# Ch9. The Basic of Capital Budgeting Goal: To understand the advantage and disadvantage in different investment analyzing tools Tool: - Net Present Value.

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Ch9. The Basic of Capital Budgeting Goal: To understand the advantage and disadvantage in different investment analyzing tools Tool: - Net Present Value (NPV) - Payback period - Discounted payback period - Average Accounting Return (ARR) - Internal Rate of Return (IRR) - Modified Internal Rate of Return (MIRR) -Profitability Index

1. Project classification Replacement Expansion of existing products Expansion into new products or markets Safety and/or environmental projects 2. Types of projects Mutually exclusive project: if one project is taken, the other will be rejected. Independent project: projects’ cash flows are independent of one another

Basic concept in criteria: To find the profitable projects to corporations or investors 3. Net Present Valuation (NPV) -Def of NPV:difference between an investment’s market value and its costs = PV of cash flow from a project – PV of the initial costs and other costs

-Here, Cost of capitals is used as a discount rate -Rule: acceptable if the NPV > 0. Ex) You want to open a bakery shop. It would generate the profits of \$1000 (1 st year), \$ 2000 (2 nd year), \$3000 (3 rd year). But it would cost \$5000 to set up the store. Is it worthwhile to open the store? (here required rate of return is 10%).

Answer: NPV = -5,000+1000/(1+0.1)+2000/(1+0.1)^2 +3000/(1+0.1)^3 = - 184.07 Therefore, it is not a good investment.

1) Problem of NPV: -Accurate cash flow? -Discount rate (cost of capitals)? -Market price? 4. Payback rule -Def of payback:the length of time it takes to recover our initial investment.

Rule: acceptable if its calculated payback period is less than pre-specified number of years Ex) Cash flow with the initial costs of \$500. 1 st year:\$100, 2 nd year: \$200 and 3 rd year: \$500. Q1) How long it will take to pay back the initial cost? Answer: 2 years + 200/500 =2.4 yrs. If the cutoff period is 3 years, a project with this cash flow may be accepted

1) Disadvantages Ignore the time value of money Ex) \$30 on the second year is not the same as \$30 on the third year Arbitrary Cutoff period Ignore cash flow beyond the cutoff period Ex) A: -100, 50, 50 B:-100, 10, 30, 70, 200 With a rule, you have to pick up “A”. But this decision ignore \$200 in B.

Biased against long-term projects Ex) Only accept investments within the cutoff period 2) Advantage Easy to understand Adjusted for uncertainty of later cash flows Biased toward liquidity.

5. Discounted payback Def: the length of time until the sum of the discounted cash flow is equal to the initial investment. This is a variation of payback to cover the time value problem. Rule: acceptable if its discounted payback is less than some pre-specified number of years

Ex) The initial costs are \$300 with 12.5% of WACC. 1 st year: \$100, 2 nd year: \$200 and 3 rd year:\$300. 1) Disadvantages Arbitrary Cutoff Reject the positive NPV Ignore the cash flow after the cut off Biased against the long term projects

2) Advantages Include the time value of money Easy to understand Not accept the negative NPV Biased toward liquidity

6. Average Accounting Return (AAR) =Average net income /Average book value Here the average book value is (initial cost+0)/2, assuming 0 book value at the end of maturity. Acceptable if AAR exceeds a target average accounting return.

7. Internal Rate of Return (IRR) Def: the discount rate that makes the NPV of investment zero. In other word, it is break-even discount rate and minimum return Rule: acceptable if the IRR exceeds the pre- specified return (required rate of return) How to calculate IRR: Trial and Error method or NPV profile

Ex) Initial costs :\$100 1 st year: \$60 and 2 nd year:\$60 0 = -100+60/(1+r)+60/((1+r)^2) Here r=13.1%. If the cutoff rate is 12%, then a project with this cash flow may be accepted

8. Comparison of NPV to IRR. 1) NPV profile Using the previous example, we are able to calculate NPV with different IRRs Rate: 0% 5% 10% 15% 20% NPV:20 11.5 4.1 -2.4 -8.3 Using this information, we are able to make a graph called “net present value profile”

From the NPV profile, we indirectly realize that a point crossing X-axiom is the IRR 2)NPV rankings: comparing more than two projects’ NPV profiles - Cross rate: cost of capital at which the project’s NPVs are equal - Why the NPV profiles are crossing each other: Due to cash flows patterns

E.g) calculating a cross rate. Year Investment A Investment B B-A 0 -400 -500 -100 1 250 320 70 2 280 340 60 NPV (B-A) = 0 = -100+70/(1+R)+60/(1+R)^2 R=20% (cross rate)

3) Independent Projects They always have the same conclusion (acceptance or rejection) from NPV and IRR. 4) Mutually Exclusive Projects Two basic conditions that can cause NPV profile to cross and thus conflicts to arise between NPV and IRR

- When project size (or scale) difference exist. That is, the cost of one project is larger than that of the other. - When timing differences exist. That is, timing of cash flows from the two projects differs. Any other reason of conflicts? Due to reinvestment rate

NPV assume that cash flows will be reinvested at the cost of capital whereas the IRR assumes that the firm can reinvest at IRR. The best reinvestment rate is the cost of capital (5) Multiple IRRs Normal cash flows: one or more cash outflows (costs) followed by a series of cash inflows. Nonnormal cash flows: a large cash outflow during or at the end of its life. Nonnormal cash flows may lead to multiple IRRs Ex) Figure 9-7

9. MIRR (modified internal rate of return) Providing one return 1) Discounting approach: Discount all negative cash flows back to the present at the required rate of return and add them to the initial cost. Then calculate IRR. E.g) A project generating cash flows such as -60 (initial investment), 155 (1 st year) and -100 (2 nd year).

-60+(-100)/(1.2^2) =155/(1+MIRR) MIRR=19.75% 2) Reinvestment Approach Using the required rate of return (cost of capital) as a reinvestment rate, recalculate IRR. 60= [(155*1.2)-100]/(1+MIRR)^2 MIRR=19.72%

3) Combination approach IRR making total present value of negative cash flows equal to total future value of positive cash flows. Total present value = -60 +(-100/1.2^2) = -129.44 Total future value = 155*1.2 = 186 129.44 =186/(1+MIRR)^2 MIRR=19.87

(1) Advantage of using MIRR over IRR Reinvestment at the cost of capitals Solve Multiple IRR issue In mutually exclusive case, if the projects have same size & life, the NPV and MIRR always lead to the same decision If the projects are of equal size but differ in lives, the MIRR will always lead to the same decision as the NPV if MIRRs are calculated using the life of longer project as the terminal year (just fill zeros for the shorter projects’ missing cash flows)

If the size differ, the conflicts happen Among the tools, NPV is the best one. 10. Profitability Index: Present value of an investment’s future cash flows divided by its initial cost, called benefit-cost ratio. E.g) cost of project is \$200 and present value of project’s cash flows is 220. The profitability index is 220/200=1.1

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