Introduction to Discounted Cash Flow Professor Sid Balachandran Finance and Accounting for Non-Financial Executives Columbia Business School Agenda Introducing Discounted Cashflow Applying DCF to Evaluate a Major Corporate Investment 2 1
Key Takeaways Valuation is the approach used in finance to determine how much something is intrinsically worth Discounted cashflow is a technique used to determine net present value and make decisions The value of a project is the net present value of its discounted cashflows The value of a company is the net present value of all of the company s cash flows 3 The Basics Cash Inflow, the receipt of cash at a point in time Denoted by an Up Arrow cf 4 t = 0 t = 4 4 2
The Basics Cash Outflow, the payment of cash at a specific point in time Denoted by a Down Arrow t = 2 t = 0 -cf 2 5 Discounting A financial technique that allows you to determine the value of a given cashflow at any point in time Today (Present Value) Later (Future Value) Key Intuition: money today is worth more than money in the future 6 3
Key Dimensions of Discounting Timing of cashflows, What s worth more Giving you a dollar today Giving you a dollar tomorrow Riskiness of cashflows, What s worth more A firm commitment to give you a dollar today A firm commitment to flip a coin today and give you $2 if it is heads, or $0 if it is tails 7 The Math of Discounting One Period (Year) Ahead cf 1 t = 0 t = 1 PV 0 = cf 1 (1+r) 8 4
The Math of Discounting Two Periods (Years) Ahead cf 2 t = 0 t = 1 t = 2 PV 0 = cf 2 (1+r) 2 9 The Math of Discounting N Periods (Years) Ahead cf n t = 0. t = n PV 0 = cf n (1+r) n 10 5
The Math of Discounting Multiple Cashflows, at Multiple Times cf 1 cf 2 cf 3 cf 4 -cf 0 PV 0 = cf 1 cf 2 cf 3 -cf 0 (1+r) 1 (1+r) 2 (1+r) 3 + + + + cf 4 (1+r) 4 11 The Profiles of Investments We May Observe Investments can include any combination and sequence of cash inflows and outflows We often refer to the sequence as a stream of cashflows Typically we observe cash outflows first followed by cash inflows Projects might alternate between inflows and outflows 12 6
The Math of Discounting The General Formula (Net Present Value) n PV 0 = t=0 cf t (1+r t ) t 13 The Math of Discounting A Comment On The Discount Rate It increases as the cashflows become more uncertain (up to this point all examples have assumed cashflow is certain) It may change from one point in time to the other because of economic factors (ie. The federal reserve changes rates) 14 7
A Few Special Types of Investments The Annuity: An annuity provides you with a fixed periodic cashflow for a fixed number of periods in the future The Perpetuity: The perpetuity provides you with a fixed periodic cashflow for all future periods The Perpetuity with Growth: Provides you with a periodic cashflow that grows by a constant proportion each period 15 Decision Making Using Net Present Value In order to choose optimally Never invest in projects with negative net present values If the amount you invest is UNLIMITED choose all projects that have positive net present value If the amount you invest is LIMITED, begin by choosing the project with largest NPV, and continue choosing in decreasing order 16 8
DCF Analysis, Examples 17 Other Decision Rules You May Hear About Payback Period A payback period is the number of periods in which the cash outflow is offset by the cash inflow Example Some argue that it is optimal to choose projects with shortest payback periods But, what if a longer payback period has a higher NPV? 18 9
Other Decision Rules You May Hear About Internal Rate of Return An internal rate of return is the discount rate for an investment that makes its net present value zero Example Some argue it is optimal to choose projects with highest IRR Using internal rates of return do not always lead to the same decision as DCF Common problems, higher IRR projects may have lower NPV, projects with multiple IRR s 19 Future Values, Another Way To Apply DCF Future Value is the value of a stream of cashflows sometime in the future For example, with 5% per year discount rate, $1 today is worth $1.05 next year (its future value) As long as all projects are evaluated at a constant future date, selecting based on magnitude of future value yields same decision making as using net present value 20 10
Applying Discounted Cashflows to A Company Companies Produce Cashflows We can Form Expectations of a Company s Future Cashflows based on Its historical performance It strategic business prospects going forward Detailed financial analysis These cashflows Can Be Discounted to Determine The Company s Net Present Value Other Models of Determining Value are Also Valid and Useful 21 Key Takeaways Valuation is the approach used in finance to determine how much something is intrinsically worth Discounted cashflow is a technique used to determine net present value and make decisions The value of a project is the net present value of its discounted cashflows 22 11