Example:

Project cost: $1,000

Cash flows (3 years): $400, $500, $600

Discount rate (WACC): 10%

Answer:

IRR

NPV=

IRR

Modified IRR

Formula

Example Project Details

Initial Investment (Year 0): $10,000
Cash Inflows:

Year 1: $4,000
Year 2: $5,000
Year 3: $6,000
Finance Rate (Borrowing Cost): 8%
Reinvestment Rate (Earnings on Cash Inflows): 6%

Practice Problem (Test Yourself!)

Project X:
Initial Cost: $8,000
 Cash Inflows: Year 1: $3,000, Year 2: $4,000, Year 3: $5,000
Finance Rate: 7%, Reinvestment Rate: 5%
Calculate MIRR.

4. Payback Period
What it is: Time to recover the initial investment.
Example:
Project cost: $1,000
Cash flows: $300, $400, $500, $600
Calculation:

Example:
PV of inflows = $1,227.65 (from NPV example)
Initial cost = $1,000

Practice Problem:
Budget: $1,500
Projects:
Project
P
Q
R
S
What’s the best combination?
*(Answer: P + S = $1,400 → NPV $560; or P + Q + R = $1,500
→ NPV $535. Choose P + S for higher NPV.)*

Answer:

P
S
Q
 R
Budget: $1,500
Combination 1

Combination 2

Combination 2 is best combination.

APV=

Example: APV Calculation

Project:
Initial Investment: $1,000
FCF (Year 1-3): $400, $500, $600
Unlevered Cost of Equity (r₀): 12%
Debt: $500 at 6% interest
Tax Rate: 30%

APV=

Capital Investment Appraisal Techniques – Simplified

Guide
We’ll break down each method with examples and progress
to ICAP-level problems.

1. Net Present Value (NPV)

What it is: Calculates the present value of future cash
flows minus the initial investment.
Formula:
NPV=∑(CFt(1+r)t)−Initial InvestmentNPV=∑((1+r)tCFt)​

−Initial Investment
Decision Rule:
NPV > 0 → Accept project (adds value)
NPV < 0 → Reject project
Example:
Project cost: $1,000
Cash flows (3 years): $400, $500, $600
Discount rate (WACC): 10%
Calculation:
 NPV=400(1.10)1+500(1.10)2+600(1.10)3−1000NPV=(1.10)14
00+(1.10)2500+(1.10)3600
​ ​ ​

−1000=363.64+413.22+450.79−1000= ∗∗+227.65 ∗∗=363.64

+413.22+450.79−1000=∗∗+227.65∗∗
Verdict: ✅ Accept (NPV > 0)

2. Internal Rate of Return (IRR)

What it is: The discount rate where NPV = 0 (break-even
return).
Decision Rule:
IRR > WACC → Accept
IRR < WACC → Reject
Example: Same project as above.
Solve for IRR where:
0=400(1+IRR)1+500(1+IRR)2+600(1+IRR)3−10000=(1+IRR
)1400+(1+IRR)2500+(1+IRR)3600−1000
​ ​ ​

Trial & Error (or Excel): IRR ≈ 23.4%

Verdict: ✅ Accept (23.4% > 10%)

3. Modified IRR (MIRR)

Why use it? Fixes IRR’s unrealistic reinvestment assumption.
Formula:
MIRR=(Terminal Value of Cash InflowsPV of Outflows)1/
n−1MIRR=(PV of OutflowsTerminal Value of Cash Inflows ​

)1/n−1
Example:
Reinvestment rate = 10%, Finance rate = 8%
Terminal Value = 400(1.10)² + 500(1.10)¹ + 600
= 1,634
PV Outflows = 1,000
MIRR=(16341000)1/3−1≈∗∗17.8 MIRR=(10001634 ​

)1/3−1≈∗∗17.8

4. Payback Period
What it is: Time to recover the initial investment.
Example:
Project cost: $1,000
Cash flows: $300, $400, $500, $600
Calculation:
Year 1: $300 (Remaining: $700)
Year 2: $400 (Remaining: $300)
Year 3: $500 → Only need $300 → 2.6 years
Decision Rule:
If company’s max payback = 3 years, accept.

5. Profitability Index (PI)

What it is: Measures value per dollar invested.
Formula:
PI=PV of Cash InflowsInitial InvestmentPI=Initial Investment
PV of Cash Inflows ​

Example:
PV of inflows = $1,227.65 (from NPV example)
Initial cost = $1,000
PI=1227.651000=∗∗1.23∗∗PI=10001227.65=∗∗1.23∗∗
​

Verdict: ✅ Accept (PI > 1)

6. Scenario & Sensitivity Analysis

What it is: Tests how changes in assumptions affect NPV.
Example:
Base Case NPV = $227.65
What if sales drop 20%?

