Principles of Corporate Finance Brealey and Myers Sixth Edition Making Investment Decisions with the Net Present Value Rule Slides by Matthew Will Irwin/McGraw Hill Chapter ©The McGraw-Hill Companies, Inc., 200 6- Topics Covered What To Discount IM&C Project Project Interaction Timing Equivalent Annual Cost Replacement Cost of Excess Capacity Fluctuating Load Factors Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- What To Discount Only Cash Flow is Relevant Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- What To Discount Only Cash Flow is Relevant Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- What To Discount Points to “Watch Out For” Do not confuse average with incremental payoff Include all incidental effects Do not forget working capital requirements Forget sunk costs Include opportunity costs Beware of allocated overhead costs Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation INFLATION RULE Be consistent in how you handle inflation!! Use nominal interest rates to discount nominal cash flows Use real interest rates to discount real cash flows You will get the same results, whether you use nominal or real figures Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for additional years (4 years total) If discount rates are 10% what is the present value cost of the lease? Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation Example You own a lease that will cost you $8,000 next year, increasing at 3% a year (the forecasted inflation rate) for additional years (4 years total) If discount rates are 10% what is the present value cost of the lease? 1+nominal interest rate + real interest rate = 1+inflation rate Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- Inflation Example - nominal figures Year Cash Flow PV @ 10% 8000 8000 1.10 8000x1.03 = 8240 8000x1.032 = 8240 8240 1.102 8487 20 1.103 8741.82 1.104 8000x1.03 = 8487.20 = 7272.73 = 6809.92 = 6376.56 = 5970.78 $26,429.99 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 10 Inflation Example - real figures Year Cash Flow 8000 1.03 8240 1.032 8487.20 1.033 8741.82 1.034 = 7766.99 = 7766.99 = 7766.99 = 7766.99 PV@6.7961% 7766.99 1.068 7766.99 1.0682 7766.99 1.0683 7766.99 1.0684 = 7272.73 = 6809.92 = 6376.56 = 5970.78 = $26,429.99 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 17 IM&C’s Guano Project Revised cash flow analysis ($1000s) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 18 Timing Even projects with positive NPV may be more valuable if deferred The actual NPV is then the current value of some future value of the deferred project Net future value as of date t Current NPV = t (1 + r ) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 19 Timing Example You may harvest a set of trees at anytime over the next years Given the FV of delaying the harvest, which harvest date maximizes current NPV? Harvest Year Net FV ($1000s) 50 64.4 77.5 89.4 % change in value 28.8 20.3 15.4 11.9 Irwin/McGraw Hill 100 109.4 9.4 ©The McGraw-Hill Companies, Inc., 200 6- 20 Timing Example - continued You may harvest a set of trees at anytime over the next years Given the FV of delaying the harvest, which harvest date maximizes current NPV? 64.4 NPV if harvested in year = = 58.5 1.10 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 21 Timing Example - continued You may harvest a set of trees at anytime over the next years Given the FV of delaying the harvest, which harvest date maximizes current NPV? 64.4 NPV if harvested in year = = 58.5 1.10 NPV ($1000s) 50 58.5 Irwin/McGraw Hill Harvest Year 64.0 67.2 68.3 67.9 ©The McGraw-Hill Companies, Inc., 200 6- 22 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 23 Equivalent Annual Cost Equivalent Annual Cost - The cost per period with the same present value as the cost of buying and operating a machine present value of costs Equivalent annual cost = annuity factor Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 24 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 25 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method Machine A B Irwin/McGraw Hill Year 15 10 6 PV@6% 28.37 21.00 EAC ©The McGraw-Hill Companies, Inc., 200 6- 26 Equivalent Annual Cost Example Given the following costs of operating two machines and a 6% cost of capital, select the lower cost machine using equivalent annual cost method Machine A B Irwin/McGraw Hill Year 15 10 6 PV@6% 28.37 21.00 EAC 10.61 11.45 ©The McGraw-Hill Companies, Inc., 200 6- 27 Machinery Replacement Annual operating cost of old machine = Cost of new machine Year: 15 5 NPV @ 10% 27.4 Equivalent annual cost of new machine = 27.4/(3-year annuity factor) = 27.4/2.5 = 11 MORAL: Do not replace until operating cost of old machine exceeds 11 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 28 Cost of Excess Capacity A project uses existing warehouse and requires a new one to be built in Year rather than Year 10 A warehouse costs 100 & lasts 20 years Equivalent annual cost @ 10% = 100/8.5 = 11.7 10 11 With project 0 11.7 11.7 11.7 Without project 0 0 11.7 Difference 0 11.7 11.7 PV extra cost = 11.7 + 11.77 + + 11.7 10 = 27.6 (1.1) (1.1) (1.1) Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 29 Fluctuating Load Factors Annual output per machine Two Old Machines 750 units Operating cost per machine × 750 = $1,500 PV operating cost per pachine 1,500/.10 = $15,000 PV operating cost of two machines ì 15,000 = $30,000 Irwin/McGraw Hill âThe McGraw-Hill Companies, Inc., 200 6- 30 Fluctuating Load Factors Two New Machines Annual output per machine 750 units Capital cost pe machine $6,000 Operating cost per machine × 750 = $750 PV operating cost per pachine 6,000 + 750/.10 = $13,500 PV operating cost of two machines × 13,500 = $27,000 Irwin/McGraw Hill ©The McGraw-Hill Companies, Inc., 200 6- 31 Fluctuating Load Factors One Old Machine Annual output per machine 500 units Capital cost pe machine Operating cost per machine × 500 = $1,000 PV operating cost per pachine 1,000/.10 = $10,000 PV operating cost of two machines $26,000 Irwin/McGraw Hill One New Machine 1,000 units $6,000 × 1,000 = $1,000 6,000 + 1,000 / 10 = $16,000 ©The McGraw-Hill Companies, Inc., 200 ... 8741.82 1.034 = 7766.99 = 7766.99 = 7766.99 = 7766.99 PV@6.7961% 7766.99 1 .068 7766.99 1 .068 2 7766.99 1 .068 3 7766.99 1 .068 4 = 7272.73 = 6809.92 = 6376.56 = 5970.78 = $26,429.99 Irwin/McGraw Hill... valuable if deferred The actual NPV is then the current value of some future value of the deferred project Net future value as of date t Current NPV = t (1 + r ) Irwin/McGraw Hill ©The McGraw-Hill... 200 6- 27 Machinery Replacement Annual operating cost of old machine = Cost of new machine Year: 15 5 NPV @ 10% 27.4 Equivalent annual cost of new machine = 27.4/(3-year annuity factor) = 27.4/2.5