# Chapter 6 - Capital Budgeting Techniques Capital Budgeting Techniques What What is is Capital Capital Budgeting? Budgeting? The process of identifying, analyzing, and selecting investment projects whose returns (cash flows) are expected to extend beyond one year. Project Classifications

Independent Projects: Projects whose cash flows are not affected by decisions made about other projects. Mutually Exclusive Projects: A set of projects where the acceptance of one project means the others cannot be accepted. e.g. buying computers of different brands. Dependent( contingent)projects: e.g. buying a new machine may force to extend the construction 3 Project Evaluation: Alternative Methods Payback Period (PBP)

Net Present Value (NPV) Internal Rate of Return (IRR) Profitability Index (PI) Net Cash Flows for Project S and Project L Expected Afte r-Tax ^ Net Cash Flows, CF t Year (T) 0a 1 2 3 4

Project S \$(3,000) 1,500 1,200 800 300 Project L \$(3,000) 400 900 1,300 1,500 5 What is the Payback Period? The length of time before the original cost of an investment is recovered from the

expected cash flows or . . . How long it takes to get our money back. Unre cov ered cost at start Number of years before of full - recovery year Payback PB full recovery of Total cash flow during original investment

full recovery year 6 Payback Period for Project S 0 1 2 PBS 3

4 Net Cash Flow -3,000 1,500 1,200 800 300 Cumulative Net CF

-3,000 -1,500 -300 500 800 PaybackS = 2 + 300/800 = 2.375 years 7 Payback Period for Project L 0 1

2 3 PB L 4 Net Cash Flow - 3,000 400 900 1,300

1,500 Cumulative Net CF - 3,000 - 2,600 - 1,700 - 400 1,100 PaybackL = 3 + 400/1,500 = 3.3 years 8

Net Present Value (NPV) NPV is the present value of an investment projects net cash flows minus the projects initial cash outflow. CF1 NPV = (1+k)1 + CF2 (1+k)2 CFn ICO +...+ (1+k)n

9 Proposed Project Data Julie Miller is evaluating a new project for her firm, Basket Wonders (BW). She has determined that the after-tax cash flows for the project will be \$10,000; \$12,000; \$15,000; \$10,000; and \$7,000, respectively, for each of the Years 1 through 5. The initial cash outlay will be \$40,000. 10 NPV Solution Basket Wonders has determined that the appropriate discount rate (k) for this project is 13%. NPV = \$10,000 +\$12,000 +\$15,000 + (1.13)1 (1.13)2 (1.13)3

\$10,000 \$7,000 4 + 5 - \$40,000 (1.13) (1.13) 11 NPV Solution NPV = \$10,000(PVIF13%,1) + \$12,000(PVIF13%,2) + \$15,000(PVIF13%,3) + \$10,000(PVIF13%,4) + \$ 7,000(PVIF13%,5) - \$40,000 NPV = \$10,000(.885) + \$12,000(.783) + \$15,000(.693) + \$10,000(.613) + \$ 7,000(.543) - \$40,000 NPV = \$8,850 + \$9,396 + \$10,395 + \$6,130 + \$3,801 - \$40,000

= - \$1,428 12 NPV Acceptance Criterion The management of Basket Wonders has determined that the required rate is 13% for projects of this type. Should this project be accepted? No! The NPV is negative. This means that the project is reducing shareholder wealth. [Reject as NPV < 0 ] 13 Internal Internal Rate Rate of of Return Return (IRR)

(IRR) IRR is the discount rate that equates the present value of the future net cash flows from an investment project with the projects initial cash outflow. CF1 CF2 + +...+ ICO = 1 (1+IRR) (1+IRR)2 CFn (1+IRR) IRR Solution

\$10,000 \$12,000 \$40,000 = + + (1+IRR)1 (1+IRR)2 \$15,000 \$10,000 \$7,000 + + (1+IRR)3 (1+IRR)4 (1+IRR)5 Find the interest rate (IRR) that causes the discounted cash flows to equal \$40,000. IRR Solution (Try 10%) \$40,000 = \$10,000(PVIF10%,1) + \$12,000(PVIF10%,2) +

\$15,000(PVIF10%,3) + \$10,000(PVIF10%,4) + 7,000(PVIF10%,5) \$40,000 = \$10,000(.909) + \$12,000(.826) + \$15,000(.751) + \$10,000(.683) + \$ 7,000(.621) \$40,000 = \$9,090 + \$9,912 + \$11,265 + \$6,830 + \$4,347 = \$41,444 [Rate is too low!!] \$ IRR Solution (Try 15%) \$40,000 = \$10,000(PVIF15%,1) + \$12,000(PVIF15%,2) + \$15,000(PVIF15%,3) + \$10,000(PVIF15%,4) + 7,000(PVIF15%,5)

\$40,000 = \$10,000(.870) + \$12,000(.756) + \$15,000(.658) + \$10,000(.572) + \$ 7,000(.497) \$40,000 = \$8,700 + \$9,072 + \$9,870 + \$5,720 + \$3,479 = \$36,841 [Rate is too high!!] \$ IRR Solution (Try 15%) NPV at Lower Rate (10%) NPV = PV - ICO NPV = \$ 41,444 - \$ 40,000 = \$ 1,444 NPV at Higher Rate (15%) NPV = PV - ICO

NPV = \$ 36,881 - \$ 40,000 = \$ - 3159 IRR Solution IRR= LR + NPv L X (HR LR) NPVL NPvH 19 IRR Solution IRR= 10 +

1444 x (15 10) 1444 (-3159) IRR= 10 + 1444 x 5 4603 IRR= 10 + 0.3137 x 5 IRR= 10+ 1.57 = 11.57% 20 Profitability Index (PI) PI is the ratio of the present value of a projects future net cash flows to the projects initial cash outflow. PI = PV / ICO

PI Acceptance Criterion PI = \$38,572 / \$40,000 = .9643 Should this project be accepted? No! The PI is less than 1.00. This means that the project is not profitable. [Reject as PI < 1.00 ] Assignment Calculate NPV,PBP,IRR and PI for the following projects. Which project should be selected.(discount rate =13%) Years

Project A Project B 0 \$ 28,000 \$ 20,000 1 8000 5000 2

8000 5000 3 8000 6000 4 8000 6000 5

8000 7000 6 8000 7000 7 8000 7000