The current worth of a future sum of money or stream of cash flows given a specified rate of return. • To compute the PV of money you’ll receive some years from now, a discount rate is applied – PV = FV/(1+r) n – If someone offered you $500 today or $1000 in ten years, and inflation is 3%, which would you take? – What if inflation rate is 1%? Or 8%? Future cash flows are discounted at the discount rate : - Reflects time value of money, risk or uncertainty of future cash flows - More uncertainty of cash flows: the higher the discount rate and lower the PV of future cash flows
DCF Concept: Future Value Future Value : The value of an asset or cash at a specified date in the future that is equivalent in value to a specified sum today. • Most common application of is compounding: – The Future Value of money you have today at an interest rate – FV = PV x (1+r) n (r = interest rate, n = # periods) – Exampl e: $1000 invested today, Interest rate = 10%, Time = 5 years would have a Future Value of $1,611.00.
FV PMT 1 2 3 4 … n 0 … Concept PV = $1000 5 years = $1611 r = 10%
Compounding and Discounting • The future value received in a year, from $1 invested today at 10%, is $1.10. • The present value of $1.10 to be paid in a year when the interest rate is 10% is $1. • With compounding, the future value received in 2 years, from $1 invested today at 10%, is $1.21 = 1 x 1.1 x 1.1. • In reverse, the present value of $1.21 to be paid in two years when the interest rate is 10% is obtained by dividing the 1.21 by 1.1 2 .
Uses • You expect sales will grow so you will need more product. Is it better to build a plant or “rent” the capacity from someone else? • You want to buy another company and merge it with yours. Will your increased profitability over time be worth the cost? What else could you do with the money? • We’ve developed a new technology. It will take many years and a lot of money to bring to market. Will the expected future sales be worth the investment? • Other examples?
DCF Steps -> Figures of Merit Steps: 1. Estimate the relevant cash flows. 2. Calculate the rate of return for the investment. 3. Compare the returns to your acceptance criterion. But: 4. Step #1 is challenging. 5. Doing it well requires a thorough understanding of the company ’ s markets, competitive position, and long-run intentions. 6. Potential estimation difficulties arise with depreciation, financing costs, working capital investments, shared resources, excess capacity, contingent opportunities, etc….
Cash Flows for Container-Loading Pier ($M)
Cash Flow Diagram for Container-Loading Pier
Payback Period & Accounting Rate of Return, and Related Issues Concepts: • Payback Period : Amount of time the company must wait before recouping its original investment. – The pier ’ s payback period is 5 1/3 years ($40M / $7.5M).
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- Winter '16