Analysis 5 and 6

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Cash Discounting Concepts

Learning Objectives

1. Discuss the cash discounting concepts used in risk management applications. (p. 2)

2. Discuss the definitions and differences in the methods used in evaluating capital investment projects. (p. 21)

3. Discuss additional considerations when choosing capital investment projects. (p. 33)

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Learning Objective #1: Discuss the cash discounting concepts used in risk management applications.

I. Cash Discounting

A. Used to prepare cost-benefit analyses to

1. Determine the present value (or today’s value) of a future cash flow and/or

2. Determine the future value (or tomorrow’s value) of today’s cash flow

B. Basic cash discounting concepts

1. Time value of money (TVOM) – the value of money over a given amount of time considering a given amount of interest; refers to the concepts of present value (PV) and future value (FV); subjects discussed include compounding, compounding more than once per year, the present value of a single sum, and the present value of annuities

2. Net present value (NPV) and internal rate of return (IRR) – addresses the capital budgeting techniques used by most organizations to determine whether or not to undertake a long-term commitment of capital to a project; three cash discounting-based approaches to compare the costs of a project to its benefits are outlined: NPV, IRR, and the benefit cost ratio (BCR)

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3. Discount rate/cost of capital – when organizations analyze a long-term commitment of capital to a project, the PV of the benefits is compared to the PV of the cost of the project. The discount rate used to calculate the PV of the benefits is the organization’s average cost of capital, or its weighted cost of capital, commonly referred to as the WACC. The organization’s CFO normally provides the organization’s WACC to the risk manager and/or advises the appropriate discount rate to use.

Commentary

Nearly all organizations have four sources of capital: common stock, preferred stock, long-term debt, and retained earnings. (Exceptions include the so-called “non-profit organizations” and all partnerships do not issue stock, although all organizations have (or should have) some form of retained earnings, even though the number isn’t called that.) Each source of capital has an associated cost. The actual method of calculating the cost of each source is beyond the scope of this course and beyond the responsibility of the risk manager (See Appendix for a detailed explanation). Similarly, the calculation of the WACC is beyond the responsibility of the risk manager, but understanding its make-up is important.

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II. Financial Decisions

A. Financial decisions, including most risk management decisions, involve cash inflows and outflows. When making financial decisions, managers expect the benefits to exceed the costs.

B. Examples of risk management financial decisions

1. Increase or decrease of retention levels

2. Implementation of risk control programs

3. Formation of a captive

C. Because cash inflows and outflows often occur in different time periods, the only way to correctly compare benefits and costs is to use TVOM concepts to determine the PV of the benefits and costs.

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III. Time Value of Money

A. Cash management rules

1. Delay paying what you owe as long as possible without creating legal, operational, or reputational problems

2. Accelerate collecting what is owed to you as quickly as possible without creating legal, operational, or reputational problems

Alternative financing or insurance methods allow the payment of transfer costs at a later time; the longer the delay, the less it costs in current dollars. Therefore, financing options are best evaluated in terms of PV. Note: The discount rate used by the organization (WACC) impacts the value of postponing expenditures. The higher the discount rate, the lower the cost of future expenditures expressed in current dollars (PV).

