Part II: Evaluating business & engineering assets

Transcription

1 Part II: Evaluating business & engineering assets Ch 5: Present worth analysis Ch 6: Annual equivalence analysis Ch 7: Rate-of-return analysis Rate of return Methods for finding rate of return Internal rate-of-return criterion Incremental analysis for comparing mutually exclusive alternatives Rate of return (RoR): a relative percentage method that measures the yield as a percent of investment over the life of a project

2 Comparing mutually exclusive alternatives based on IRR Cash flow n Project A1 Project A2 0 -$1,000 -$5,000 1 $2,000 $7,000 RoR PW(10%) 100% $818 40% $1,364 Question: Assume that you have $5,000 in your investment pool. Should you invest in project A1, which provides a higher RoR or in project A2, which has a higher PW?

3 Incremental investment n Project A1 Project A2 Incremental investment (A2 A1) 0 -$1,000 -$5,000 -$4,000 1 $2,000 $7,000 $5,000 ROR 100% 40% 25% PW(10%) $818 $1,364 $546 Assuming a MARR of 10%, you can always earn that rate from other investment source, i.e., $4,400 balance at the end of one year for $4,000 investment. By investing the additional $4,000 in A2, you would make an additional $5,000, which is equivalent to earning at the rate of 25%. Therefore, the incremental investment in A2 is justified.

4 Incremental analysis (procedure) Step 1: Compute the cash flow for the difference between the projects (A,B) by subtracting the cash flow of the lower investment cost project (A) from that of the higher investment cost project (B). Step 2: Compute the IRR on this incremental investment (IRR B-A ). Step 3:Accept the investment B if and only if IRR B-A > MARR NOTE: Make sure that both IRR A and IRR B are greater than MARR.

5 Ex Incremental rate of return n B1 B2 B2 - B1 0 -$3,000 -$12,000 -$9, ,350 4,200 2, ,800 6,225 4, ,500 6,330 4,830 IRR 25% 17.43% 15% Given MARR = 10%, which project is a better choice? Since IRR B2-B1 =15% > 10%, and also IRR B2 > 10%, select B2.

6 IRR on increment investment: three alternatives n D1 D2 D3 0 -$2,000 -$1,000 -$3, , , , , ,000 IRR 34.37% 40.76% 24.81% Step 1: Examine the IRR for each project to eliminate any project that fails to meet the MARR. Step 2: Compare D1 & D2: IRR D1-D2 = 27.61% > 15%, so D1 is better Step 3: Compare D1 & D3: IRR D3-D1 = 8.8% < 15%, so D1 is best

7 Practice problem You are considering four types of engineering designs. The project lasts 10 years with the estimated cash flows at the right. The interest rate (MARR) is 10%. Which of the four is more attractive? A B C D Initial cost $150 $220 $300 $340 Revenues/yr $115 $125 $160 $185 Expenses/yr $70 $65 $60 $80

8 Incremental analysis for cost-only projects Items CMS Option FMS Option Annual O&M costs: labor $1,169,600 $707,200 material 832, ,400 overhead 3,150,000 1,950,000 tooling 470, ,000 inventory 141,000 31,500 income taxes 1,650,000 1,917,000 Total annual costs $7,412,920 $5,504,100 Investment $4,500,000 $12,500,000 Net salvage value $500,000 $1,000,000 Since we assume revenues would be the same for each project, these are cost-only projects Cannot calculate IRR unless revenue given

9 Ex. 7.9 Incremental cash flow (FMS CMS) n CMS Option FMS Option Incremental (FMS-CMS) 0 -$4,500,000 -$12,500,000 -$8,000, ,412,920-5,504,100 1,908, ,412,920-5,504,100 1,908, ,412,920-5,504,100 1,908, ,412,920-5,504,100 1,908, ,412,920-5,504,100 1,908, ,412,920-5,504,100 Salvage + $500,000 + $1,000,000 $2,408,820

10 Solution: Ex. 7.9 Incremental cash flow (FMS CMS) PW(i) FMS-CMS = $8,000,000 + $1,908,820(P/A,i,5) + $2,408,820(P/F,i,6) = 0 IRR FMS-CMS = 12.43% < 15% Select CMS

11 Ultimate decision rule: If IRR > MARR, accept This rule works for any investment situation In many situations, IRR = RoR but this relationship does not hold for an investment with multiple ROR s.

