for 4 years has a present value of $5.71 million at a 15% discount rate.

The chart below shows how $5.71 million can be transformed into the cash flows from the contract.

Higgins, Analysis for Financial Management, 12e

Net Present Value

Net present value is the present value of the future expected cash flows minus the initial investment.

NPV measures the amount of value creation.

Decision Rule: Accept projects with NPV>0, reject projects with NPV<0.

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Higgins, Analysis for Financial Management, 12e

NPV of the Container Pier Project

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NPV = $49.75 million - $40 million = $9.75 million

Higgins, Analysis for Financial Management, 12e

Benefit-Cost Ratio

The BCR is also known as the profitability index.

The BCR of the container pier project is:

49.75/40 = 1.24

Decision Rule: Accept projects with BCR>1, reject projects with BCR<1.

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Higgins, Analysis for Financial Management, 12e

Internal Rate of Return

The internal rate of return (IRR) is “the” discount rate that makes the PV of a stream of cash flows equal to zero.

Loosely speaking, the IRR can be regarded as the rate of return associated with the cash flows.

Decision Rule: Accept projects with IRR>K, reject projects with IRR<K. (K = cost of capital)

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Higgins, Analysis for Financial Management, 12e

TABLE 7.2 NPV of Container Pier at Different Discount Rates

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Higgins, Analysis for Financial Management, 12e

FIGURE 7.2 NPV of Container Pier at Different Discount Rates

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Higgins, Analysis for Financial Management, 12e

Uneven Cash Flows

If the payment is not the same in every period, then we use different functions.

Instead of the spreadsheet functions PV or RATE, use NPV or IRR.

With a calculator, use the Cash Flow keys (e.g., CFj) instead of the Annuity keys (N, I/YR, PMT, etc.)

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Higgins, Analysis for Financial Management, 12e

Example of Uneven Cash Flows

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Higgins, Analysis for Financial Management, 12e

TABLE 7.3 Finding the IRR and NPV with Uneven Cash Flows

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Why is the first value B4 instead of B3?

Higgins, Analysis for Financial Management, 12e

Ch. 5 31

You try it. Find the NPV and IRR of this project.

Higgins, Analysis for Financial Management, 12e

=NPV(B4,C2:G2)+B2 = 599.37

=IRR(B2:G2) = 50.2%

Applications and Extensions: Bond Valuation

Par value of $1,000

Coupon rate of 8%

Maturity is 9 years

Required return is 7%

PV = $1,065.15

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Why is the present value higher than the par value?

Higgins, Analysis for Financial Management, 12e

Ch. 5 33

You try it. Bond valuation.

Wells Fargo has a $1,000 par value bond that matures in 9 years and carries a coupon rate of 4.95% (assume annual coupon payments). If the appropriate discount rate is 4.0%, what is the value of the Wells Fargo bond?

Higgins, Analysis for Financial Management, 12e

=PV(0.04,9,49.5,1000) = -1,070.64

Applications and Extensions: IRR of a Perpetuity

Formula for PV of a perpetuity (A=annual payment, r=discount rate):

Solving for r gives the IRR of a perpetuity:

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Higgins, Analysis for Financial Management, 12e

Applications and Extensions: Equivalent Annual Cost

The equivalent annual cost is an annuity payment that has the same present value as the actual cash flows on an investment.

Example: What annual lease payment would have to be charged to recover the cost of the $40 million container pier (assume a life of 12 years and a $4 million residual value at the end of 12 years).

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Higgins, Analysis for Financial Management, 12e

Mutually Exclusive Alternatives

Situation: there is more than one way to accomplish an objective, and the investment problem is to select the best alternative.

When investments are independent, all three figures of merit—NPV, IRR, BCR—will generate the same investment decision.

With mutually exclusive investments, this is no longer true.

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Higgins, Analysis for Financial Management, 12e

Capital Rationing

Situation: The decision maker has a fixed investment budget that is not to be exceeded.

Task is to rank the opportunities according to their investment merit.

Capital rationing can alter the ranking of alternative independent investments.

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Higgins, Analysis for Financial Management, 12e

IRR in Perspective

IRR has more intuitive appeal than NPV and BCR.

IRR can sometimes allow the decision maker to sidestep the question of what is the right discount rate for the investment.

At the same time, there might be multiple values for IRR, or no IRR at all.

IRR might be invalid for analyzing mutually exclusive alternatives under capital rationing.

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Higgins, Analysis for Financial Management, 12e

Determining the Relevant Cash Flows

Two principles:

Cash flow principle: time stamp cash flows, recording them when they actually occur.

With-without principle: record only cash flow differences that occur because an investment is made as opposed to not made.

