Capital Budgeting Contents TI BAII Plus Calculator Advanced Features Uneven Cash Flows Mean, Variance, and Standard Deviation Covariance, Correlation, and Regression Deprecation Net Present Value (NPV) Capital Budgeting The sum of the present values of a series of cash flows CF CF CF NPV = CF + + +... + (1+ k) (1+ k) (1+ k) 1 2 n 0 1 2 n Discount rate (k): cost of capital to the firm doing that project; NPV is very useful for assessing feasibility of projects NPV 0 ACCEPT PROJECT! NPV < 0 REJECT PROJECT! Net Present Value (NPV) Example: using a 10% discount rate T0 T1 T2 T3 T4 i = 10% Net Present Value (NPV) CF Enters cash flow mode CFO = $175 $175 $25 $100 $75 $50 C01 = $25 NPV is the change in wealth in present value terms from a series of cash flows F01 = You will not need to change frequency C02 = $100 F02 =
C03 = $75 F03 = NPV NPV = Enter discount rate CPT Net Present Value (NPV) C04 = $50 Enters Net Present Value mode I = 10 = $20.87 Internal Rate of Return (IRR) IRR is the discount rate that equates the PV of a series of cash flows to their cost The IRR is the discount rate that makes the NPV = 0 CF1 CF2 CFn NPV = 0 = CF + + +... + (1+ IRR) (1+ IRR) (1+ IRR) 0 1 2 n Internal Rate of Return (IRR) Internal Rate of Return (IRR) CF Enters cash flow mode T0 T1 T2 T3 T4 CFO= $175 $175 $25 $100 $75 $50 C01= $25 F01= You will not need to change frequency C02= $100 F02= C03= $75 IRR IRR= Internal Rate of Return (IRR) F03= CPT C04= $50 Enters Internal Rate of Return Mode = 15.067% Payback Period & Discounted Payback Primarily a measure of liquidity Assess how long it will take to recover the initial investment on a project Projects with payback periods longer than an arbitrary number of years are rejected Limitations Not a measure of value Ignores time value of money (solved by using discounted payback) Ignores CFs beyond the payback period
i = 10% Payback Period & Discounted Payback T0 T1 T2 T3 T4 Payback Period & Discounted Payback CF Enters cash flow mode CFO = $175 $175 $25 $100 $75 $50 C01 = $25 Calculate the payback period and discounted payback period NB This functionality is only available on the BAII+ Professional F01 = You will not need to change frequency C02 = $100 F02 = C03 = $75 F03 = NPV Payback Period & Discounted Payback C04 = $50 Enters Net Present Value mode I = 10 NPV = Payback Period & Discounted Payback NFV = PB = CPT = 2.67 Years DPB = CPT = 3.39 Years Enter discount rate Breakeven Quantity of Sales Breakeven quantity is the level of sales at which a firm s EBIT is zero. Total Fixed Costs Q BE = Price Var. Cost per unit Breakeven Quantity of Sales 6 Enters breakeven mode FC= $500,000 VC= $60 Example: If P = $85; V = $60; F = $500,000; What is the firm s breakeven point? P= $85 PFT= Q= CPT Breakeven is the quantity at which 0 profit is made, so leave blank = 20,000 units
PV of Uneven Cash Flows i = 10% T0 T1 T2 T3 Uneven Cash Flows? $300 $600 $200 Note that the cash flows are at the end of the period so ensure you are in END mode CF PV of Uneven Cash Flows Enters cash flow mode PV of Uneven Cash Flows (cont) C03 = 200 CFO = This example has no T0 cash flow NPV Enters Net Present Value mode C01 = 300 F01 = You will not need to change frequency C02 = 600 I = 10 Enter discount rate NPV = CPT = $918.86 F02 = Net Present Value FV of Uneven Cash Flows T0 T1 T2 T3 i = 10% FV of Uneven Cash Flows CF Enters cash flow mode $300 $600 $200 Note that the cash flows are at the end of the period so ensure you are in END mode? CFO = C01 = 300 F01 = This example has no T0 cash flow You will not need to change frequency C02 = 600 F02 =
