Principles of Engineering Economic Analysis, 5th edition Chapter 4 Establishing the Planning Horizon & MARR

Principles of Engineering Economic Analysis, 5th edition Systematic Economic Analysis Technique 1. Identify the investment alternatives 2. Define the planning horizon 3. Specify the discount rate 4. Estimate the cash flows 5. Compare the alternatives 6. Perform supplementary analyses 7. Select the preferred investment

Principles of Engineering Economic Analysis, 5th edition Systematic Economic Analysis Technique 1. Identify the investment alternatives 2. Define the planning horizon 3. Specify the discount rate 4. Estimate the cash flows 5. Compare the alternatives 6. Perform supplementary analyses 7. Select the preferred investment

Principles of Engineering Economic Analysis, 5th edition Determining the Planning Horizon  Least common multiple of lives  Longest life  Shortest life  Standard horizon  Organizational need  Infinitely long

Principles of Engineering Economic Analysis, 5th edition Example 4.1 Three production machines are being considered. The pertinent data are as follows: Based on the least common multiple of the lives, the planning horizon is 60 years; based on the shortest life, the planning horizon is 4 years; based on the longest life, the planning horizon is 6 years; and based on the firm’s “standard”, the planning horizon is 10 years.

Principles of Engineering Economic Analysis, 5th edition CFD for Least Common Multiple of Lives

Principles of Engineering Economic Analysis, 5th edition Example 4.1: 60-Year Planning Horizon With a 60-yr planning horizon, it is assumed the successive replacements will have identical cash flow profiles. MARR = 12% PW A (12%) = -$15,500 - $8,750(P|A 12%,60) + $2,500(P|F 12%,60) - $13,000[(P|F 12%,4) + (P|F 12%,8) + … + (P|F 12%,56)] = -$110, PW B (12%) = -$20,250 - $5,850(P|A 12%,60) + $3,000(P|F 12%,60) - $17,250[(P|F 12%,5) + (P|F 12%,10) + … + (P|F 12%,55)] = -$91, PW C (12%) = -$30,750 - $3,175(P|A 12%,60) + $3,250(P|F 12%,60) - $27,500[(P|F 12%,6) + (P|F 12%,12) + … + (P|F 12%,54)] = -$85,352.36

Principles of Engineering Economic Analysis, 5th edition CFD for “Shortest Life” Planning Horizon

Principles of Engineering Economic Analysis, 5th edition Example 4.1: 4-Year Horizon With a 4-yr planning horizon, it is assumed the salvage value for B will be $6,000 and the salvage value of C will be $11,000. MARR = 12% PW A (12%) = -$15,500 - $8,750(P|A 12%,4) + $2,500(P|F 12%,4) = -$15,500 - $8,750( ) + $2,500( ) = -$40, =PV(12%,4,8750,-2500) = -$40, PW B (12%)= -$20,250 - $5,850(P|A 12%,4) + $6,000(P|F 12%,4) = -$20,250 - $5,850( ) + $6,000( ) = -$34, =PV(12%,4,5850,-6000) = -$34, PW C (12%)= -$30,750 - $3,175(P|A 12%,4) + $11,000(P|F 12%,4) = -$30,750 - $3,175( ) + $11,000( ) = -$33, =PV(12%,4,3175,-11000) = -$33,402.89

Principles of Engineering Economic Analysis, 5th edition CFD for “Longest Life” Planning Horizon

Principles of Engineering Economic Analysis, 5th edition Example 4.1: 6-Year Horizon With a 6-yr planning horizon, it is assumed A will be replaced with an identical machine and have a $9,000 salvage value; similar assumptions are made for B, including a $14,500 salvage value. PW A (12%)=PV(12%,6,8750,-9000) PV(12%,4,,13000) = -$55, PW B (12%)=PV(12%,6,5850,-14500) PV(12%,5,,17250) = -$46, PW C (12%)=PV(12%,6,3175,-3250) = -$42,157.17

Principles of Engineering Economic Analysis, 5th edition CFD for 10-Year Planning Horizon

Principles of Engineering Economic Analysis, 5th edition Example 4.1: 10-Year Horizon With a 10-yr planning horizon, it is assumed A will be replaced with an identical machine and have a $9,000 salvage value; for B, two complete life cycles occur; and for C, a salvage value of $11,000 is assumed. PW A (12%)=PV(12%,10,8750,-9000) PV(12%,4,,13000) +PV(12%,8,,13000) = -$75, PW B (12%)=PV(12%,10,5850,-3000) PV(12%,5,,17250) = -$62, PW C (12%)=PV(12%,10,3175,-11000) PV(12%,6,,27500) = -$59,080.11

