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**Capital Investment Analysis**

10 Capital Investment Analysis

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**Explain the nature and importance of capital investment analysis.**

10-1 Objective 1 Explain the nature and importance of capital investment analysis.

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Capital Investment Analysis 10-1 Capital investment analysis (or capital budgeting) is the process by which management plans, evaluates, and controls investments in fixed assets.

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10-2 Objective 2 Evaluate capital investment proposals, using the following methods: average rate of return, cash payback, net present value, and internal rate of return.

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**Methods that ignore present values: The average rate of return method **

Methods of Evaluating Capital Investment Proposals 10-2 Methods that ignore present values: The average rate of return method The cash payback method Methods that use present values: The net present value method The internal rate of return method

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Percentage of Respondents Reporting the Use of the Method as “Always” or “Often” 10-2 Average rate of return Cash payback method Net present value method Internal rate of return method 15% 53% 85% 76% 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 9 Source: Patricia A. Ryan and Glenn P. Ryan. “Capital Budgeting Practices of the Fortune 1,000. How Have Things Changed? Journal of Business and Management (Winter 2002).

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**Considers accounting income (often used to evaluate managers)**

Average Rate of Return Method 10-2 Advantages: Easy to calculate Considers accounting income (often used to evaluate managers) Disadvantages: Ignores cash flows Ignores the time value of money

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**Expected useful life 4 years Residual value none **

Purchase of Machine Example 10-2 Assumptions: Machine cost $500,000 Expected useful life 4 years Residual value none Expected total income $200,000 Average rate of return Estimated Average Annual Income Average Investment = Average rate of return $200,000/4 ($500,000 + $0)/2 = = 20% 11

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**Estimated average annual income $ 30,000 $ 36,000 **

10-2 Proposal A Proposal B Estimated average annual income $ 30,000 $ 36,000 Average investment $120,000 $180,000 25% Average rate of return $30,000 $120,000 12

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**Proposal A would be preferred over Proposal B.**

10-2 Proposal A Proposal B Estimated average annual income $ 30,000 $ 36,000 Average investment $120,000 $180,000 25% Average rate of return 20% Proposal A would be preferred over Proposal B. $360,000 $180,000 13

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**Est. average annual income: $91,200 ($273,600/3 years) **

10-2 Example Exercise 10-1 Determine the average rate of return for a project that is estimated to yield total income of $273,600 over three years, cost $690,000, and has a $70,000 residual value. Follow My Example 10-1 Est. average annual income: $91,200 ($273,600/3 years) Average investment: $380,000 ($690, $70,000)/2 Average rate of return: 24% ($91,200/$380,000) 14 For Practice: PE 10-1A, PE 10-1B

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Cash Payback Method 10-2 The expected period of time that will pass between the date of an investment and the complete recovery in cash (or equivalent) of the amount invested is the cash payback period.

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10-2 The excess of cash flowing in from revenue over the cash flowing out for expenses is termed net cash flow.

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**Assumptions: Investment cost $200,000 Expected annual net**

10-2 Assumptions: Investment cost $200,000 Expected annual net cash flow (equal) $40,000 Cash payback period Total Investment Annual Net Cash Flow = = 5 years Cash payback period $200,000 $40,000 = 17

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**Shows when funds are available for reinvestment**

Advantages and Disadvantages of the Cash Payback Method 10-2 Advantages: Considers cash flows Shows when funds are available for reinvestment Disadvantages: Ignores profitability (accounting income) Ignores cash flows after the payback period

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10-2 Example Exercise 10-2 A project has estimated annual net cash flows of $30,000. It is estimated to cost $105,000. Determine the cash payback period. Follow My Example 10-2 3.5 years ($105,000/$30,000) 21 For Practice: PE 10-2A, PE 10-2B

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**Present value concepts can be divided into:**

Present Value Concepts 10-2 Present value concepts can be divided into: the present value of an amount and the present value of an annuity.

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Present Value of an Amount 10-2 On January 1, 2008, you invest $1 in an account that earns 12% interest compounded annually. Interest earning interest is called compounding.

