FINC2012 NOTES
MAKING INVESTMENT DECISIONS WITH THE NET PRESENT VALUE RULE: CH 6
APPLYING THE NET PRESENT VALUE RULE
RULE 1: ONLY CASH FLOW IS RELEVANT
• Capital Expenses
o Record capital expenditures when they occur
o To determine cash flow from income, add back depreciation and subtract capital expenditure
• Working Capital
o Difference between company’s short-term assets and liabilities
RULE 2: ESTIMATE CASH FLOWS ON AN INCREMENTAL BASIS
• Remember to include taxes
• Do not confuse average (accrual) with incremental payoffs – only care about difference
• Include all incidental effects – after-sale effects/indirect (incidental negative/positive effects on other projects)
• Forecast sales today and recognize after-sales cash flows to come later
• Include opportunity costs – the benefits of opportunity forgone
• Forget sunk costs – include if incremental sunk cost however
• Beware of allocated overhead costs
• Remember salvage value
RULE 3: TREAT INFLATION CONSISTENTLY
• 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 – typically nominal in financial statements
EXAMPLE
• You invest in a project that will produce real cash flows of -$100 in year zero and then $35, $50, and $30 in the three
respective years. If the nominal discount rate is 15% and the inflation rate is 10%, what is the NPV of the project?
Real discount rate = 1 + nominal discount rate - 1
1 + inflation rate
• Nominal figures
Year Cash Flow PV @ 15%
0 - 100 - 100
1 35 ´1.10 = 38.5 138.15.5 = 33.48
2 50 ´1.10 2 = 60.5 160.15.52 = 45.75
3 30 ´1.103 = 39.9 139.15.93 = 26.23
$5.5
• You invest in a project that will produce real cash flows of -$100 in year zero and then $35, $50, and $30 in the three
respective years. If the nominal discount rate is 15% and the inflation rate is 10%, what is the NPV of the project?
1
,Real discount rate = 1 + nominal discount rate - 1
1 + inflation rate
1.15
= - 1 = .045
1.10
• Real figures
Year Cash Flow PV@4.50%
0 - 100 - 100
1 35 35
1.045
= -33.49
2 50 50
1.045 2
= 45.79
3 30 30
1.0453
= 26.29
= $5.5
RULE 4: SEPARATE INVESTMENT AND FINANCING DECISION
• Question: How should you treat the proceeds from the debt issue and the interest and principal payments on the debt?
• Answer: You should neither subtract the debt proceeds from the required investment nor recognize the interest and
principal payments on the debt as cash outflows.
EXAMPLE - IM&C FERTILIZER PROJECT
• Revised projections ($1000s) reflecting inflation
• NPV using nominal cash flows
1,630 2,381 6,205 10,685 10,136
NPV = -12,600 - + + + +
1.20 (1.20 )2 (1.20 )3 (1.20 )4 (1.20 )5
6,110 3,444
+ + = 3,520 or $3,520,000
(1.20)6 (1.20)7
• Cash flow analysis ($1000s)
• Details of cash flow forecast in year 3 ($1000s)
2
, • Tax depreciation allowed under the modified accelerated cost recovery system (MACRS)
• (Figures in percent of depreciable investment)
• Tax Payments ($1000s)
• Revised cash flow analysis ($1000s)
USING THE NPV RULE TO CHOOSE AMONG PROJECTS
PROBLEM 1: INVESTMENT TIMING DECISION
• Some projects are more valuable if undertaken in the future
• Examine start dates (t) for investment and calculate net future value for each date
• Discount net values back to present
567 8979:6 ;<=96 <7 ><76 ?
• Net present value of investment if undertaken at date 𝑡 = (ABC)E
EXAMPLE
• You own a large tract of inaccessible timber. To harvest it, you have to invest a substantial amount in access roads and
other facilities. The longer you wait, the higher the investment required. On the other hand, lumber prices will rise as
you wait, and the trees will keep growing, although at a gradually decreasing rate. Given the following data and a 10%
discount rate, when should you harvest?
• Answer: Year 4
3
, PROBLEM 2: THE CHOICE BETWEEN LONG AND SHORT-LIVED EQUIPMENT
• Equivalent Annual Cash Flow:
o The cash flow per period with the same present value as the actual cash flow as the project
present value of cash flows
Equivalent annual cost (annuity) =
annuity factor
EXAMPLE
• Given the following COSTS from operating two machines and a 6% cost of capital, which machine has the lower
equivalent annual cost?
Example (with a twist)
• Select one of the two following projects, based on highest “equivalent annual annuity” (r = 9%)
PROBLEM 3: WHEN TO REPLACE AN OLD MACHINE
EXAMPLE
• A machine is expected to produce a net inflow of $4,000 this year and $4,000 next year before breaking. You can replace
it now with a machine that costs $15,000 and will produce an inflow of $8,000 per year for three years. Should you
replace now or wait a year?
• Answer: Wait
PROBLEM 4: COST OF EXCESS CAPACITY
EXAMPLE
• A computer system costs $500,000 to buy and operate at a discount rate of 6% and lasts five years.