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B. TVOM Exhibit

Time Line

Present Value Future Value

PV FV

0 1 2 3 4 5

%i n

Interest Number of Periods

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Compound Sum of $1

n* 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12%

1 1.010 1.020 1.030 1.040 1.050 1.060 1.070 1.080 1.090 1.100 1.110 1.120

2 1.020 1.040 1.061 1.082 1.103 1.124 1.145 1.166 1.188 1.210 1.232 1.254

3 1.030 1.061 1.093 1.125 1.158 1.191 1.225 1.260 1.295 1.331 1.368 1.405

4 1.041 1.082 1.126 1.170 1.216 1.262 1.311 1.360 1.412 1.464 1.518 1.574

5 1.051 1.104 1.159 1.217 1.276 1.338 1.403 1.469 1.539 1.611 1.685 1.762

6 1.062 1.126 1.194 1.265 1.340 1.419 1.501 1.587 1.677 1.772 1.870 1.974

7 1.072 1.149 1.230 1.316 1.407 1.504 1.606 1.714 1.828 1.949 2.076 2.211

8 1.083 1.172 1.267 1.369 1.477 1.594 1.718 1.851 1.993 2.144 2.305 2.476

9 1.094 1.195 1.305 1.423 1.551 1.689 1.838 1.999 2.172 2.358 2.558 2.773

10 1.105 1.219 1.344 1.480 1.629 1.791 1.967 2.159 2.367 2.594 2.839 3.106

11 1.116 1.243 1.384 1.539 1.710 1.898 2.105 2.332 2.580 2.853 3.152 3.479

12 1.127 1.268 1.426 1.601 1.796 2.012 2.252 2.518 2.813 3.138 3.498 3.896

13 1.138 1.294 1.469 1.665 1.886 2.133 2.410 2.720 3.066 3.452 3.883 4.363

14 1.149 1.319 1.513 1.732 1.980 2.261 2.579 2.937 3.342 3.797 4.310 4.887

15 1.161 1.346 1.558 1.801 2.079 2.397 2.759 3.172 3.642 4.177 4.785 5.474

16 1.173 1.373 1.605 1.873 2.183 2.540 2.952 3.426 3.970 4.595 5.311 6.130

17 1.184 1.400 1.653 1.948 2.292 2.693 3.159 3.700 4.328 5.054 5.895 6.866

18 1.196 1.428 1.702 2.026 2.407 2.854 3.380 3.996 4.717 5.560 6.544 7.690

19 1.208 1.457 1.754 2.107 2.527 3.026 3.617 4.316 5.142 6.116 7.263 8.613

20 1.220 1.486 1.806 2.191 2.653 3.207 3.870 4.661 5.604 6.727 8.062 9.646

*n = number of periods (not just number of years)

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C. Compound interest

$1,000 deposited in the bank on January 1 at 8% interest compounded annually (i.e., interest is added to principal at end of the period, in year 1, to create new principal). The principal amount on January 1 the next year is calculated below to be $1,080.

Example: PV = $1,000 n = 1 year i = 8% FV = ?

FV = PV(1 + i)n = $1,000 (1.08) = $1,080 FV = $1,080

This can also be solved using the Compound Sum of $1 table (pg. 7).

FV = PV x Compound Sum Factor FV = $1,000 x 1.080 = $1,080

PV FV

%i n

0 1 Years

$1,000 ?

for i = interest and n = years or rate periods

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Examples:

1. Assuming the interest rate is 8% and the period is 5 years, what is the table factor and how does it compare to 8% and 1 year? What do we learn from this?

2. Now, assuming the interest rate is 10% and the period is 1 year, what is the table factor and how does it compare to 1 year and 8%? What do we learn from this?

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3. What if the money is left to compound for 3 years or what is the FV of $1,000 left in the bank for 3 years?

Example: PV = $1,000 n = 3 years i = 8% FV = ?

PV FV

%i n

0 1 2 3Years

3 8%

$1,000 ?

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4. FV of single sum compounded more than once per year

Equation adjustment:

FV = PV(1 + i/m)n x m

Where m = the number of times compounded during a period n = number of periods i = interest rate

Examples:

1. $1,000 at 8% compounded semi-annually for 3 years Use 1/2 the interest rate (.08 ÷ 2 = .04) Twice as often (n x m = 3 × 2 = 6) FV = $1,000 (1 + .04)6 = ???

Table factor:

2. What if the interest is compounded quarterly?

Quarterly: i = .08 ÷ 4 = .02 n x m = 3 x 4 = 12

FV = $1,000 (1.02)12 = ???

Table factor:

Factor from Compound Sum Table would be for i = 4% interest for n = 6 periods.

Factor from Compound Sum Table would be i = ___% interest for n = ___ periods.

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5. FV of a mixed stream of deposits (or payments) made at end of each year

i = 8%

What is the value after 3 years? Year 1 deposit $1,000 Year 2 deposit $1,500 Year 3 deposit $1,000

Deposits $1,000 $1,500 $1,000

0 1 2 3

FV?

FV = PV1(1 + i) 2 + PV2(1 + i)

1 + PV3(1 + i) 0

FV = $1,000 (1.08)2 + $1,500 (1.08)1 + $1,000 From the Compound Sum of $1 table, we get:

FV = $1,000 (1.166) + $1,500 (1.080) + $1,000 (1) FV = $1,166 + $1,620 + $1,000 FV = $3,786

i = 8% for n = 2 years or periods

i = 8% for n = 1 years or periods

i = 8% for n = 0 year or period

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Compound Sum of an Annuity of $1 n* 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12%

