Discounted Cash Flow Valuation 2024-25 PDF

C39FN – Corporate Financial Theory Discounted Cash Flow Valuation  Valuation: The One Period Case Valuation: The Multi-Period Case Compounding Periods Simplifications Textbook: Corporate Finance - Chapter 4  Discounted Valuation...

C39FN – Corporate Financial Theory Discounted Cash Flow Valuation  Valuation: The One Period Case Valuation: The Multi-Period Case Compounding Periods Simplifications Textbook: Corporate Finance - Chapter 4  Discounted Valuation Rationale Compensation for: Time Value – a pound today is worth more than a pound a year from now Inflation Risk NB: Discount rate reflects time, risk and inflation. From the firm’s point of view, it is the % cost of capital  Present Value When looking at firm investment, we often want to translate future £s back to the present value. This is because £100 receivable in 2023 ≠ £100 in 2022 ≠ £100 in 2021. The further away in time a Cash Flow (CF) is, the less valuable Valuation: The One Period Case  Formula for Single Period Valuation C1 PV  1 r where C1 is cash flow at date 1 and r is the rate of return that Keith Vaughan requires on his land sale. It is sometimes referred to as the discount rate.  Example 1 Lida Jennings, a financial analyst at Kaufman & Broad, a leading real estate firm, is thinking about recommending that Kaufman & Broad invest in a piece of land that costs €85,000. She is certain that next year the land will be worth €91,000, a sure €6,000 gain. Given that the guaranteed interest rate in the bank is 10 percent, should Kaufman & Broad undertake the investment in land?  Solution €91,000 Present value   €82, 727.27 1.10 Do not purchase the property  Example: Uncertainty and Valuation Professional Artworks plc is a firm that speculates in modern paintings. The manager is thinking of buying an original Picasso for £400,000 with the intention of selling it at the end of one year. The bank interest rate is 10 percent. The manager expects that the painting will be worth £480,000 in one year. The relevant expected cash flows are depicted below:  Example: Uncertainty and Valuation Discount Cash Flows at Discount Cash Flows at 10 percent: 25 percent: £480, 000 £480, 000 £436,364 £384, 000 1.10 1.25 The 10 percent interest is Do not buy the painting! for riskless cash flows. We need a higher discount rate to reflect the riskiness of the investment.  Valuation: The Multi-Period Case Future The Power Value and of Compoundi Compoundi ng ng Present The Value and Algebraic Discounting Formula Multi-Period Formula Future Value of an Investment: FV = C0  (1 + r)T  The Power of Compounding Simple Interest Compound Interest R = 8.47 percent R = 8.47 percent Invest £1 for 208 Years Invest £1 for 208 Years Interest = £0.0847 Value of investment at end of Value of investment at end of 208 years 208 years: FV = £1(1.0847)208 £1 + (208 x £0.0847) = £22,100,655 = £1 + £17.62 = £18.62 A Big Difference!  Example 4.6: Manhattan Island New Netherlands, in 1626, allegedly bought Manhattan Island for 60 guilders’ worth of trinkets from native Americans. It is reported that 60 guilders was worth about $24 at the prevailing exchange rate. Was this a good deal for the Native Americans? If the Native Americans had sold the trinkets at a fair market value and invested the $24 at 5 percent (tax free), it would in 2006, about 380 years later, be worth more than $2.5 billion. Today, Manhattan is undoubtedly worth more than $2.5 billion, so at a 5 percent rate of return the native Americans got the worst of the deal. What if the interest rate was10 percent?  Example 4.6: Manhattan Island C = $24 T = 380 years (2006) r = 10% FV = $24(1  r)T = 24  1.1380  $129 quadrillion $129 quadrillion is more than all the real estate in the world is worth today. Valuation: Multi-period Case  Present Value and Discounting Present Value of Investment: Ct PV  T (4.4) (1  r )  Example 4.7: Multi-Period Discounting Allan Hodgson will receive €10,000 three years from now. Allan can earn 8 percent on his investments, so the appropriate discount rate is 8 percent. What is the present value of his future cash flow? 3  1  PV  €10, 000    1.08   €10, 000 .7938  €7,938  Example 4.8: Finding the Rate A customer of Chaffkin GmbH wants to buy a tugboat today. Rather than paying immediately, he will pay €50,000 in three years. It will cost Chaffkin GmbH €38,610 to build the tugboat immediately. The relevant cash flows to Chaffkin GmbH are displayed in Figure 4.9. At what interest rate would Chaffkin GmbH neither gain nor lose on the sale?  Example 4.8: Finding the Rate The ratio of construction cost (present value) to sale price (future value) is: €38, 610 0.7722 €50, 000 The interest rate that allows €1 to be received in three years to have a present value of €.7722 is 9 percent. Why?  Example 4.9: Cash Flow Valuation Paul Draper has won a crossword competition and will receive the following set of cash flows over the next two years: Year Cash Flow 1 £2,000 2 £5,000 Mr. Draper can currently earn 6 percent in his money market account. What is the present value of the cash flows?  Example 4.9: Discounted Cash Flow Valuation Year 1 1 £2, 000  £2, 000 .943 £1,887 1.06 Year 2 2  1  £5, 000   £5, 000 .890 £4, 450  1.06  Total Value: £4,450 + £1,887 = £6,337 End of Topic