• Equivalent annual cost of $118,700
• Undertaking project in year 4 has a present value of 118,700/(1.06)4, or about $94,000
4
MAKING INVESTMENT DECISIONS WITH THE NET PRESENT VALUE RULE: CH 6
APPLYING THE NET PRESENT VALUE RULE
RULE 1: ONLY CASH FLOW IS RELEVANT
• Capital Expenses
o Record capital expenditures when they occur
o To determine cash flow from income, add back depreciation and subtract capital expenditure
• Working Capital
o Difference between company’s short-term assets and liabilities
RULE 2: ESTIMATE CASH FLOWS ON AN INCREMENTAL BASIS
• Remember to include taxes
• Do not confuse average (accrual) with incremental payoffs – only care about difference
• Include all incidental effects – after-sale effects/indirect (incidental negative/positive effects on other projects)
• Forecast sales today and recognize after-sales cash flows to come later
• Include opportunity costs – the benefits of opportunity forgone
• Forget sunk costs – include if incremental sunk cost however
• Beware of allocated overhead costs
• Remember salvage value
RULE 3: TREAT INFLATION CONSISTENTLY
• 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 – typically nominal in financial statements
EXAMPLE
• You invest in a project that will produce real cash flows of -$100 in year zero and then $35, $50, and $30 in the three
respective years. If the nominal discount rate is 15% and the inflation rate is 10%, what is the NPV of the project?
Real discount rate = 1 + nominal discount rate - 1
1 + inflation rate
• Nominal figures
Year Cash Flow PV @ 15%
0 - 100 - 100
1 35 ´1.10 = 38.5 138.15.5 = 33.48
2 50 ´1.10 2 = 60.5 160.15.52 = 45.75
3 30 ´1.103 = 39.9 139.15.93 = 26.23
$5.5
• You invest in a project that will produce real cash flows of -$100 in year zero and then $35, $50, and $30 in the three
respective years. If the nominal discount rate is 15% and the inflation rate is 10%, what is the NPV of the project?
1
,Real discount rate = 1 + nominal discount rate - 1
1 + inflation rate
1.15
= - 1 = .045
1.10
• Real figures
Year Cash Flow PV@4.50%
0 - 100 - 100
1 35 35
1.045
= -33.49
2 50 50
1.045 2
= 45.79
3 30 30
1.0453
= 26.29
= $5.5
RULE 4: SEPARATE INVESTMENT AND FINANCING DECISION
• Question: How should you treat the proceeds from the debt issue and the interest and principal payments on the debt?
• Answer: You should neither subtract the debt proceeds from the required investment nor recognize the interest and
principal payments on the debt as cash outflows.
EXAMPLE - IM&C FERTILIZER PROJECT
• Revised projections ($1000s) reflecting inflation
• NPV using nominal cash flows
1,630 2,381 6,205 10,685 10,136
NPV = -12,600 - + + + +
1.20 (1.20 )2 (1.20 )3 (1.20 )4 (1.20 )5
6,110 3,444
+ + = 3,520 or $3,520,000
(1.20)6 (1.20)7
• Cash flow analysis ($1000s)
• Details of cash flow forecast in year 3 ($1000s)
2
, • Tax depreciation allowed under the modified accelerated cost recovery system (MACRS)
• (Figures in percent of depreciable investment)
• Tax Payments ($1000s)
• Revised cash flow analysis ($1000s)
USING THE NPV RULE TO CHOOSE AMONG PROJECTS
PROBLEM 1: INVESTMENT TIMING DECISION
• Some projects are more valuable if undertaken in the future
• Examine start dates (t) for investment and calculate net future value for each date
• Discount net values back to present
567 8979:6 ;<=96 <7 ><76 ?
• Net present value of investment if undertaken at date 𝑡 = (ABC)E
EXAMPLE
• You own a large tract of inaccessible timber. To harvest it, you have to invest a substantial amount in access roads and
other facilities. The longer you wait, the higher the investment required. On the other hand, lumber prices will rise as
you wait, and the trees will keep growing, although at a gradually decreasing rate. Given the following data and a 10%
discount rate, when should you harvest?
• Answer: Year 4
3
, PROBLEM 2: THE CHOICE BETWEEN LONG AND SHORT-LIVED EQUIPMENT
• Equivalent Annual Cash Flow:
o The cash flow per period with the same present value as the actual cash flow as the project
present value of cash flows
Equivalent annual cost (annuity) =
annuity factor
EXAMPLE
• Given the following COSTS from operating two machines and a 6% cost of capital, which machine has the lower
equivalent annual cost?
Example (with a twist)
• Select one of the two following projects, based on highest “equivalent annual annuity” (r = 9%)
PROBLEM 3: WHEN TO REPLACE AN OLD MACHINE
EXAMPLE
• A machine is expected to produce a net inflow of $4,000 this year and $4,000 next year before breaking. You can replace
it now with a machine that costs $15,000 and will produce an inflow of $8,000 per year for three years. Should you
replace now or wait a year?
• Answer: Wait
PROBLEM 4: COST OF EXCESS CAPACITY
EXAMPLE
• A computer system costs $500,000 to buy and operate at a discount rate of 6% and lasts five years.
• Equivalent annual cost of $118,700
• Undertaking project in year 4 has a present value of 118,700/(1.06)4, or about $94,000
4