1 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000

2 2.010 2.020 2.030 2.040 2.050 2.060 2.070 2.080 2.090 2.100 2.110 2.120

3 3.030 3.060 3.091 3.122 3.153 3.184 3.215 3.246 3.278 3.310 3.342 3.374

4 4.060 4.122 4.184 4.246 4.310 4.375 4.440 4.506 4.573 4.641 4.710 4.779

5 5.101 5.204 5.309 5.416 5.526 5.637 5.751 5.867 5.985 6.105 6.228 6.353

6 6.152 6.308 6.468 6.633 6.802 6.975 7.153 7.336 7.523 7.716 7.913 8.115

7 7.214 7.434 7.662 7.898 8.142 8.394 8.654 8.923 9.200 9.487 9.783 10.089

8 8.286 8.583 8.892 9.214 9.549 9.897 10.260 10.637 11.028 11.436 11.859 12.300

9 9.369 9.755 10.159 10.583 11.027 11.491 11.978 12.488 13.021 13.579 14.164 14.776

10 10.462 10.950 11.464 12.006 12.578 13.181 13.816 14.487 15.193 15.937 16.722 17.549

11 11.567 12.169 12.808 13.486 14.207 14.972 15.784 16.645 17.560 18.531 19.561 20.655

12 12.683 13.412 14.192 15.026 15.917 16.870 17.888 18.977 20.141 21.384 22.713 24.133

13 13.809 14.680 15.618 16.627 17.713 18.882 20.141 21.495 22.953 24.523 26.212 28.029

14 14.947 15.974 17.086 18.292 19.599 21.015 22.550 24.215 26.019 27.975 30.095 32.393

15 16.097 17.293 18.599 20.024 21.579 23.276 25.129 27.152 29.361 31.772 34.405 37.280

16 17.258 18.639 20.157 21.825 23.657 25.673 27.888 30.324 33.003 35.950 39.190 42.753

17 18.430 20.012 21.762 23.698 25.840 28.213 30.840 33.750 36.974 40.545 44.501 48.884

18 19.615 21.412 23.414 25.645 28.132 30.906 33.999 37.450 41.301 45.599 50.396 55.750

19 20.811 22.841 25.117 27.671 30.539 33.760 37.379 41.446 46.018 51.159 56.939 63.440

20 22.019 24.297 26.870 29.778 33.066 36.786 40.995 45.762 51.160 57.275 64.203 72.052

*n = number of periods (not just number of years)

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6. Annuity – stream of periodic payments made over a specified period of time

What is the FV of $1,000 per year at 8% after 3 years, assuming 3 end-of-the-year payments? Using another table, Compound Sum of an Annuity of $1 (pg. 13), is

$1,000 $1,000 $1,000

0 1 2 3 FV?

From the Compound Sum of an Annuity of $1 table, set up for end of the year payments and where i = 8% and n = 3 results in 3.246, the FV is calculated as follows: FV = $1,000 x 3.246 = $3,246 What is the FV after 5 years, assuming 5 end-of-the-year payments?

$1,000 $1,000 $1,000 $1,000 $1,000 0 1 2 3 4 5

FV = $1,000 x ________ = $________

FV?