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Higgins, Analysis for Financial Management, 12e

Example

Consider Table 7.4, showing forecasted costs and benefits for a project introducing a new line of smartphones.

The Capital Expenditure Review Committee attacked the proposal from all sides.

Where are the problems?

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Higgins, Analysis for Financial Management, 12e

Structure of Table 7.4

Top portion shows initial investment and anticipated salvage value.

Center portion shows forecasted income statement.

Bottom portion shows “Free Cash Flow.”

FCF = Earnings after tax + Noncash charges − Investment

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Higgins, Analysis for Financial Management, 12e

TABLE 7.4 Division Financial Analysis of New Line of Smartphones ($ millions)

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Higgins, Analysis for Financial Management, 12e

Depreciation

Is it OK to subtract depreciation from gross profit to compute profit after tax?

Is physical depreciation captured by salvage value being less than the initial investment?

Does including both depreciation and salvage value amount to double counting?

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Higgins, Analysis for Financial Management, 12e

Tax

Depreciation is relevant for computing tax.

After-tax cash flow = Operating income − Taxes

Deduct depreciation to compute tax and then add it back to find relevant cash flow ATCF (investment’s after-tax cash flow).

The next slide illustrates the concept.

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Higgins, Analysis for Financial Management, 12e

The Two-Step Treatment of Depreciation when Calculating After-tax Cash Flow (ATCF)

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Higgins, Analysis for Financial Management, 12e

Working Capital and Spontaneous Sources

The with-without principle indicates that changes in working capital that are the result of an investment decision are relevant to the decision.

Working capital needs typically fluctuate with sales.

Working capital investments typically have large salvage values, with associated inflows approximately as large as the outflows.

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Higgins, Analysis for Financial Management, 12e

Calculating the Investment in Working Capital

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Higgins, Analysis for Financial Management, 12e

Sunk Costs

The with-without principle implies that sunk costs are not part of project cash flows.

They might need to be recorded, but elsewhere.

Psychologically difficult to ignore sunk costs.

In some circumstances, it will have been unwise to adopt a project, but once undertaken, it is appropriate to continue the project.

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Higgins, Analysis for Financial Management, 12e

Allocated Costs

Bearing the fair share of overhead?

With-without principle says to ignore allocated overhead because it’s fixed.

The problem is that, over time, overhead might not be fixed but may indeed vary with the size of the business.

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Higgins, Analysis for Financial Management, 12e

Cannibalization

Should we account for the fact that sales of the new product will eat into sales of old products?

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Higgins, Analysis for Financial Management, 12e

Excess Capacity

Is the use of excess capacity free?

If the excess capacity has no alternative use, then that is the case.

If using the excess capacity prevents the generation of cash flows from an alternative, then the with-without principle indicates that the foregone cash flows should be part of the analysis to reflect the opportunity cost.

Often important to link to future decisions.

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Higgins, Analysis for Financial Management, 12e

Financing Costs

Financing costs refer to any dividend, interest, or principal payments associated with financing an investment.

The standard procedure is to reflect the cost of money in the discount rate and ignore financing costs in the cash flow projections.

This issue comes up again in the next chapter.

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Higgins, Analysis for Financial Management, 12e

Revised Smartphone Proposal

The following table (7.5) presents the revised figures for the project proposal.

The bold figures reflect changes stemming from the treatment of depreciation, working capital, sunk costs, interest expenses, allocated expenses, and excess capacity.

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Higgins, Analysis for Financial Management, 12e

TABLE 7.5 Revised Financial Analysis of New Line of Smartphones ($ millions)

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Higgins, Analysis for Financial Management, 12e

TABLE 7.5 Revised Financial Analysis of New Line of Smartphones ($ millions) (cont.)

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Higgins, Analysis for Financial Management, 12e

Ch. 5 56

You try it. Find the project NPV.

Anwar Corporation is considering a new project to manufacture solar calculators.

The project is expected to generate $2.5 million in incremental revenues and $0.6 million in incremental operating expenses each year for 5 years.

The project will require an initial expenditure of $5 million for new equipment. The machinery will be depreciated straight line to a salvage value of $0 over 5 years.

The project will require a one-time increase in working capital of $0.5 million in year 0.

The tax rate is 30%; the appropriate discount rate is 12%.

Higgins, Analysis for Financial Management, 12e

This is a long problem, so the solution is on the next slide.

Ch. 5 57

You try it. Solution

Higgins, Analysis for Financial Management, 12e

APPENDIX: Mutually Exclusive Alternatives and Capital Rationing

When investments are independent, the decision to accept or reject is the same regardless of which figure of merit is employed.

