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What is capital budgeting?
Capital budgeting is the process of deciding whether a long-term investment project should be accepted or rejected.
Typical examples include buying equipment, opening a new location, launching a product line, upgrading technology,
or replacing an old machine.
Main question: Does this project create value for the firm?
It focuses on future cash flows, not accounting profit.
It uses the time value of money.
It helps firms compare projects consistently.
It connects project choice to shareholder value.
Why do we study it?
Capital budgeting matters because large investment decisions can help or hurt a firm for many years.
A bad project can lock a company into weak returns, while a good project can add value immediately.
Why it matters
Value
Main lens
Cash flow
Core idea
Discounting
In practice, managers use capital budgeting when the decision is large, long-term, risky, and difficult to reverse.
How do we evaluate projects, and when do we use each tool?
NPV
Use when: you want the best value-creation decision.
Best for mutually exclusive projects
Directly measures value added in dollars
Usually the preferred decision rule
IRR
Use when: you want a return expressed as a percentage.
Popular and intuitive
Can conflict with NPV
Can mislead with unusual cash-flow patterns
MIRR
Use when: you want an improved version of IRR.
Uses a finance rate and reinvestment rate
Often more realistic than IRR
Good supplement to NPV
Payback
Use when: liquidity and speed of recovery matter.
Simple and fast
Ignores later cash flows
Useful as a rough screening tool
Discounted payback
Use when: you want payback plus time value of money.
Better than regular payback
Still ignores later cash flows
Good secondary measure
PI
Use when: capital is rationed or projects have different sizes.
Relative measure
Good for ranking efficiency
Do not let it override NPV for mutually exclusive choices
Bottom line: If NPV and IRR disagree for mutually exclusive projects, the usual rule is to follow NPV.
Excel syntax and classroom formulas
1) NPV in Excel
Syntax: NPV(rate, value1, value2, ...)
Excel discounts the cash flows from year 1 onward, so year 0 is usually added separately.
Example:
=NPV(11%, 350, 350, 350) - 800
Reminder: the cash flows inside NPV() must be equally spaced and listed in the correct order.
IRR is the discount rate that makes NPV equal to zero. When cash flows are non-conventional,
Excel's guess can matter. A default guess of 10% often finds the lower root,
while a higher guess such as 40% can find the second IRR.
3) MIRR in Excel
Syntax: MIRR(values, finance_rate, reinvest_rate)
Example:
=MIRR(B2:E2, 11%, 11%)
MIRR separates the borrowing cost from the reinvestment rate and avoids some of the problems that traditional IRR can create.
4) PI formulas
PI = Present value of inflows / |CF0|
PI = 1 + NPV / |CF0|
Method summary table
Method
Equation / idea
Ease of use
Potential problems
Popularity
NPV
Σ(CF / (1+r)n) − Initial investment
Easy in Excel
Sensitive to cash-flow estimates and discount rate
Very popular because it focuses on value creation
IRR
Discount rate that makes NPV = 0
Easy in Excel
Assumes reinvestment at IRR; can mislead with multiple sign changes
Very popular because it gives a % return
MIRR
Uses finance rate + reinvestment rate
Moderate
Less familiar to some users
Used less often, but helpful in tricky cases
Payback
Time needed to recover initial investment
Very easy
Ignores cash flows after payback
Common for quick screening
PI
PV inflows / Initial investment
Easy
Relative measure; can be less clear for mutually exclusive projects
Used less than NPV and IRR, but still useful
Worked example using the JU capital budgeting calculator
Example: a new store near JU plans to spend $10,000 today, operate for
4 years, and then close at the end of Year 4. Assume the store generates
these annual net cash inflows:
$3,000, $3,500, $4,000, and $4,500.
The firm's WACC is 10%.
Classroom takeaway: because NPV is positive and both
IRR and MIRR are above the 10% WACC,
this project should be accepted.
Single-project calculator (Part I classroom example)
Enter the WACC and the project cash flows. The page computes NPV, IRR, MIRR, PI, payback period, and discounted payback period.
The default values match the classroom example.
Default guess is 10%. For multiple IRRs, try a higher guess such as
40% to find the second root.
Payback:
Add undiscounted cash inflows until the initial outlay is recovered.
Discounted payback:
First discount each inflow by WACC, then add the present values until the initial outlay is recovered.
How the IRR guess works
Normal cash flows:
A project usually has one IRR, so the guess does not matter much.
Non-conventional cash flows:
If the signs change more than once, there may be more than one IRR.
A guess near 10% often finds the lower IRR.
A higher guess such as 40% can find the second IRR.