i = 8% n = ____

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Present Value of $1

n* 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12%

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893

2 0.980 0.961 0.943 0.925 0.907 0.890 0.873 0.857 0.842 0.826 0.812 0.797

3 0.971 0.942 0.915 0.889 0.864 0.840 0.816 0.794 0.772 0.751 0.731 0.712

4 0.961 0.924 0.888 0.855 0.823 0.792 0.763 0.735 0.708 0.683 0.659 0.636

5 0.951 0.906 0.863 0.822 0.784 0.747 0.713 0.681 0.650 0.621 0.593 0.567

6 0.942 0.888 0.837 0.790 0.746 0.705 0.666 0.630 0.596 0.564 0.535 0.507

7 0.933 0.871 0.813 0.760 0.711 0.665 0.623 0.583 0.547 0.513 0.482 0.452

8 0.923 0.853 0.789 0.731 0.677 0.627 0.582 0.540 0.502 0.467 0.434 0.404

9 0.914 0.837 0.766 0.703 0.645 0.592 0.544 0.500 0.460 0.424 0.391 0.361

10 0.905 0.820 0.744 0.676 0.614 0.558 0.508 0.463 0.422 0.386 0.352 0.322

11 0.896 0.804 0.722 0.650 0.585 0.527 0.475 0.429 0.388 0.350 0.317 0.287

12 0.887 0.788 0.701 0.625 0.557 0.497 0.444 0.397 0.356 0.319 0.286 0.257

13 0.879 0.773 0.681 0.601 0.530 0.469 0.415 0.368 0.326 0.290 0.258 0.229

14 0.870 0.758 0.661 0.577 0.505 0.442 0.388 0.340 0.299 0.263 0.232 0.205

15 0.861 0.743 0.642 0.555 0.481 0.417 0.362 0.315 0.275 0.239 0.209 0.183

16 0.853 0.728 0.623 0.534 0.458 0.394 0.339 0.292 0.252 0.218 0.188 0.163

17 0.844 0.714 0.605 0.513 0.436 0.371 0.317 0.270 0.231 0.198 0.170 0.146

18 0.836 0.700 0.587 0.494 0.416 0.350 0.296 0.250 0.212 0.180 0.153 0.130

19 0.828 0.686 0.570 0.475 0.396 0.331 0.277 0.232 0.194 0.164 0.138 0.116

20 0.820 0.673 0.554 0.456 0.377 0.312 0.258 0.215 0.178 0.149 0.124 0.104

*n = number of periods (not just number of years)

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7. PV of a single sum (PVSS)

If FV = PV(1 + i)n then

The PV is the FV received in the nth period discounted at i% (per period). Example: You want to accumulate $20,000 at the end of 10 years; assuming you can earn 8%, how much must you put aside now? FV = $20,000, i = 8%, and n = 10 PV = $20,000 x .463 PV = $9,260

PV FV $20,000

This factor can be found on the Present Value of $1 table where n=10 and i=8%  PV = FV x PV factor

This factor can be found on the Present Value of $1 table (pg. 15)

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Observation: If the required rate of return changes from 5% to 10% to 12%, the value of $1,000 received in 5 years also changes. PV FV

5% $784 $1,000 10% $621 $1,000 12% $567 $1,000

As i increases, the PV of cash flows decreases. This is how risk in capital budgeting is adjusted. Riskier projects get higher required rates of return which lowers the value of their cash flows.

The sooner funds are received, the more they are worth.

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8. PV of a stream of cash flows

a. PV of a mixed stream – you will receive $1,000 at the end of the first year, $1,500 at the end of the second year, and $1,000 at the end of the third year. How much will you pay for this stream of cash flows?

i = 8% 1 2 3

PV $1,000 $1,500 $1,000 PV $1,000 n = 1, i = 8% PV = $1,000 x _______ = _______ + PV $1,500 n = 2, i = 8% PV = $1,500 x _______ = _______ + PV $1,000 n = 3, i = 8% PV = $1,000 x _______ = _______

Factor from PV of $1 table where n =__ and i =__%.

Factor from PV of $1 table where n = 1 and i = 8%.

Factor from PV of $1 table where n =__ and i =__%.

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Present Value of an Annuity of $1

n* 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12%

1 0.990 0.980 0.971 0.962 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.893

2 1.970 1.942 1.913 1.886 1.859 1.833 1.808 1.783 1.759 1.736 1.713 1.690

3 2.941 2.884 2.829 2.775 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402

4 3.902 3.808 3.717 3.630 3.546 3.465 3.387 3.312 3.240 3.170 3.102 3.037

5 4.853 4.713 4.580 4.452 4.329 4.212 4.100 3.993 3.890 3.791 3.696 3.605

6 5.795 5.601 5.417 5.242 5.076 4.917 4.767 4.623 4.486 4.355 4.231 4.111

7 6.728 6.472 6.230 6.002 5.786 5.582 5.389 5.206 5.033 4.868 4.712 4.564

8 7.652 7.325 7.020 6.733 6.463 6.210 5.971 5.747 5.535 5.335 5.146 4.968

9 8.566 8.162 7.786 7.435 7.108 6.802 6.515 6.247 5.995 5.759 5.537 5.328

10 9.471 8.983 8.530 8.111 7.722 7.360 7.024 6.710 6.418 6.145 5.889 5.650

11 10.368 9.787 9.253 8.760 8.306 7.887 7.499 7.139 6.805 6.495 6.207 5.938

12 11.255 10.575 9.954 9.385 8.863 8.384 7.943 7.536 7.161 6.814 6.492 6.194

13 12.134 11.348 10.635 9.986 9.394 8.853 8.358 7.904 7.487 7.103 6.750 6.424

14 13.004 12.106 11.296 10.563 9.899 9.295 8.745 8.244 7.786 7.367 6.982 6.628

15 13.865 12.849 11.938 11.118 10.380 9.712 9.108 8.559 8.061 7.606 7.191 6.811

16 14.718 13.578 12.561 11.652 10.838 10.106 9.447 8.851 8.313 7.824 7.379 6.974

17 15.562 14.292 13.166 12.166 11.274 10.477 9.763 9.122 8.544 8.022 7.549 7.120

18 16.398 14.992 13.754 12.659 11.690 10.828 10.059 9.372 8.756 8.201 7.702 7.250