New cash flows: $320, $400, $480

New NPV = $49.42 (still positive, but riskier).

7. Capital Rationing
What it is: Choosing projects under a limited budget.
Rule: Rank by PI (highest to lowest) and select within budget.
Example:
Project
A
B
C
Budget = $800 → Pick A + B (Total NPV = $320).

8. Advanced Techniques (APV, EIRR)

Adjusted Present Value (APV)
Formula:
APV=NPVUnlevered+PV(Tax Shield)APV=NPVUnlevered ​

+PV(Tax Shield)
Use: For projects with changing debt levels.
Equivalent IRR (EIRR)
Used in: Public sector projects (adjusts for social
costs/benefits).

ICAP-Level Practice Problems

1. NPV + IRR Conflict:

Project X: NPV = $100, IRR = 12%

Project Y: NPV = $80, IRR = 15%
WACC = 10%. Which to choose?
Answer: Project X (higher NPV).
2. MIRR Calculation:

Cash flows: -$1,000, $400, $600, $800

Reinvestment rate = 12%, Finance rate = 8%
Answer: MIRR ≈ 18.2%
3. Capital Rationing:

Budget = $1M. Projects:

A (Cost: $600K, PI=1.5)

B (Cost: $400K, PI=1.8)
C (Cost: $500K, PI=1.2)
Optimal Choice: B + A (Total PI = 3.3).

Key Takeaways
NPV = Best for absolute value.
IRR = Easy %, but can mislead.
MIRR = More realistic than IRR.
Payback = Simple but ignores time value.
Ready for mock questions? Or dive deeper into any
technique? 😊
show how to calculate IRR using two assumed rates
How to Calculate IRR Using Two Assumed Rates
(Trial & Error Method)
Since IRR is the discount rate that makes NPV = 0, we
estimate it by:
1. Assume two discount rates (one giving +NPV,
another giving -NPV).
2. Use linear interpolation to find the exact IRR.

Step-by-Step Example
Project:
Initial Investment = $1,000
Cash Flows (3 years) = $400, $500, $600
Step 1: Assume Two Rates
Rate 1 (r₁) = 20% → Try a rate that gives NPV > 0
Rate 2 (r₂) = 25% → Try a higher rate for NPV < 0
Step 2: Calculate NPV for Both Rates
At 20% (r₁):
NPV=400(1.20)1+500(1.20)2+600(1.20)3−1000NPV=(1.20)14
00+(1.20)2500+(1.20)3600−1000
​ ​ ​

Plugging in the numbers:

IRR=20%+(27.77×(25%−20%)27.77−(−52.80))IRR=20%
+(27.77−(−52.80)27.77×(25%−20%))=20%
​

+(27.77×5%80.57)=20%+(80.5727.77×5%) ​

eXPLAIN THIS IRR’s unrealistic reinvestment assumption

IRR’s Unrealistic Reinvestment Assumption –
Explained Simply
The Core Problem
The Internal Rate of Return (IRR) implicitly assumes that all
future cash flows generated by a project are reinvested at the
IRR itself. This is often unrealistic because:
1. IRR can be very high (e.g., 30%), but in reality, you
may not find other projects with such high returns to
reinvest in.
2. Market conditions change – actual reinvestment
rates (like WACC or bank interest) are usually lower.

Why This is Misleading?

Example: Two Projects with Same IRR but Different Reality

Project A:
Investment: $1,000
Cash Flows: $500 in Year 1, $500 in Year 2
IRR = 15%
IRR’s Hidden Assumption:
The $500 received in Year 1 is reinvested at 15% for
Year 2.
But if your actual reinvestment rate is just 5% (e.g., in
a bank), the true return is lower!
Real-World Calculation (5% Reinvestment):
Year 1: $500 → Reinvested at 5% → $525 in Year 2
Year 2: Another $500
Total Future Value = $525 + $500 = $1,025
Actual Annualized Return ≈ 12.2% (not 15%)
→ IRR overstates returns if reinvestment rates are lower.