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**$1.12 $1.254 $1.404 Present Value Concepts 10-2 Jan. 1 2008 Jan. 1**

Present Value Concepts 10-2 $1.00 x 1.12 $1.12 x 1.12 $1.254 x 1.12 Jan. 1 2008 $1.00 $1.12 $1.254 $1.404 Jan. 1 2009 2010 2011 24

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10-2 Assume that today is January 1, 2008 and the current interest rate is 12 percent. What is the present value of $1,404 to be received on January 1, 2011? To determine the answer, we need to go to Exhibit 1 and find the table value for three years at 12 percent.

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**Present Value of $1 with Compound Interest**

Partial Present Value of $1 Table 10-2 Present Value of $1 with Compound Interest Year % % % % % 0.712 26 Left click the mouse for solution.

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**Amount to be received on January 1, 2011**

10-2 Amount to be received on January 1, 2011 Table value x Present value = Present value = x $1,404 Present value = $1, (rounded) Summary: If the interest rate is 12%, then $1,404 in three years is worth $1,000 today. 27

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Present Value of an Annuity 10-2 An annuity is a series of equal net cash flows at fixed time intervals. The present value of an annuity is the amount of cash needed today to yield a series of equal net cash flows at fixed time intervals in the future.

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Net Present Value Method 10-2 The net present value method (also called the discounted cash flow method) analyzes capital investment proposals by comparing the initial cash investment with the present value of the net cash flows.

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Equipment Example 10-2 At the beginning of 2008, equipment with an expected life of five years can be purchased for $200,000. At the end of five years it is anticipated that the equipment will have no residual value. (Continued)

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Equipment Example 10-2 A net cash flow of $70,000 is expected at the end of This net cash flow is expected to decline $10,000 each year (except 2012) until the machine is retired. The firm expects a minimum rate of return of 10%. Should the equipment be purchased? (Continued)

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**(Continued) Equipment Example 10-2 $70,000 x 0.909 (n = 1; i =10%)**

Equipment Example 10-2 Jan. 1 2008 Dec. 31 2009 2010 2011 2012 $(200,000) $70, $60, $50, $40, $40,000 $ 63,630 $70,000 x (n = 1; i =10%) (Continued) 32

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**(Continued) Equipment Example 10-2 $60,000 x 0.826 (n = 2; i = 10%)**

Equipment Example 10-2 Jan. 1 2008 Dec. 31 2009 2010 2011 2012 $(200,000) $70, $60, $50, $40, $40,000 $ 63,630 $ 49,560 $60,000 x (n = 2; i = 10%) (Continued) 33

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**(Continued) Equipment Example 10-2 $50,000 x 0.751 (n = 3; i = 10%)**

Equipment Example 10-2 Jan. 1 2008 Dec. 31 2009 2010 2011 2012 $(200,000) $70, $60, $50, $40, $40,000 $ 63,630 $ 49,560 $ 37,550 $50,000 x (n = 3; i = 10%) (Continued) 34

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**(Continued) Equipment Example 10-2 $40,000 x 0.683 (n = 4; i =10%)**

Equipment Example 10-2 Jan. 1 2008 Dec. 31 2009 2010 2011 2012 $(200,000) $70, $60, $50, $40, $40,000 $ 63,630 $ 49,560 $40,000 x (n = 4; i =10%) $ 37,550 $ 27,320 (Continued) 35

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**(Continued) Equipment Example 10-2 $40,000 x 0.621 (n = 5; i = 10%)**

Equipment Example 10-2 Jan. 1 2008 Dec. 31 2009 2010 2011 2012 $(200,000) $70, $60, $50, $40, $40,000 $ 63,630 $ 49,560 $ 37,550 $40,000 x (n = 5; i = 10%) $ 27,320 $ 24,840 (Continued) 36

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**Total present value of the net cash flow is $202,900**

Equipment Example 10-2 Jan. 1 2008 Dec. 31 2009 2010 2011 2012 $(200,000) $70, $60, $50, $40, $40,000 $ 63,630 The equipment should be purchased because the net present value is positive. $ 49,560 $ 37,550 $ 27,320 $ 24,840 $ 2,900 Net present value 37 Total present value of the net cash flow is $202,900 (Concluded)

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Present Value Index 10-2 When capital investment funds are limited and the alternative proposals involve different amounts of investment, it is useful to prepare a ranking of the proposals by using a present value index.

