slide thuyết trình TIME VALUE OF MONEY AND DCF MODEL

TIME VALUE OF MONEY DCFAND MODEL “I think being in love with life is a key to eternal youth.” —Doug Hutchison ThS Nguyễn Thị Thu Trang LECTURE CONTENT • Part 1: Time value of money • • • • The importance of time value of money Single cash flow formula Simple interest and compound interest Present value and future value of cash flows • Part 2: Discounted cash flow valuation model ThS Nguyễn Thị Thu Trang OBJECTIVE LEARNING Explain what the time value of money is and why it is so important in the field of finance Explain the concept of future value, including the meaning of the terms principal, simple interest and compound interest, and use the future value formula to make business decisions Explain the concept of present value, how it relates to future value, and use the present value formula to make business decisions ThS Nguyễn Thị Thu Trang TIME VALUE OF MONEY Opportunity cost Risk ThS Nguyễn Thị Thu Trang Inflation CF s at different times are not directly comparable Why Is The Time Value Which asset wouldof you rather own? Money Important? $1,000 now or next year? Put two CFs in comparable terms I SINGLE CASH FLOW FORMULA • •• n-1 n PVo FV1 FV2 • •• FVn-1 FVn Following: =PV(1 Present Value n FVPV = + i) n FV = Future Value i = Interest n = Number of period I SIMPLE INTEREST Time 10% 1 _1 $100 ? $100110% Interest Earned = $10 Amount at the $100+ $10 end of each period, = $110 FVn The interest in each period is earned only using the original Principal ? $100*10% = $10 $110+ $10 = $120 1 ? $100*10% = $10 $120+ $10 = $130 • ‘Interest on interest’- interest earned on reinvestment of previously COMPOUND INTEREST earned interest Time $100 Interest Earned Amount at the end of each period, FVn 10% ? $100*10% = $10 $100+ $10 = $110 1 ? $110*10% = $11 $110 + $11 = $121 ? $121*10% = $12.1 $121 + $12.1 = $133.1 The interest in each period is earned using both the original Principal and the interest you previously earned ThS Nguyễn Thị Thu Trang I ORDINARY ANNUITY - EXAMPLE Starting with her next monthly salary payment, Maria intends to save $300 each month If the interest rate is 3% per year, payable monthly, how much can Maria save after years? 0If you can afford a $2,000 monthly car payment for years, how much car can you afford if interest rates are 6% compounded monthly? ThS Nguyễn Thị Thu Trang 15 FUTURE VALUE OF AN ANNUITY DUE Time r% CF CF CF CF CF • There are payments, but the first payment occurs immediately • This is the same as each CF of an ordinary annuity of (5) payments earns one year interest more • In general term, the formula for the FV of an annuity due is: Annuity due value = Ordinary annuity value x (1+r) FVADUE = FVAt (1 + r) = CF ThS Nguyễn Thị Thu Trang (1 + r)f - r (1 + r) 16 PRESENT VALUE OF AN ANNUITY DUE • There are payments, and the first payment occurs immediately Timeis $CF today plus an ordinary annuity of (5-1) payments • This r% • In general due is: CF term, the CF formula CF for the PV CF CF of an annuity Annuity due value = Ordinary annuity value x (1+r) PVADUE = PVA(1 + r) = CF ThS Nguyễn Thị Thu Trang (1 + r) 17 ANNUITY DUE - EXAMPLE • Suppose you rent a house for $12,000 a year and deposit all the money received each year at the 10% annual compound interest savings account, the first deposit occur immediately Ask how much money you will have at the end of the third year? • Kathy’s uncle promised her an allowance of $1,000 per year, starting today, with a final payment to be made at the beginning of Year If the interest rate is 7% per year, what is the present value of these cash flows? ThS Nguyễn Thị Thu Trang 18 PRESENT VALUE OF A PERPETUITY • A perpetuity is the cash flow with inflows or outflows incurred forever • We have present value of normal cash flows • Khi n TO 1/i(1+i)n 0, lúc