slide thuyết trình TIME VALUE OF MONEY AND DCF MODEL

TIME VALUE OF MONEY AND DCF 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 CFs at different times are not directly comparable Why Is The Time Value of Money Important? Which asset would you rather own? $1,000 now or next year? Put two CFs in comparable terms ThS Nguyễn Thị Thu Trang SINGLE CASH FLOW FORMULA n-1 n PV0 FV1 FV2 FVn-1 FVn FV! = PV(1 + i)! Following: PV = Present Value FV = Future Value i = Interest n = Number of period ThS Nguyễn Thị Thu Trang SIMPLE INTEREST Time $100 Interest Earned Amount at the end of each period, FVn ? $100*10% = $10 ? $100*10% = $10 ? $100*10% = $10 $100 + $10 = $110 $110 + $10 = $120 $120 + $10 = $130 10% • The interest in each period is earned only using the original principal ThS Nguyễn Thị Thu Trang COMPOUND INTEREST • ‘Interest on interest’- interest earned on reinvestment of previously earned interest Time $100 Interest Earned Amount at the end of each period, FVn ? $100*10% = $10 ? $110*10% = $11 ? $121*10% = $12.1 $100 + $10 = $110 $110 + $11 = $121 $121 + $12.1 = $133.1 10% • The interest in each period is earned using both the original principal and the interest you previously earned ThS Nguyễn Thị Thu Trang SIMPLE INTEREST VS COMPOUND INTEREST ThS Nguyễn Thị Thu Trang CHANGING THE COMPOUNDING PERIOD • So far it has been assumed that the cash flows are yearly (annual compounding) • There are however many possible compounding periods that occur depending on the nature of the asset § Bonds generally pay interest semi-annually § Banks pay often pay interest on a monthly basis • Thus, how does this affect FV and PV calculations? • Steps: The annual interest rate (i) must be converted to a ‘periodic’ rate (i/m) The number of periods in years (t) must be converted to a total number of compounding periods (t*m) ThS Nguyễn Thị Thu Trang FUTURE VALUE OF AN ORDINARY ANNUITY Time i% CF CF … … n-1 n CF CF CF(1+i)n-n = CF(1+i)0 CF(1+i)n-(n-1) = CF(1+i)1 … CF(1+i)n-2 CF(1+i)n-1 • CF(1 + i)!"#+CF(1 + i)!"$+ ⋯ + CF + i • FVA! = CF # + CF + i % = FVA! (#'()! "# ( ThS Nguyễn Thị Thu Trang 13 PRESENT VALUE OF AN ORDINARY ANNUITY Time i% … n-1 n CF CF … CF CF CF/(1+i)1 CF/(1+i)2 … CF/(1+i)n-1 CF/(1+i)n • PVA = *+ (#'()" • PVA = CF *+ + (#'()# + ⋯+ *+ #'( !$" + *+ #'( ! #"(#'()$! ( ThS Nguyễn Thị Thu Trang 14 ORDINARY ANNUITY - EXAMPLE Ø 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? ØIf 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 CF r% 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) 𝟏+𝒓 𝒕−𝟏 𝑭𝑽𝑨𝑫𝑼𝑬 = 𝑭𝑽𝑨𝒕 (𝟏 + 𝒓) = 𝑪𝑭 (𝟏 + 𝒓) 𝒓 ThS Nguyễn Thị Thu Trang 16 PRESENT VALUE OF AN ANNUITY DUE Time CF r% CF CF CF CF • There are payments, and the first payment occurs immediately • This is $CF today plus an ordinary annuity of (5-1) payments • In general term, the formula for the PV of an annuity due is: Annuity due value = Ordinary annuity value x (1+r) 𝟏− 𝟏+𝐫 𝐏𝐕𝐀𝐃𝐔𝐄 = 𝐏𝐕𝐀 𝟏 + 𝐫 = 𝐂𝐅 𝐫 ThS Nguyễn Thị Thu Trang "𝐭 (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 1− 1 1+i ! PVA = CF = CF − i i i 1+i ! • Khi n ∞ 1/i(1+i)n 0, lúc đó: CF PVA" = CF − = i i • Using to valuate preference stock ThS Nguyễn Thị Thu Trang 19 FUTURE VALUE OF MULTIPLE CASH FLOWS Time 7% • Q1:You deposit $100 in Year 1, $200 in Year and $300 in Year How much will you have in years with 7% interest per annum $100 $200 $300 $300 $214=200(1.07) • Q2: How much will it be in years if you don’t add additional cash? $114.49=100(1.07)2 FV at Year Solution $628.49 628.49(1.07)2 $719.56 FV at Year ThS Nguyễn Thị Thu Trang 20 FUTURE VALUE OF MULTIPLE CASH FLOWS Time 7% $100 $200 $300 • Q1:You deposit $100 in Year 1, $200 in Year and $300 in Year How much will you have in years with 7% interest per annum =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? $178.57 $318.88 $200 $400 $600 $800 12% =200/(1.12) =400/(1.12)2 =600/(1.12)3 $427.07 =800/(1.12)4 $508.41 PV $178.57 ThS Nguyễn Thị Thu Trang 22 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% Year Cash Flow How much will it be in years if you don’t add additional cash? ThS Nguyễn Thị Thu Trang $100 $200 $200 $300 $300 23 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?” • FV" = 100x(1 + #.% &'" ) & = 100x(1.05)( =$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 24 Effective Annual Rates of Interest • FV3 = 100 x (1 + EAR)3 = $134 " • (1 + EAR) = %") %## = 1.34 ! " • EAR = 1.34 − = 0.1025 = 10.25% • So, investing at 10.25 % compounded annually is the same as investing at 10% compounded semiannually ThS Nguyễn Thị Thu Trang 25 The Discounted Cash Flow Model - DCF • The discounted cash flow model is built on the basis of the concept of monetary price and the relationship between profit and risk (will be detailed in the following chapters) CF% CF# CF$ CF!"# CF! PV = + + + ⋯+ + % # $ !"# (1 + r) (1 + r) (1 + r) 1+r (1 + r)! ! CF =A (1 + r) ./% ThS Nguyễn Thị Thu Trang 26 DCF MODEL APPLICATION 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 investment project Analyzing, evaluating and deciding whether to buy or rent a fixed asset Analyze, evaluate and decide whether or not to buy a business ThS Nguyễn Thị Thu Trang 27 ... 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... 25 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