Results
NPV:—
IRR:—
All IRRs found (if multiple):—
MIRR:—
PI:—
Payback period:—
Discounted payback:—
Decision by NPV:—
Math equations + Excel formulas for IRR and MIRR
NPV = ∑ [ CFt / (1 + r)t ]
IRR solves: 0 = ∑ [ CFt / (1 + IRR)t ]
MIRR = ( FV of positive cash flows at reinvestment rate / |PV of negative cash flows at finance rate| )1/n − 1
PI = PV of inflows / |CF0| = 1 + NPV / |CF0|
Payback = years before full recovery + (unrecovered amount / current year cash flow)
Discounted payback = years before PV recovery + (unrecovered amount / current year discounted cash flow)
IRR uses one internal rate for the whole project. MIRR uses two rates:
a finance rate for negative cash flows and a reinvestment rate for positive cash flows.
In the MIRR picture, negative cash flows move left to today and positive cash flows move right to the end.
Interpretation: IRR forces the project into one rate. MIRR separates the financing side from the reinvestment side, so it is often easier to explain and usually gives one cleaner answer.
Video: What is MIRR? How does it address the challenges of internal rate of return?
When projects are mutually exclusive, choosing one means giving up the other.
In that setting, the standard classroom rule is to choose the project with the higher NPV.
Question 1: Projects S and L
Year
Project S
Project L
0
-$1,100
-$2,700
1
$550
$650
2
$600
$725
3
$100
$800
4
$100
$1,400
Key idea: if one manager chooses by IRR and another chooses by NPV, the value forgone is the difference between the NPV of the project actually chosen and the highest available NPV.
Question 2: Project A vs. Project B
Period
Project A
Project B
0
-500
-400
1
325
325
2
325
200
Crossover rate: 11.8%
If required return is 10%: NPV of A is slightly higher than NPV of B.
If required return is 13%: NPV of B is higher than NPV of A.
Mutually exclusive rule: choose the project with the higher NPV at the required return.
If independent: choose both if both have positive NPV.
Math work for the crossover rate
NPV(A) = -500 + 325/(1+r) + 325/(1+r)2
NPV(B) = -400 + 325/(1+r) + 200/(1+r)2
Set the two NPVs equal to find the crossover rate:
-500 + 325/(1+r) + 325/(1+r)2 = -400 + 325/(1+r) + 200/(1+r)2
-100 + 125/(1+r)2 = 0
125/(1+r)2 = 100
(1+r)2 = 1.25
1+r = √1.25
r = √1.25 - 1 = 0.1180 = 11.80%
The crossover rate is the discount rate where the two projects have the same NPV. Below that rate, one project can have the higher NPV; above that rate, the ranking can switch.
NPV profiles and the crossover rate
Non-conventional cash flow: why IRR can give two answers but MIRR gives one
Non-conventional cash flows change sign more than once. That can make the NPV profile cross zero more than once, which means IRR can produce more than one economically meaningful answer.
Year
Cash flow
0
-$90,000
1
$132,000
2
$100,000
3
-$150,000
IRR math work: why there are two IRR solutions
Set NPV equal to zero:
0 = -90,000 + 132,000/(1+r) + 100,000/(1+r)2 - 150,000/(1+r)3
Multiply both sides by (1+r)3:
0 = -90,000(1+r)3 + 132,000(1+r)2 + 100,000(1+r) - 150,000
This equation has two positive solutions for r:
IRR1 ≈ 10.11%
IRR2 ≈ 42.66%
Excel can find both if you change the guess:
=IRR({-90000,132000,100000,-150000},0.10) → 10.11%
=IRR({-90000,132000,100000,-150000},0.40) → 42.66%
Because the cash-flow signs switch more than once, the NPV curve crosses zero twice. That is why there are two IRR answers in this example.
MIRR math work: move negatives left and positives right
Use finance rate = 15% and reinvestment rate = 15%.
Step 1: Move negative cash flows to year 0:
PV of negatives = 90,000 + 150,000/(1.15)3
PV of negatives = 188,627.43
Step 2: Move positive cash flows to the end of year 3:
FV of positives = 132,000(1.15)2 + 100,000(1.15)
FV of positives = 289,570.00
Step 3: Solve for one rate over 3 years:
MIRR = (289,570.00 / 188,627.43)1/3 - 1
MIRR ≈ 15.36%
Excel:
=MIRR({-90000,132000,100000,-150000},15%,15%) → 15.36%
Try these cash flows in the calculator above:
-90000, 132000, 100000, -150000.
Use Guess 10% to find the first IRR and Guess 40% to find the second IRR.
NPV profile: the curve crosses zero twice
MIRR timeline: negatives move left, positives move right
Positive cash flow moved to the rightNegative cash flow moved to the leftSingle MIRR result
Class video of Chapter 11 case study
Students can click the button or watch directly on the page.