12 Resolution of multiple RoR s (Chapter 7A) Net investment: project balances (PB s) computed at i * are all < 0 throughout investment, with A 0 = 0 Also called pure investment, i.e. firm does not overdraw on its return & borrow from the project A positive balance at some time during the project indicates that the firm acts as a borrower, i.e. mixed investment n A B C D 0 -$1,000 -$1,000 -$1,000 -$1, $1,000 $1,600 $500 $3,900 2 $2,000 -$300 -$500 -$5,030 3 $1,500 -$200 $2,000 $2,145 i *, % , 30, 50

13 Ex. 7A.1 Project balances A: pure n A n PB(i * ) 0 -$1,000 -$1, $1,000 -$ $2,000 -$ $1,500 0 B: mixed n A n PB(i * ) 0 -$1,000 -$1,000 1 $1,600 -$381 2 $300 $164 3 $200 0 C: pure n A n PB(i * ) 0 -$1,000 -$1,000 1 $500 -$800 2 $500 -$1,539 3 $2,000 0 D: mixed n A n PB(i * ) 0 -$1,000 -$1, $3,900 $2, $5,030 -$1,430 3 $2,145 0

14 Need for an external interest rate In prior analyses, case borrowed (released) from a project was assumed to earn i * This may not be possible, since external investments may earn less than i * That is, the rate of return on the project is generally higher than that from external investments Thus it may be necessary to calculate project balances for a project s cash flow at 2 rates of interest: one on internal & one on external investments By separating these interest rates, can compute the true rate of return (true IRR) on internal investments, or the return on invested capital (RIC)

15 Steps to calculate IRR for a mixed investment 1. Identify MARR, or external rate 2. Calculate PB(i, MARR) n or simply PB n PB(i, MARR) 0 = A 0 PB 0 (1+i) + A i if PB 0 <0 PB(i, MARR) i = { PB 0 (1+MARR) + A i if PB 0 >0 PB n-1 (1+i) + A n if PB n-1 <0 PB(i, MARR) n-1 = { PB n-1 (1+MARR) + A n if PB n-1 >0 3. Determine i by solving he terminal project balance equation Accept a project if IRR > MARR

16 Ex. 7A.2 reconsider Ex 7.6 i* =20% n = 0 n = 1 n = 2 Beg. balance Interest Payment -$1,000 -$1,000 -$200 +$2,300 +$1,100 +$220 -$1,320 End balance -$1,000 +$1,100 $0 PB(i, 15%) 0 = $1,000,000 PB(i, 15%) 1 = $1,000,000(1 + i) + $2,300,000 = $1,300,000 $1,000,000i = $1,000,000(1.3 i) If i < 1.3 -> PB(I,15%) 1 > 0 PB(i, 15%) 2 = $1,000,000(1.3 i)( ) $1,320,000 = $175,000 $1,150,000i = 0 IRR = % If i < 1.3 -> PB(I,15%) 1 > 0 PB(i, 15%) 2 = $1,000,000(1.3 i)(1 + i) $1,320,000 = -$20,000 + $305,000i $1,000,000i 2 = 0 IRR = 0.1 or 0.2, which violates the assumption that i > 1.3

17 Summary Rate of return (ROR) is the interest rate earned on unrecovered project balances such that an investment s cash receipts make the terminal project balance zero. Rate of return is an intuitively familiar & understandable measure of project profitability that many managers prefer to NPW or other equivalence measures. Mathematically we can determine the rate of return for a given project cash flow series by locating an interest rate that equates the net present worth of its cash flows to zero. This break-even interest rate is denoted by i*.

18 Summary (cont.) Internal rate of return (IRR) is another term for RoR that stresses the fact that we are concerned with the interest earned on the portion of the project that is internally invested, not those portions that are released by (borrowed from) the project. To apply rate of return analysis correctly, we need to classify an investment into either a simple or a nonsimple investment. A simple investment is defined as one in which the initial cash flows are negative and only one sign change occurs in the net cash flow, whereas a non-simple investment is one for which more than one sign change occurs in the net cash flow series. Multiple i* s occur only in non-simple investments. However, not all non-simple investments will have multiple i* s either.

19 Summary (cont.) For a simple investment, the solving rate of return (i*) is the rate of return internal to the project; so the decision rule is: If IRR > MARR, accept the project. If IRR = MARR, remain indifferent. If IRR < MARR, reject the project. IRR analysis yields results consistent with NPW and other equivalence methods. For a nonsimple investment, because of the possibility of having multiple rates of return, we need to calculate the true IRR, or known as return on invested capital. However, if your objective is to make an accept or reject decision, it is recommended either the NPW or AE analysis be used. When properly selecting among alternative projects by IRR analysis, incremental investment must be used.