Principles of Engineering Economic Analysis, 5th edition Example 4.1: Infinitely Long Horizon With an indefinitely long planning horizon, we assume successive replacements have identical cash flow profiles, as with the LCML approach. Here, we compute the annual worth for an individual life cycle (LC), recognizing the annual worth will occur indefinitely. AW A (12%)=PMT(12%,4,15500,-2500)-8750 = -$13, AW B (12%)=PMT(12%,5,20250,-3000)-5850 = -$10, AW C (12%)=PMT(12%,6,30750,-3250)-3175 = -$10,253.71

Principles of Engineering Economic Analysis, 5th edition Observation Consider the ratios of annual worths for the indefinitely long planning horizon versus the ratios of present worths for the least common multiple of lives planning horizon. AW A (12%)/AW B (12%) = -$13,330.05/-$10, = AW A (12%)/AW C (12%) = -$13,330.05/-$10, = AW B (12%)/AW C (12%) = -$10,995.32/-$10, = PW A (12%)/PW B (12%) = -$110,959.97/-$91, = PW A (12%)/PW C (12%) = -$110,959.97/-$85, = PW B (12%)/PW C (12%) = -$91,525.57/-$85, = 1.072

Principles of Engineering Economic Analysis, 5th edition Observations 1.Evaluating alternatives based on a LCML planning horizon will yield the same recommendations as for an infinitely long planning horizon under the assumption of identical replacements over the planning horizon. 2.When we consider capitalized worth and capitalized cost in the next chapter, we will explicitly consider an infinitely long planning horizon, because we will be interested in knowing the magnitude of the present worth for an infinitely long planning horizon. 3.PW(LCML) = AW(LC)(P|A MARR,LCML) The present worth over a LCML horizon equals the product of the annual worth for a life cycle and the P|A factor for a period of time equal to the LCML. (See the text for the calculations for Example 4.1.)

Principles of Engineering Economic Analysis, 5th edition Example 4.2: One-Shot Investments Consider the two investments shown below, only one of which can be chosen. They are one-shot investments. Given a MARR of 15%, which (if either) should be chosen? PW 1 (15%)=PV(15%,4,-3500,-1000)-4000 = $ PW 2 (15%)=NPV(15%,1000,2000,3000,4000,5000,6000)-5000 = $

Principles of Engineering Economic Analysis, 5th edition If we had assumed LCML for the planning horizon, then AW 1 (15%) =1000*PMT(15%,4,4,-1)+3500 = $2, AW 2 (15%) =1000*PMT(15%,6,5-NPV(15%,1,2,3,4,5, 6)) = $1, With one-shot investments, use a longest life planning horizon and assign $0 to “missing years” for the shorter lived alternatives. Example 4.2: One-Shot Investments (Continued)

Principles of Engineering Economic Analysis, 5th edition Systematic Economic Analysis Technique 1. Identify the investment alternatives 2. Define the planning horizon 3. Specify the discount rate 4. Estimate the cash flows 5. Compare the alternatives 6. Perform supplementary analyses 7. Select the preferred investment

Principles of Engineering Economic Analysis, 5th edition Factors Influencing Discount Rate  Opportunity for investment elsewhere at comparable risks  Cost of capital  Risk associated with the investment  Duration of investment opportunity  Category of investment  Magnitude of investment  Competition for investment capital

Principles of Engineering Economic Analysis, 5th edition Determining the Cost of Capital  the cost of capital reflects the cost of obtaining investment capital  it is made up of a combination of the cost of debt capital and equity capital  debt capital is derived by selling bonds  equity capital is obtained from selling stock

Principles of Engineering Economic Analysis, 5th edition US Treasuries US Large Cap equities US Micro Cap equities Venture Capitalists Private Equity Corporate Bonds Junk Bonds US Small Cap Equities

Principles of Engineering Economic Analysis, 5th edition Weighted Average Cost of Capital WACC = (E/V)i e + (D/V)i d (1 – T) where E = firm’s total equity ($) D = firm’s total debt and leases ($) V = E + D, a firm’s total invested capital ($) i e = cost of equity or expected ROR on equity (%) i d = cost of debt or expected ROR on borrowing (%) T =corporate tax rate (%)

Principles of Engineering Economic Analysis, 5th edition

Cost of Capital Components Debt capital obtained from loans k l = i eff (1 - itr) where k l = effective after-tax interest rate i eff = effective before-tax interest rate itr = corporate income tax rate Debt capital obtained from bond financing k b = i b (1 – itr) where k b = cost of debt capital from bonds i b = annual effective bond yield itr = corporate income tax rate

Principles of Engineering Economic Analysis, 5th edition Example 4.3 A firm borrows money at an effective annual rate of 10%. If its tax rate is 40%, what is its cost of capital from the loan? k l = i eff (1 - itr) k l = 0.10(0.60) k l = 6%