19 17.226 15.678 14.324 13.134 12.085 11.158 10.336 9.604 8.950 8.365 7.839 7.366

20 18.046 16.351 14.877 13.590 12.462 11.470 10.594 9.818 9.129 8.514 7.963 7.469

*n = number of periods (not just number of years)

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b. PV of an annuity – you can receive $2,000 at the end of each of the next 3 years. Your required rate of return is 8%. How much would you pay for this income stream?

PVA = A × Factor from Present Value of an Annuity of $1 table (pg. 19) for 3 years at 8% interest

$5,154 = $2,000 x 2.577 1 2 3 PV $2,000 $2,000 $2,000

From PV of an Annuity of $1 table where n = 3 and i = 8%.

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Learning Objective #2: Discuss the definitions and differences in the methods used in evaluating capital investment projects.

IV. Methods of Evaluating Capital Investment Projects

A. Capital budgeting techniques

1. Payback – measurement of the length of time needed to recoup the cost of a capital investment.

2. Accounting rate of return (ARR) – measurement of the percentage return of average annual cash flows on initial investment. The ARR is average annual cash flow divided by the initial investment.

3. Net present value (NPV) – measurement of the PV of future cash inflows compared to the net investment of a project. If the discounted cash inflows are greater than or equal to the cash outflows (the NPV), the project is financially viable and should be accepted. The discount rate is the organization’s WACC.

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4. Benefit-cost ratio (BCR) – the measurement of the

discounted values of the inflows divided by the net investment used in comparing the NPV of various projects. These projects may be competing for the same source of limited funds (capital rationing) or may require differing investment commitments. It answers the question, “which project from those having positive NPV’s represents the greater or greatest return on the investment”?

5. Internal rate of return (IRR) – this measurement is the “unknown” discount rate found by a process of trial and error that makes the PV of future cash inflows exactly equal to the net investment at time zero. If a project has an IRR greater than or equal to the organization’s WACC, the project is accepted.

Note: Payback and accounting rate of return are “quick and dirty” methods of evaluating a capital investment project, but these techniques do not consider the time value of money or the value of cash flows occurring after the investment has been paid back. While useful in some situations, such as very short investments or small amounts, the lack of recognition of the time value of money is a severe limitation on their broad application in financial decision- making.

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B. Contrast various capital budgeting techniques

Net Expected Cash Flows

Year Project A Project B

Investment outflow 0 (100) (200)

Cash inflows 1 10 140

2 60 100

3 80 40

Capital Budgeting Techniques

1. Payback

2. ARR

3. NPV

4. BCR

5. IRR

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C. Payback

Year Project A Project B

0 ($100) ($100) ($200) ($200)

1 10 (90) 140 (60)

2 60 (30) 100 40

3 80 50 40 80

Project A Payback = 2 plus $30/$80 = 2.4 years Project B Payback = 1 plus $60/$100 = 1.6 years Payback decision rule: Accept project with shortest payback (Project B)

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D. ARR

Project A ARR = $50*/$100 = 50%

Project B ARR = $93*/$200 = 46.5%

ARR decision rule: Accept project with highest ARR (Project A)

Drawbacks:

1. Does not explicitly take into account TVOM

2. Distortion because of unequal annual returns

Advantages:

1. Conceptually simple

2. Easy to understand

* average of cash inflows [Project A = (10+60+80)/3 = $50]

[Project B = (140+100+40)/3= $93]

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E. NPV = sum of PV of positive cash inflows and negative outflows

Net expected cash flows

(interest rate is 10%)

Year Project A Project B Investment outflow 0 (100) (200) Cash inflows 1 10 140 2 60 100 3 80 40

Project A NPV

Tables: Cash Inflows × PV Factor PVSS 10 0.909 = $ 9.09 60 0.826 = 49.56 80 0.751 = 60.08 $118.73

Less initial investment -100.00 $ 18.73

PV Table where n = 2 and i = 10%

PV Table where n = 3 and i = 10%

PV Table where n = 1 and i = 10%

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Project B NPV

Tables: Cash Inflows × PV Factor PVSS 140 0.909 = $127.26 100 0.826 = 82.60 40 0.751 = 30.04 $239.90