How MIRR Fixes This

The Modified IRR (MIRR) lets you explicitly set:
1. Finance Rate (cost of borrowing, e.g., WACC).
2. Reinvestment Rate (realistic return on cash flows,
e.g., 5-10%).
Formula:

MIRR=(Terminal Value of InflowsPV of Outflows)1/

n−1MIRR=(PV of OutflowsTerminal Value of Inflows )1/n−1
​

Same Project A with MIRR (Reinvest at 5%):

1. Terminal Value = $500(1.05)¹ + $500 = $1,025
2. PV Outflows = $1,000
3. MIRR = (1025/1000)^(1/2) - 1 ≈ 12.2% (matches
reality!)

Key Takeaways
1. IRR’s Flaw: Assumes cash flows are reinvested at
IRR, which is often too optimistic.
2. MIRR’s Solution: Uses realistic reinvestment
rates for accurate returns.
 3. ICAP Exam Tip: If a question asks
about reinvestment risk, IRR’s assumption is a critical
weakness!

Practice Question
Project B:
Investment: $2,000
Cash Flows: $1,000 Year 1, $1,200 Year 2
IRR = 18%
Q: If you can only reinvest at 6%, what’s the true annualized
return (MIRR)?
*(Answer: Terminal Value = $1,000(1.06) + $1,200 = $2,260
→ MIRR ≈ 6.3%)*
Need more clarification? 😊
explain MIRR fORMULA IN DETAIL AND GIVE AN DETAILED
EXAMPLE
Modified Internal Rate of Return (MIRR) – Detailed
Explanation with Example
The MIRR fixes IRR’s unrealistic reinvestment assumption
by explicitly defining two key rates:
1. Finance Rate (Cost of Capital): The rate at which
cash outflows (investments) are discounted.
2. Reinvestment Rate: The rate at which cash inflows
(profits) are reinvested.

MIRR Formula Breakdown

MIRR=(Future Value of Cash Inflows (Compounded at Reinv
estment Rate)Present Value of Cash Outflows (Discounted at F
inance Rate))1n−1MIRR=(Present Value of Cash Outflows (D
iscounted at Finance Rate)Future Value of Cash Inflows (Com
pounded at Reinvestment Rate))n1−1
​ ​

Where:
Future Value of Inflows (FVI) = Sum of all cash inflows
compounded at the reinvestment rate.
Present Value of Outflows (PVO) = Initial investment
(if no further outflows) or discounted at the finance
rate.
n = Project life in years.
Step-by-Step Example
Project Details
Initial Investment (Year 0): $10,000
Cash Inflows:

Year 1: $4,000
Year 2: $5,000
Year 3: $6,000
Finance Rate (Borrowing Cost): 8%
Reinvestment Rate (Earnings on Cash Inflows): 6%

Step 1: Calculate Future Value of Cash Inflows (FVI)

We compound each cash inflow to Year 3 (project end) at

the reinvestment rate (6%):
Year 1 Cash Flow ($4,000):

Compounded for 2 years (Year 1 → Year 3)

Year 2 Cash Flow ($5,000):

Compounded for 1 year (Year 2 → Year 3)

Year 3 Cash Flow ($6,000):

Already at Year 3 → No compounding needed

Total FVI = $4,494.40 + $5,300 + $6,000 = $15,794.40

Step 2: Calculate Present Value of Cash Outflows

(PVO)
Since the only outflow is the initial investment ($10,000 at
Year 0), PVO = $10,000.
(If there were later outflows, we’d discount them at
the finance rate (8%).)

Step 3: Apply MIRR Formula

MIRR=(FVIPVO)1n−1=(15,794.4010,000)13−1MIRR=(PVO
FVI)n1−1=(10,00015,794.40)31−1
​ ​ ​ ​

Interpretation:
 The project’s true annualized return, considering a 6%
reinvestment rate, is 16.5% (vs. IRR’s unrealistic
assumption).

Comparison with IRR

Metric

IRR

MIRR

Conclusion: MIRR gives a more conservative and

realistic return estimate.

Why MIRR Matters in ICAP Exams?

1. More accurate than IRR for capital budgeting.
2. Reflects real-world reinvestment conditions (e.g., if
profits are kept in a bank at 6%).
3. Avoids misleading high returns from IRR’s flawed
assumption.

Practice Problem (Test Yourself!)