Principles of Engineering Economic Analysis, 5th edition Example 4.4 A firm issues $50 million of $1000, 8% annual, 10-year bonds at a selling price of $985, after commissions. If its tax rate is 40%, what is its cost of capital from the bonds? k b =RATE(10,80,-985,1000)*(1–0.40) k b = %

Principles of Engineering Economic Analysis, 5th edition Cost of Capital Components Debt capital obtained from accounts payable k ap = {[1/(1 – d)] 365/(D2 – D1) – 1}(1 - itr) where k ap = cost of capital from delayed payments of accounts payable d = discount rate on invoice for “early payment” D1= # days after invoice receipt by which payments must occur in order to obtain the discount D2= maximum # days to pay invoice without penalty itr = corporate income tax rate Equity capital from issuing preferred stock e ps = PSD/(P ps - C ps ) where e ps = equity interest rate for preferred stock PSD= preferred stock dividend P ps = share price of preferred stock at time of issuance C ps = cost of selling a share of preferred stock

Principles of Engineering Economic Analysis, 5th edition Example 4.5 A firm receives an invoice for $75,000 having a 1.5% discount if paid in full within 10 days of receipt, payable in full no later than 45 days after receipt. If the firm foregoes early payment and pays 45 days after receipt, what is its cost of capital from the delayed payment? Its tax rate is 40%. k ap = {[1/(1 – d)] 365/(D2 – D1) – 1}(1 - itr) k ap = {[1/(1–0.015)] 365/(45–10) –1}(1-0.40) k ap = %

Principles of Engineering Economic Analysis, 5th edition Example 4.6 A firm issues preferred stock having a value of $230 and paying a $15 annual dividend. The firm pays a brokerage fee of $5/share. If its tax rate is 40%, what is its cost of capital from the preferred stock? e ps = PSD/(P ps - C ps ) e ps = $15/($230 - $5) e ps = 6.667%

Principles of Engineering Economic Analysis, 5th edition Cost of Capital Components Equity capital from issuing common stock e cs = CSD/PC s + g where e cs = cost of equity capital from common stock CSD = dividend per share of common stock PC s = current trading price per share of common stock g = growth rate for the share price of common stock or, using a simplified approach, e cs ≈ EPS/PC s where EPS = earning per share after interest and taxes

Principles of Engineering Economic Analysis, 5th edition Example 4.7 Over a 2-year period, a firm averages 55¢ in its earnings per share. The market value of its common stock averages $9.75 over the same 2-year period. What is its cost of capital for the common stock? e cs ≈ EPS/PC s e cs ≈ $0.55/$9.75 e cs ≈ 5.64%

Principles of Engineering Economic Analysis, 5th edition Cost of Capital Components Retained earnings Because retained earnings are “owned” by the shareholders, the cost of capital for retained earnings is generally considered to be equal to that for common stock. Hence e re = CSD/PC s + g where e re = cost of capital for retained earnings CSD = dividend per share of common stock PC s = current trading price per share of common stock g = growth rate for the share price of common stock

Principles of Engineering Economic Analysis, 5th edition WACC = k l p l + k m p m + k b p b + k ap p ap + e ps p ps + e cs+re p cs+re where p l = percent of capital from loans p m = percent of capital from mortgages p b = percent of capital from bonds p ap = percent of capital from accounts payable p ps = percent of capital from preferred stocks p cs+re = percent of capital from the combination of common stock and retained earnings Note: the sum of the percentages equals 1 Weighted Average Cost of Capital

Principles of Engineering Economic Analysis, 5th edition Example 4.8 The capital structure for a firm consists of $1 million in loans having an after-tax cost of capital of 9.3%, $1.8 million in bonds having an after-tax cost of capital of 5.5%, and $8 million in common stocks having an after-tax cost of capital of 9.8%. What is the firm’s WACC? WACC= k l p l + k b p b + e cs p cs WACC= (0.093)($1/$10.8) + (0.055)($1.8/$10.8) + (0.098)($8/$10.8) WACC= 9.037%

Principles of Engineering Economic Analysis, 5th edition Cost of Capital Robert Kaplan, distinguished Harvard Business School accounting professor, found that the real cost of capital in the U.S. from 1926 to 1984 was less than 8%. Kaplan, R. S., “Must CIM be Justified by Faith Alone?,” Harvard Business Review, 64 (2), March – April 1986, pp

Principles of Engineering Economic Analysis, 5th edition Example 4.9 A team of process engineers proposes spending $2.5M to debottleneck an existing U.S. site using existing technology. The minor expansion of the site is justified on the basis of 100% cost savings. The annual growth rate in sales is assumed to be 4%. Allocated capital of no more than 5% of total capital is assumed. The base corporate WACC is currently 9%. What hurdle rate is to be used in the economic justification?