FV of Uneven Cash Flows (cont) C03 200 NPV I = 10 Enter discount rate NPV= Used for calculating present value NFV= CPT = $1,223 Enters Net Present Value mode Net Future Value (BAII+ Professional only) Mean, Variance, and Standard Deviation Measures of Central Tendency: Population and Sample Means Population and sample means have different symbols but are both arithmetic means Population Mean : µ = Sample Mean : X = n i=1 n N i=1 X N i X i Population and Sample Means Over the last 3 years Cerny Plc s stock returns have been as follows: Year % Return 1 6 2 8 3 4 Calculate the mean return May be entered as decimals or whole numbers Population and Sample Means X01 = 6 Y01 = 7 Enters data entry mode This is used for entering the probability of the X variable occurring as we are using historic data, this can be left blank X02 = 8 Population and Sample Means (cont) X03 = 4 8 Enters statistics mode Keep pressing until 1-V appears 1-V = 1 Variable Pressing the down arrow repeatedly now allows you to review the statistic for the data you entered Y02 = X = 6
Population Mean with Probabilities Cerny Plc s expected stock return for next year is as follows: May be entered as decimals or whole numbers % Return Probability 6 0.3 8 0.2 4 0.5 Calculate the mean return Must be entered as whole numbers Population and Sample Means X01 = 6 Y01 = 7 30 Enters data entry mode The calculator requires the probability to be entered as a whole number not a decimal X02 = 8 Y02 = 20 Population and Sample Means (cont) X03 = 4 X = 5.4 8 Y03 = 50 Enters statistics mode Keep pressing until 1-V appears 1-V = 1 Variable Pressing the down arrow repeatedly now allows you to review the statistic for the data you entered Sample Variance (s 2 ) and Sample Standard Deviation (s) n ( Xi X) ( Xi X) n 2 2 2 i=1 i=1 s = s = n 1 n 1 Key difference between calculation of σ 2 and s 2 is that the sum of the squared deviations for s 2 is divided by n 1 instead of n Sample Variance (Sx 2 ) Over the last 3 years, Cerny Plc s stock returns have been as follows: Year % Return 1 6 2 8 3 4 May be entered as decimals or whole numbers Calculate the sample standard deviation and variance. With this data, it is more likely that sample standard deviation will be of use as it appears we only have a sample of three years. Sample Variance (Sx 2 ) Solution X01 = 6 Y01 = 7 Enters data entry mode This is used for entering the probability of the X variable occurring as we are using historic data, this can be left blank X02 = 8 Y02 =
X03 = 4 Sx = 2 8 Sample Variance (Sx 2 ) Solution x 2 Sx 2 = 4 Enters statistics mode Keep pressing until 1-V appears 1-V = 1 Variable Pressing the down arrow repeatedly now allows you to review the statistic for the data you entered Sx = Sample standard deviation Population Variance and Standard Deviation Variance is the average of the squared deviations from the mean Standard deviation is the square root of variance N 2 ( X i µ ) 2 i=1 2 σ = σ = σ N Expected Population Variance (σ x2 ) Cerny Plc s expected stock return for next year is as follows: % Return Probability 6 0.3 Must be entered as 8 0.2 whole May be entered as decimals or whole numbers 4 0.5 numbers Calculate the population standard deviation and variance. With this data, it is more likely that population standard deviation will be of use as the probabilities sum to one, indicating we have the full range of possible outcomes. X01 = 6 Y01 = 7 30 Population Variance (σ x2 ) Enters data entry mode The calculator requires the probability to be entered as a whole number not a decimal X02 = 8 Y02 = 20 Population Variance (σ x2 ) X03 = 4 Y03 = 50 8 Enters statistics mode Keep pressing until 1-V appears 1-V = 1 Variable Covariance, Correlation, and Regression Pressing the down arrow repeatedly now allows you to review the statistic for the data you entered σ x = 1.56 σ x 2 = 2.44