Less initial investment -200.00 $ 39.90

NPV decision rule: Accept project if the PV of cash inflows less outflows is greater than or equal to zero (accept both projects)

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F. BCR (comparing NPV’s)

Equation: ∑ PV of inflows/net investment

Project A BCR B/CA = $118.73/100 = 1.1873

Project B BCR B/CB = $239.90/200 = 1.1995

BCR decision rule: If BCR is > 1, accept or if BCR is < 1, reject Rationing: Accept the project with the highest BCR If accepting only one, accept Project B

Used when:

1. Capital rationing (limited funds for competing projects)

2. Two or more competing projects with positive NPV’s have different investment requirements

Note: Be sure to remember the BCR technique used in comparing the NPV of various projects.

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G. IRR

To solve: 1) trial and error, depending upon the cash flows and the luck of having a calculated factor close to a discount rate

2) financial calculator/computer

Assume: Project A IRR = 18.1%*

Project B IRR = 23.6%

IRR decision rule: Accept the project if the IRR is greater than or equal to the cost of capital (cost of capital is 10%, so accept both projects)

*IRR of Project A: NI = 100

The IRR is the discount rate that causes PV of inflows = NI (so, NPV = 0)

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Potential problems with IRR

1. IRR assumes the reinvestment of positive cash flows. When positive cash flows cannot be reinvested, the IRR overstates the return.

2. IRR assumes all reinvestments will occur generating the same yields and ignores the possibility that reinvestments may occur at inopportune moments, such as during an economic period when the yield of the reinvestment is different.

3. Some projects will have multiple IRRs, such as during an investment period with positive and negative cash flows. A common investment scenario of this type is the operation of a strip mine or nuclear power plant, when a large cash outflow is required at the end of the investment period.

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H. BCR (NPV based) versus IRR

1. To avoid problems associated with IRR, use the BCR. The NPV-based approach of BCR uses the assumption that the inflows can be reinvested at the cost of capital or the discount rate, a rate that is generally less than the IRR. After all, projects that are acceptable under an NPV approach must return a yield greater than the cost of capital.

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Review and Comparison of Capital Budgeting Techniques

Year Project A Project B Investment outflow 0 (100) (200) Cash inflows 1 10 140 2 60 100 3 80 40

Assume cost of capital is 10%

Payback Payback of Project A = 2.4 years Payback of Project B = 1.6 years Decision rule: accept project with shortest payback Decision: accept Project B

ARR ARR of Project A = 50% ARR of Project B = 46.5% Decision rule: accept project with highest ARR Decision: accept Project A NPV NPV = sum of PV of positive cash inflows and negative outflows NPV of Project A = $18.73 NPV of Project B = $39.90 Decision rule: accept project if the PV of cash inflows less outflows is greater than or equal to zero. Decision: accept both projects BCR (comparing NPVs) Equation:  PV of inflows ÷ net investment Decision rule: if BCR is > 1, accept and if BCR is < 1, reject Rationing: accept the project with the highest BCR B/CA = 1.1873 > 1, accept B/CB = 1.1995 > 1, accept If accepting only one: accept Project B IRR IRR = the discount rate that makes the PV of future inflows = net investment (so, NPV = 0) IRR of Project A = 18.1% IRR of Project B = 23.6% Decision rule: accept project if the IRR is greater than or equal to the cost of capital Decision: accept both projects

ANA:5:11/13 - 33 -

Learning Objective #3: Discuss additional considerations when choosing capital investment projects.

V. Additional Considerations when Choosing Capital Investment Projects

A. Inflation’s impact on choosing capital investment projects

1. Adequacy of depreciation pools

2. Increase of the discount rate

3. Should increase cash flow, but is difficult and dangerous to forecast

B. Projects with different lives

1. NPV to least common multiple

Since projects may have different lives, the projects can be evaluated based on the least common multiple. For example, if an automatic sprinkler system has an expected life of 20 years (the outflows and expected savings in the cost of risk will last 20 years) and a smoke/heat alarm system has an expected life of 10 years, the projects can be evaluated on the basis of 20 years, the least common multiple.

ANA:5:11/13 - 34 -

2. NPV to infinity

a. Some projects have an “infinite life”. For example, the NPV of a fire-resistant building versus that of an ordinary construction building would consider “infinite life” cash flows.

b. Most decisions have a shorter event horizon than “infinite”; therefore, the “infinite” NPV can be calculated. Since the NPV factors decrease with time, the factors for extended time periods have much less impact on the NPV than do the earlier years.

