Lecture 5 NPV Calculation

Topics covered in this lecture What are incremental cash flows? Main types of cash flows Basic Net Present Value (NPV) formula Steps to calculating NPV Numerical Example Practice Question

Incremental cash flows Include: All cash flows that occur as a direct consequence of taking up the project Exclude: All cash flows that occur whether or not the project is taken up THE Question to ask: Will this cash flow or cash flow stream occur if we do not take up the project?

Main cash flow types Cash Outflows Cash Inflows Initial project cost, C0 Initial investment in Net Working Capital, NWC0 Cash Inflows After-tax operating cash flows (ATOCF) or cost savings (ATCS) Salvage value, S Recovery of Net Working Capital investment, NWCN Depreciation (CCA) tax shields, CCATS

Net Working Capital (NWC) NWC = Current Assets – Current Liabilities NWC increases if Current Assets increase Cash Accounts Receivable Inventory Current Liabilities decrease Accounts Payable Notes Payable Note that initial NWC investment is normally assumed to be recovered at the end of the project/asset life unless otherwise stated.

Net Present Value (NPV) The basic Net Present Value formula is: NPV = PV(All Cash Inflows) – PV(All Cash Outflows) NPV = PV(ATOCF) + PV(S) + PV(NWCN) + PV(CCATS) – C0 – NWC0 Basic NPV rule: Accept a project if its NPV > 0.

Steps to calculating NPV Identify the cash outflows and cash inflows incremental to the project Identify the types of cash flows in Step 1 Annuity Lump sum Perpetuity Identify the formulas needed to discount types of cash flows in Step 2 to obtain their present values Calculate the present values of the cash flows in Step 1 using the formulas from Step 3 Calculate NPV = PV(All cash inflows) – PV(All cash outflows)

Numerical Example XYZ Ltd. is considering a project that will bring in before-tax operating cash flows of $2 million per year for the next 15 years. This project will cost $13 million in initial project costs, as well as initial investment of $300,000 in net working capital. At the end of the project, the assets used in this project can be sold at an estimated $500,000. These assets have a CCA rate of 30%, and it is assumed that the CCA asset class will remain open at the end of the project. If XYZ’s marginal corporate tax rate is 40% and its required rate of return on this type of projects is 10%, should the company take on this project?

Numerical Example (cont.) – Step 1 Identify Incremental Cash Flows Cash outflows: Initial cost, C0 = Initial investment in NWC, NWC0 = Cash inflows: ATOCF = Salvage, S = NWC Recovery, NWCN = CCATS

Numerical Example (cont.) – Step 2 Identify Types of Cash Flows Cash outflows: C0 - lump sum @ t=0 NWC0 - lump sum @ t=0 Cash inflows: ATOCF - Annuity @ t=1,2,3,…,15 S - lump sum @ t=15 NWCN - lump sum @ t=15 CCATS - perpetuity, declining balance

Numerical Example (cont.) Step 3: Identify PV formulas Cash outflows: C0 - No need to discount NWC0 - No need to discount Cash inflows: ATOCF - PV(Annuity) S - PV(lump sum) NWCN - PV(lump sum) CCATS - perpetuity, declining balance

Numerical Example (cont.) Step 4: Calculate PVs of cash flows Cash outflows: PV(C0) = C0 = PV(NWC0) = NWC0 =

Numerical Example (cont.) Step 4: Calculate PVs of cash flows Cash inflows: PV(ATOCF) = PV(S) = PV(NWCN) = PV(CCATS) =

Numerical Example (cont.) Step 5: Calculate NPV NPV = PV(All Cash Inflows) – PV(All Cash Outflows) = PV(ATOCF) + PV(S) + PV(NWCN) + PV(CCATS) – C0 – NWC0 =

No Practice, No Gain ABC Inc., is considering purchasing a new equipment that will cost $1 million and will generate $500,000 in cost savings in each of the next 3 years. The equipment has a CCA rate of 30% and will have a salvage value of $100,000 at the end of the third year. If the new equipment is purchased, inventory will increase by $15,000 and accounts payable will increase by $10,000. ABC’s marginal corporate tax rate is 35% and its required rate of return on the equipment is 12%. Should ABC purchase this new equipment? NPV = $69,144.72 Conclusion: Buy this equipment.