When investments are mutually exclusive, the decision task is not as simple.

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Higgins, Analysis for Financial Management, 12e

Example of Mutually Exclusive Projects

Figure 7A-1 illustrates two alternative projects, an inexpensive option and an expensive option.

At the bottom of the figure, the three figures of merit are displayed.

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Higgins, Analysis for Financial Management, 12e

FIGURE/TABLE 7A.1 Alternative Service Station Designs

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Since the projects are mutually exclusive, which should be chosen?

Higgins, Analysis for Financial Management, 12e

NPV

Although the inexpensive option has higher IRR and BCR, it is NPV that is the criterion that is relevant.

NPV measures total value creation, not value creation per dollar invested.

BCR and IRR are insensitive to the scale of the investment.

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Higgins, Analysis for Financial Management, 12e

Unequal Lives

In the previous example, the two projects had the same lives.

What happens if they have different lives?

Suppose alternative #1 has a lower initial cost, higher maintenance costs, and a shorter life than alternative #2.

Straight NPV is not apples-to-apples comparison because the time frames are different, and some cash flows are implicitly neglected.

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Higgins, Analysis for Financial Management, 12e

What to Do?

Restructure the problem with a common investment horizon to factor in omitted cash flows, such as replacement for alternative #1 at the end of its life.

Compute equivalent annual cost in an attempt to measure apples-to-apples.

Beware of hidden assumptions when doing either, such as inflation, changing prices, etc.

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Higgins, Analysis for Financial Management, 12e

Capital Rationing

Table 7A.2 describes 4 investments to analyze in a capital rationing decision environment.

The capital budget is capped at $200K.

One approach is to rank order alternative investments by BCR, and proceed down the list until the budget is exhausted or BCR falls below 1.

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Higgins, Analysis for Financial Management, 12e

TABLE 7A.2 Four Independent Investment Opportunities under Capital Rationing

(Capital Budget = $200,000)

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Higgins, Analysis for Financial Management, 12e

Fractional Investments

The “rank by BCR” rule will work if fractional investments are possible.

For example, choose C, D, and 7/12 of B.

Otherwise, it is typically necessary to look at every possible configuration of projects selected to choose the one that creates the most value.

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Higgins, Analysis for Financial Management, 12e

Additional Issues

What’s wrong with just ranking by NPV?

In this setting, the goal is to maximize total NPV across project configurations, but because of the different investment amounts, doing so requires looking at NPV per dollar first.

This is what BCR does.

Be careful about IRR, because it does not always give the same answer as BCR.

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Higgins, Analysis for Financial Management, 12e

Future Opportunities

Keep in mind that budgets apply over time periods, not just at points in time.

Therefore, focus on future opportunities as well as current opportunities, since undertaking an investment today can preclude undertaking a better investment in the future if they fall within the same budgeting period.

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Higgins, Analysis for Financial Management, 12e

A Decision Tree

Figure 7A.2 provides a capsule summary of the key points involved in choosing an appropriate figure of merit.

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Higgins, Analysis for Financial Management, 12e

FIGURE 7A.2 Capital Budgeting Decision Tree

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Higgins, Analysis for Financial Management, 12e

Operating income $20

Less Depreciation 3

Profit before tax 17

Less Tax at 40% 7

Income after tax 10

Plus Depreciation 3

Aftertax cash flow $13

Operating income	$20
Less Depreciation	3
Profit before tax	17
Less Tax at 40%	7
Income after tax	10
Plus Depreciation	3
Aftertax cash flow	$13

Year012345

Initial cost5.00

Inc. working capital0.50 (0.50)

Revenue2.50 2.50 2.50 2.50 2.50

Expenses0.60 0.60 0.60 0.60 0.60

Depreciation1.00 1.00 1.00 1.00 1.00

Income before tax- 0.90 0.90 0.90 0.90 0.90

Income after tax- 0.63 0.63 0.63 0.63 0.63

Free cash flow(5.50) 1.63 1.63 1.63 1.63 2.13

NPV @ 12%0.66

Sheet1

Year	0	1	2	3	4	5
Initial cost	5.00
Inc. working capital	0.50					(0.50)
Revenue		2.50	2.50	2.50	2.50	2.50
Expenses		0.60	0.60	0.60	0.60	0.60
Depreciation		1.00	1.00	1.00	1.00	1.00
Income before tax	- 0	0.90	0.90	0.90	0.90	0.90
Income after tax	- 0	0.63	0.63	0.63	0.63	0.63
Free cash flow	(5.50)	1.63	1.63	1.63	1.63	2.13
NPV @ 12%	0.66