C. Validity of assumptions and the games people play

1. If everyone knows the hurdle rate (minimum amount of return an organization requires before they will make an investment in a project) is 20%, all projects miraculously come in at least at 20%

2. The corporate staff knows that divisions may tend to be overly optimistic in their forecasts so they reduce their estimates by 20%

3. The division knows this so they add an extra 25%

4. Now, all projects miraculously come in at least at 25%

5. The corporate staff knows that divisions may tend to be overly optimistic

ANA:5:11/13 - 35 -

Example of NPV analyses

Sprinkler decision – without TVOM considered

Expected return (probability weighted mean): Illustrates the calculation of the expected loss to an asset related to a fire exposure with and without loss control procedures (automatic sprinkler system) in place.

1. Without loss control

Severity Probability Prob. x (Loss) 0 0.79 0 10,000 0.12 1,200 50,000 0.06 3,000 100,000 0.03 3,000 1.00 7,200

Expected loss = $7,200

2. With loss control (does not impact probability of loss,

just severity)

Severity Probability Prob. x (Loss) 0 0.79 0 5,000 0.12 600 7,500 0.06 450 50,000 0.03 1,500 1.00 2,550

Expected loss = $2,550

ANA:5:11/13 - 36 -

NPV Analysis Initial cost $20,000 Project life 10 years Depreciation straight line Tax rate 34% WACC 10%

Cash flows:

Decrease in expected losses ($7,200 - $2,550) $4,650

Less depreciation ($20,000 x 10%) (2,000) Incremental EBT $2,650 Less taxes (34%) (901)

After-tax cash flow for next 10 years $1,749 Plus non-cash expenses 2,000 After-tax cash flow for next 10 years $3,749

Analysis: NPV: PV of inflows ($3,749 × 6.145) $23,038 Less initial cost – 20,000 NPV $ 3,038 NPV > 0, Accept

IRR (from an Excel spreadsheet) = 13.43% IRR > 10%, Accept

From PV of an Annuity of $1 table (10 years or periods at 10% interest annually)

ANA:5:11/13 - 37 -

Skills Application Scenario #11

Investment in a Risk Control Education Program

Mary received a call from Rachel and Ralph, her insurance brokers. She learned that DCRI’s professional liability insurance claims from the casino and hotel security staff, who are EMTs, have increased significantly in the past five years, and the professional liability premium, while a relatively small portion of the total insurance premium, has increased accordingly.

The professional liability insurer made DCRI an offer: if the entire DCRI EMT staff will attend a professional liability loss prevention seminar offered by the insurance carrier, DCRI will receive a discount of $25,000 per year on the renewal for the next three years, with the first savings starting one year from the current renewal date.

Mary estimated the costs for the EMT staff to attend the seminar to be approximately $60,000. In order to reserve spots in the popular seminars and secure transportation and lodging, the $60,000 must be committed immediately. Mary learned from Sarah that the DCRI WACC or required rate of return is 10%. Mary intends to calculate the PV of this project to determine if she should commit the funds and send the EMT staff to the seminar.

ANA:5:11/13 - 38 -

Step One – Problem Set Up

Step Two – Calculate the NPV

Step Three – Accept/Reject Decision

ANA:5:11/13 - 39 -

Review of Learning Objectives

1. Discuss the cash discounting concepts used in risk management applications. (p. 2)

2. Discuss the definitions and differences in the methods used in evaluating capital investment projects. (p. 21)

3. Discuss additional considerations when choosing capital investment projects. (p. 33)

ANA:5:11/13 - 40 -

Notes

Certified Risk Managers International a proud member of The National Alliance for Insurance Education & Research

www.TheNationalAlliance.com

Cash Discounting Concepts Appendix

© 2010. The National Alliance for Insurance Education & Research. All Rights Reserved. This outline or any part thereof may not be reproduced in any form or by any means or stored in any information retrieval system without the express written consent of the author.

This publication includes copyrighted material of Insurance Services Office, Inc. with its permission.

ANA:5:05/09 Appendix Page 1

Appendix A: WACC EXAMPLE

WEIGHTED AVERAGE COST OF CAPITAL: Given the following information about the AJAX Co. Debt: The company is contemplating issuing $10 million worth of 20 year 8% coupon bonds. The bonds will sell at face value, and the underwriter’s fee for floating the bond issue is 2% of the face value per bond. Preferred Stock: The company is contemplating issuance of a 9% P.S. that is expected to sell for $85 per share. The cost of issuing and marketing the stock is expected to be $3 per share. Common Stock: The current market price of the firm’s common stock is $50 per share. The firm expects to use a dividend of $4 at the end of the coming year (Year 7). Year 6’s dividend was $3.60 and Year 1’s was $2.50. Any new stock could be sold at face value, but the firm would have to pay $2 per share underwriting costs.