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**Total present value of net cash flow**

10-2 Total present value of net cash flow Present value index = Amount to be invested Present value index = $202,900* $200,000 = 39

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Ranking Various Proposals Using a Present Value Index 10-2 Proposal A Proposal B Proposal C Total present value of net cash flow $107,000 $86,400 $86,400 Amount to be invested 100, , ,000 Net present value $ 7,000 $ 6,400 $ 3,600 Present value index 1.07 $107,000 $100,000 40

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10-2 Proposal A Proposal B Proposal C Total present value of net cash flow $107,000 $86,400 $86,400 Amount to be invested 100, , ,000 Net present value $ 7,000 $ 6,400 $ 3,600 Present value index 1.07 1.08 $86,400 $80,000 41

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10-2 Proposal A Proposal B Proposal C Total present value of net cash flow $107,000 $86,400 $86,400 Amount to be invested 100, , ,000 Net present value $ 7,000 $ 6,400 $ 3,600 Present value index 1.07 1.08 0.96 $86,400 $90,000 42

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**Total present value of net cash flow $107,000 $86,400 $86,400 **

10-2 Total present value of net cash flow $107,000 $86,400 $86,400 Amount to be invested 100, , ,000 Net present value $ 7,000 $ 6,400 $ 3,600 Present value index 1.07 1.08 Proposal A Proposal B Proposal C 0.96 Proposal B has the best present value index. Management should consider the possible use of the $20,000 difference between Proposal A and Proposal B before making a decision. 43

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10-2 A proposal is made to acquire $200,000 of equipment with an expected useful life of five years (no residual value) and a minimum desired rate of return of 10%. The new equipment is expected to generate a net cash inflow of $50,000 each year. Should the firm acquire the equipment? 44

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**Present Value of an Annuity of $1 = Equal Annual Cash Flows x **

10-2 Present Value of an Annuity of $1 = Equal Annual Cash Flows x Table Value from Exhibit 2 = $50,000 x Table Value from Exhibit 2 Present Value of an Annuity of $1 Refer to Exhibit 2 45

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**Present Value of an Annuity of $1 at Compound Interest**

Partial Present Value of an Annuity Table 10-2 Present Value of an Annuity of $1 at Compound Interest Year 6% % % % % 3.791 46

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**Present Value of an Annuity of $1**

10-2 Present Value of an Annuity of $1 = $50,000 x $189,550 = $50,000 x Present Value Index = $189,550 $200,000 = 0.948 The proposal should be rejected because the present value index is less than one. 47

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**Considers cash flows and the time value of money**

Advantage and Disadvantage of Net Present Value Method 10-2 Advantage: Considers cash flows and the time value of money Disadvantage: Assumes that cash received can be reinvested at the rate of return

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10-2 Example Exercise 10-3 A project has estimated annual net cash flows of $50,000 for seven years and is estimated to cost $240,000. Assume a minimum acceptable rate of return of 12%. Using Exhibit 2, determine the (a) net present value of the project and (b) the present value index, rounded to two decimal places. 49

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10-2 Follow My Example 10-3 ($11,800) [($50,000 x 4.564) – $240,000] ($228,200/$240,000) 50 For Practice: PE 10-3A, PE 10-3B

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Internal Rate of Return Method 10-2 The internal rate of return (IRR) method (sometimes called the time-adjusted rate of return method) uses present value concepts to compute the rate of return from the net cash flows expected from capital investment proposals.

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**List and describe factors that complicate capital investment analysis.**

10-3 Objective 3 List and describe factors that complicate capital investment analysis.

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**Unequal proposal lives Lease versus capital investment Uncertainty **

Factors that Complicate Capital Investment Analysis 10-3 Income tax Unequal proposal lives Lease versus capital investment Uncertainty Changes in price levels Qualitative considerations

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Capital Rationing 10-4 Capital rationing is the process by which management allocates funds among competing capital investment proposals.

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