cov 1,2 = ( R R )( R R ) n t,1 1 t,2 2 t= 1 n 1 Sample Covariance Year Stock 1 Stock 2 1 +0.05 +0.07 2 0.02 0.04 3 +0.12 +0.18 Example: Calculate the covariance between the return on the two stocks indicated below: May be entered as decimals or whole numbers Covariance of Rates of Return 7 Enters data entry mode X01 = 5 Y01 = 7 X02 = 2 Y02 = 4 X03 = 12 Y03 = 18 8 Covariance of Rates of Return Enters statistics mode Keep pressing until LIN appears LIN = Linear Regression Pressing the down arrow repeatedly now allows you to review the statistic for the data you entered n= No of paired observations (3 in this example) x= Mean value of x variable Sx= Sample standard deviation of x variable Covariance of Rates of Return σx = Population standard deviation of x variable y = Mean value of y variable Sy = Sample standard deviation of y variable σy = Population standard deviation of y variable a = Intercept of regression line b = Gradient of regression line r = Sample correlation coefficient Covariance of Rates of Return Joint Probability Function Sx = 7 STO 1 Sy = 11 STO 2 r = 1 STO 3 Covariance = Sx Sy r RCL 1 RCL 2 RCL 3 = Cov = 77 or as a decimal 0.0077 Returns R B = 40% R A = 20% R A = 15% 0.15 R B = 20% R B = 0% 0.60 R A = 4% 0.25 E(R A ) = 13% E(R B ) = 18% Probabilities Unfortunately the calculator can t do this as there are two variables and probabilities and the calculator only has X and Y inputs (see quant for manual working)
Straight Line Method Depreciation Example: A new piece of equipment cost $4,000 on 1 January 20x0 and is likely to last for 4 years with an estimated residual value of $1,000 at the end of the period. original cost salvage value depreciation expense = depreciable life SL 4 Enters depreciation mode Straight line depreciation Once you have SL on screen LIF = Straight Line Method Cycles between all the depreciation methods 4 M01 = CST = SAL = YR = Straight Line Method $4,000 $1,000 This is used to tell the calculator if the asset was purchased partway through a month or year (i.e. 4.5 would be halfway through month 4). You will not need this in the exam. You can now choose the year you want (let s say Year 2) 2 Now just press DEP =Annual depreciation expense = 750 to review the data RBV =Reduced book value (the equivalent of NBV) (i.e. cost accumulated depreciation) = 2,500 RDV =Remaining depreciable value (i.e. the remaining amount of depreciation to be charged through the Income Statement in subsequent years) = 1,500 Straight Line Method Double Declining Balance Method Accelerated Methods Allocation of cost is greatest in early years Example: A new piece of equipment cost $4,000 on 1 January 20x0 and is likely to last for 4 years with an estimated residual value of $1,000 at the end of the period. DDB = (Cost Acc Dep n ) ( 2 / Useful Economic Life ) NBV Be careful not to depreciate below residual value!
DB= 200 4 Double Declining Balance Method Enters depreciation mode DDB depreciation Once you have DB = 200 on screen LIF = 4 Cycles between all the depreciation methods M01 = CST = SAL = YR = Double Declining Balance Method $4,000 $1,000 This is used to tell the calculator if the asset was purchased partway through a month or year (i.e. 4.5 would be halfway through month 4). You will not need this in the exam. You can now choose the year you want (let s say Year 2) 2 Now just press Double Declining Balance Method DEP =Annual depreciation expense = 1,000 to review the data RBV =Reduced book value (the equivalent of NBV) (i.e. cost accumulated depreciation) = 1,000 RDV =Remaining depreciable value (i.e. the remaining amount of depreciation to be charged through the Income Statement in subsequent years) = 0