Principles of Engineering Economic Analysis, 5th edition

Example 4.10 The plant manager proposes a minor expansion of a U.S. site using new technology. The justification is based on 100% cost savings. The annual growth rate in sales is assumed to be 3.5%. Allocated capital of no more than 7% of total capital is assumed. The base corporate WACC is currently 8.5%. What hurdle rate is to be used in the economic justification?

Principles of Engineering Economic Analysis, 5th edition

Example 4.11 A business development team proposes spending $8.5M to produce a new specialty chemical with a major expansion of an existing U.S. site using existing technology. The investment is justified on the basis of 100% revenue growth. The annual growth rate in sales is assumed to be 7%. Allocated capital of no more than 5% of total capital is assumed. The base corporate WACC is currently 9.5%. What hurdle rate is to be used in the economic justification?

Principles of Engineering Economic Analysis, 5th edition

Example 4.12 A joint venture in China is being considered, with EMN owning 40% and not having control. Slightly different technology will be used at the “condo” site. The investment is justified on the basis of 20%/80% cost savings/revenue growth. The annual growth rate in sales is assumed to be 7%. Allocated capital of no more than 8% of total capital is assumed. The base corporate WACC is currently 9%. What hurdle rate is to be used in the economic justification?

Principles of Engineering Economic Analysis, 5th edition

Example 4.13 An R&D team has discovered a chemical by- product that can be spun off into a separate company. Based on work performed to date, it qualifies as a seed-stage candidate for venture capital. What hurdle rate is to be used in the economic justification?

Principles of Engineering Economic Analysis, 5th edition

An acquisition of a division of another chemical company is being considered. If acquired, minor expansion using existing technology will be performed and justified on the basis of 40% cost savings & 60% revenue growth. The annual growth rate in sales is assumed to be 4.8%. Allocated capital of no more than 7.5% of total capital is assumed. The base corporate WACC is currently 8.5%. What hurdle rate is to be used in the economic justification? A New Example

Principles of Engineering Economic Analysis, 5th edition

Another New Example The acquisition of a publicly held company is being considered. A slightly different application of technology currently used is planned. The minor expansion of the U.S. site is to be justified on the basis of 20% cost savings/80% revenue growth. The annual growth rate in sales is assumed to be 4.5%. Allocated capital of no more than 5% of total capital is assumed. The base corporate WACC is 9%. What hurdle rate is to be used in the economic justification?

Principles of Engineering Economic Analysis, 5th edition

Pit Stop #4—Take a Deep Breath 1.True or False: When dealing with multiple alternatives having unequal lives, the planning horizon equals the least common multiple of lives. 2.True or False: The MARR should be at least as great as the firm’s weighted cost of capital and should reflect the opportunity cost for money. 3.True or False: Among the various sources of capital, U.S. large cap equities have a lower cost of capital than do U.S. small cap equities. 4.True or False: The most common method of valuing the cost of equity capital is to divide the annual dividend by the average market value of a share of stock. 5.True or False: The cost of debt capital needs to reflect the tax deductibility of costs of debt. 6.True or False: The Eastman hurdle rate calculator can be used for any company and under any conditions that are specifically targeted by the calculator. 7.True or False: A company’s beta can be used to accurately forecast its stock price during the coming year. 8.True or False: Historical beta values are not impacted by rare events that might adversely affect a firm’s stock price. 9.True or False: The Federal Reserve Bank’s prime lending rate should be used for the risk-free rate in the capital asset pricing model. 10.True or False: When using the Eastman hurdle rate calculator, if venture capital is being sought, the hurdle rate obtained will not be affected by ownership, plant site, or technology profiles.

Principles of Engineering Economic Analysis, 5th edition Pit Stop #4—Take a Deep Breath 1.True or False: When dealing with multiple alternatives having unequal lives, the planning horizon equals the least common multiple of lives. False 2.True or False: The MARR should be at least as great as the firm’s weighted cost of capital and should reflect the opportunity cost for money. True 3.True or False: Among the various sources of capital, U.S. large cap equities have a lower cost of capital than do U.S. small cap equities. True 4.True or False: The most common method of valuing the cost of equity capital is to divide the annual dividend by the average market value of a share of stock. False 5.True or False: The cost of debt capital needs to reflect the tax deductibility of costs of debt. True 6.True or False: The Eastman hurdle rate calculator can be used for any company and under any conditions that are specifically targeted by the calculator. False 7.True or False: A company’s beta can be used to accurately forecast its stock price during the coming year. False 8.True or False: Historical beta values are not impacted by rare events that might adversely affect a firm’s stock price. False 9.True or False: The Federal Reserve Bank’s prime lending rate should be used for the risk-free rate in the capital asset pricing model. False 10.True or False: When using the Eastman hurdle rate calculator, if venture capital is being sought, the hurdle rate obtained will not be affected by ownership, plant site, or technology profiles. True