đó: CF • Using to valuate preference PVA = CF stock = CF PVAro = CF ThS Nguyễn Thị Thu Trang i i(1 + 0n - 19 FUTURE VALUE OF MULTIPLE CASH FLOWS Time 2345 7% $100 Q1:You deposit$100 inYear 1, $200 in Year and $300 in Year How much will you have in years with 7% interest per annum Q2: How much will it be in years if you don’t add additional cash? Solution ThS Nguyễn Thị Thu Trang 20 FUTURE VALUE OF MULTIPLE CASH FLOWS Time Q1:You deposit$100 inYear 1, $200 in Year and $300 in Year How much will you have in years with 7% interest per annum 7% -1 i -1 =300(1.07)2 Q2: How much will it be in years if you don’t add additional cash? =200(1.07)3 ► $131.08 FV at Year ThS Nguyễn Thị Thu Trang $343.47 $245.01 =100(1.07)4 Solution -> $719.56 21 PRESENT VALUE OF MULTIPLE CASH FLOWS Time You are offered an investment that will pay $200 in Yr 1, $400 in Yr 2, $600 in Yr and $800 at the end of Yr 4.You can earn 12% on similar investments What is the most you should pay for this one? 12% $200 $178.57 « 200 (U21 $400 $600 $800 — =400/(1.12)2 $318.88 _ =600/(1.12)3 $427.07 $508.41 < PV $178.57 ThS Nguyễn Thị Thu Trang =800/ (1.12)41 22 PRESENT VALUE OF MULTIPLE CASH FLOWS ThS Nguyễn Thị Thu Trang 23 I FUTURE VALUE AND PV OF MULTIPLE CASH FLOWS Case study: we have cash flows generated through the years below, calculate the PV and FV of this cash flow, indicating the discount rate of 7% How much will it be in years if you don’t add additional cash? ThS Nguyễn Thị Thu Trang Year Cash Flow $100 $200 $200 $300 $300 24 Effective Annual Rates of Interest • A reasonable question to ask in the above example is “what is the effective annual rate of interest on that investment?” • FV3 = 100x(1 + ^)2x3 = 100x(1.05)6=$134 • The Effective Annual Rate (EAR) of interest is the annual rate that would give us the same end-of-investment wealth after years: • 100 x (1+EAR)3 = $134 ThS Nguyễn Thị Thu Trang 25 Effective Annual Rates of Interest • FV3 = 100 x (1 + EAR)3 = $134 • (1 + EAR)3 = ịỊị = 1.34 100 • EAR = 1.343 - = 0.1025 = 10.25% • So, investing at 10.25 % compounded annually is the same as investing at 10% compounded semiannually ThS Nguyễn Thị Thu Trang 26 The Discounted Cash Flow Model - DCF • The discounted cash flow model is built on the basis of the concept of monetary price and the relationship between profit and risk (will be detailed in the following chapters) PV = CF0 CF1 , CF2 \+ (1 + r) (1 + r)1 (1 + r)2 + + —1- CFn_i + r) n1 + CFn (1 + r)n n _ Ỷ CFt L-í (1 + r)t t=0 ThS Nguyễn Thị Thu Trang 27 Asset valuation, including tangible assets and financial assets, to decide whether to buy or sell the property Analyze, evaluate and make decisions on whether or not to invest in an evaluating project and deciding investment DCF Analyzing, MODEL whether to buy or rent a fixed asset APPLICATION Analyze, evaluate and decide whether or not to buy a business CF CF CF I CF(1+i) CịF I n-n I CF(1+i) CF(1+i) = Ị „ CF(1+i) n- = *1 L—————————————— ThS Nguyễn Thị Thu Trang 28 _ ị l -„ CF(1+i) l ► CF(1+i) I n-2 n +CF(1 + i)n-2 + - + CF(1 + Ị)1 + CF(1 + 00 = FVAn ~(l+i)n-1 ■ i $200 -$300 $300 ► $214=200(1.07) *1 $114.49=100(1.07)2 I FV at Year 3~| [ $628.49 T 628.49(1.07)2—►[ $719.56 FV at Year ThS Nguyễn Thị Thu Trang 29 ... CONTENT • Part 1: Time value of money • • • • The importance of time value of money Single cash flow formula Simple interest and compound interest Present value and future value of cash flows •... valuation model ThS Nguyễn Thị Thu Trang OBJECTIVE LEARNING Explain what the time value of money is and why it is so important in the field of finance Explain the concept of future value, including... 26 The Discounted Cash Flow Model - DCF • The discounted cash flow model is built on the basis of the concept of monetary price and the relationship between profit and risk (will be detailed in