Balance Sheet: Source of Capital Market Value

Long term debt 15,000,000 Preferred stock 15,000,000 Common stock 32,000,000 Retained earnings 8,000,000 TOTALS 70,000,000 NOTE: The firm’s tax rate is 34%.

ANA:5:05/09 Appendix Page 2

WACC Definition: After-tax cost to the firm of an average dollar of capital or long term funds. Capital consists of four components:

 LTD (Long Term Debt)

 PS (Preferred Stock)

 CS (Common Stock – new issues)

 R/E (Retained Earnings)

Calculation: The A/T cost of the 4 capital components is calculated, multiplied by a weighting system and summed up

KD × WT + KPS × WT + KCS × WT + KRE × WT = WACC

For AJAX Co. assume: KD = 8.205% × (1 – t) = A/T Cost = 8.205% × .66 = 5.4153% + KPS = 9.329% + KCS = 15.8983% + KRE = 15.565%

ANA:5:05/09 Appendix Page 3

WACC – MARKET VALUE WEIGHTS (MV) COST × WEIGHT KD 5.4153 15/70 or (.21428) = 1.16039 KPS 9.329 15/70 or (.21428) = 1.9990 KRE 15.565 8/70 or (.11429) = 1.7789 KCS 15.8983 32/70 or (.45714) = 7.2679

 12.2062%

ANA:5:05/09 Appendix Page 4

Appendix B: Using Excel for Cash Discounting

Year A B Investment Outflow 0 (100) (200) Cash Inflows 1 10 140

2 60 100 3 80 40

If you do not see either the NPV or IRR functions under the

"Financial" category, then select "Add-Ins…" and click

on the box to the left of "Analysis ToolPak." You will

probably need the original Excel CD and it might take a

few seconds while Excel loads the ToolPak.

PV of Cash Inflows for Project A (NPV function) PV of Cash Inflows $118.78 $239.97 (from NPV function)

NPV (sum of Outflow & PV) $18.78 $39.97

Benefit-to-Cost Ratio (ratio of PV to Outflow) 1.1878287 1.199849737

(These values do not match

those in the text because

of rounding differences.)

IRR for Project A (IRR function)

Internal Rate of Return 18.126% 23.564% (from IRR function)

Using Excel's "Paste Function" (fx ) for Section 5's First NPV, B/C, IRR Example

Certified Risk Managers International a proud member of The National Alliance for Insurance Education & Research

www.TheNationalAlliance.com

Review Problems

This publication includes copyrighted material of Insurance Services Office, Inc. with its permission.

ANA:ReviewProblems:05/09 Page 2

Skills Application Scenario #11 Investment in a Risk Control Education Program

Mary has just received a call from Rachel and Ralph, her insurance brokers. She learned that DCRI’s professional liability insurance claims from the casino and hotel security staff, who are EMTs, have increased significantly in the past five years, and the professional liability premium, while a relatively small portion of the total insurance premium, has increased accordingly.

The professional liability insurer has made DCRI an offer: if all of the DCRI EMT staff attends a professional liability loss prevention seminar offered by the insurance carrier, DCRI will receive a discount of $25,000 per year on the next three years’ renewals, with the first savings starting one year from the current renewal date.

Mary has estimated the costs involved in having the entire EMT staff attend the seminar will be $60,000. In order to reserve spots in the popular seminars and secure transportation and lodging, the $60,000 must be committed immediately. Mary learned from Sarah that the DCRI WACC or required rate of return is 10%. Mary intends to calculate the PV of this project to determine if she should commit the funds and send the EMT staff to the seminar.

ANA:ReviewProblems:05/09 Page 2

Step One – Problem Set Up

The initial investment of $60,000 is incurred today. The first of three premiums savings of $25,000 will occur one year from today. Timeline is shown below:

Step Two – Calculate the NPV

PV of Cash Flows = $25,000 × 2.487 = $62,175 NPV = $62,175 – $60,000 = $2,175

Step Three – Accept/Reject Decision

The organization should ACCEPT this project because the NPV is positive.

Note: This analysis ignores tax effects

From PV of an Annuity Table n = 3, i = 10%

0 1 2 3

(60,000) 25,000 25,000 25,000