Project X:
Initial Cost: $8,000
Cash Inflows: Year 1: $3,000, Year 2: $4,000, Year 3:
$5,000
Finance Rate: 7%, Reinvestment Rate: 5%
Calculate MIRR.
*(Answer: FVI = $3,000(1.05)² + $4,000(1.05)¹ + $5,000 =
$12,957.50 → MIRR ≈ 17.4%)*
Need further clarification? 😊
Year 1: $300 (Remaining: $700) Year 2: $400 (Remaining:
$300) Year 3: $500 → Only need $300 → 2.6 years (How did
you calculate 2.6 Years please explain)
Calculating the Exact Payback Period (2.6 Years) –
Step-by-Step Explanation
When the payback period doesn’t land exactly on a full year,
we calculate the fractional year needed to recover the
remaining investment. Here’s how it works:

Given:
Initial Investment: $1,000
Cash Flows:

Year 1: $300 *(Remaining: $1,000 - $300 = $700)*

Year 2: $400 *(Remaining: $700 - $400 = $300)*
Year 3: $500 (But we only need $300 to fully recover
the investment)

Step-by-Step Calculation:
1. After Year 2, the remaining amount to recover
= $300.
2. Year 3’s cash flow = $500 (but we only
need $300 to hit payback).
3. Fraction of Year 3 needed to recover the final $300:
Fraction=Remaining AmountYear 3 Cash Flow=300500=0.6
yearsFraction=Year 3 Cash FlowRemaining Amount =500300
​ ​

=0.6 years
4. Total Payback Period = Full years + Fractional year

=2 years+0.6 years=2.6 years=2 years+0.6 years=2.6 years

Visual Timeline:
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Year 0: Invest $1,000
Year 1: +$300 → Remaining: $700
Year 2: +$400 → Remaining: $300
Year 3: Need $300 out of $500 → Takes 0.6 of the year.
Payback = 2.6 years.

Why This Matters for ICAP Exams:

1. Accuracy: Projects rarely pay back exactly at year-
end.
 2. Exam Tricks: Questions often test whether you can
calculate fractional years.
3. Decision-Making: A shorter payback (e.g., 2.6 vs.
3.1 years) is preferred.

Practice Problem:
Project Y:
Initial Cost: $5,000
Cash Flows: Year 1: $2,000, Year 2: $1,500, Year 3:
$2,500
Calculate Payback Period.
Solution:
1. Year 1: $2,000 → Remaining: $3,000
2. Year 2: $1,500 → Remaining: $1,500
3. Year 3: Need $1,500 out of $2,500 → Fraction = 0.6
Payback = 2.6 years. (Same logic!)
Need another example? 😊
Scenario & Sensitivity Analysis. Please elaborate more with
short examples
Scenario & Sensitivity Analysis – Simplified with
Examples
1. Sensitivity Analysis ("What-If" for One Variable)
What it does: Tests how changes in a single input (e.g., sales
price, cost) affect NPV/IRR.
Example:
Project: Sell 1,000 units at $10/unit, variable
cost $6/unit, WACC = 10%.
Base Case NPV: $2,000.
Test Sensitivity to Price Changes:

Price/Unit

$9

$11

Key Insight: A 10% price drop cuts NPV by 40% → High

sensitivity!

2. Scenario Analysis ("What-If" for Multiple Variables)

What it does: Examines combinations of
changes (Best/Worst/Likely cases).
Example:
Project: Initial cost = $100K, 3-year cash flows.
Scenarios:

Scenario

Best Case
Base Case
Worst Case
Decision Rule: If Worst-Case NPV > 0, low risk.

Why This Matters?

1. Sensitivity: Identifies critical variables (e.g., price is
more impactful than cost).
2. Scenario Planning: Prepares for real-world
uncertainty (e.g., recession vs. boom).
ICAP Exam Tip: Expect questions like:
"If raw material costs rise by 15%, how much does NPV fall?"
(Calculate new cash flows and re-discount!)
Need a practice problem? 😊
Capital Rationing EXPLAIN WITH EXAMPLES
Capital Rationing Explained with Examples
Capital rationing occurs when a company has limited funds to
invest and must choose between competing projects
to maximize returns within the budget.

Types of Capital Rationing

1. Hard Rationing: External limits (e.g., no access to
loans).
2. Soft Rationing: Internal limits (e.g., management
sets a budget cap).

How to Allocate Funds?

Rank projects by Profitability Index (PI) or NPV per dollar
invested and select the best combination within the budget.
Formula:
 Profitability Index (PI)=PV of Future Cash FlowsInitial Invest
mentProfitability Index (PI)=Initial InvestmentPV of Future C
ash Flows ​

Rule: Accept projects with PI > 1.0 (NPV > 0).

Example 1: Single-Period Rationing

Budget: $1,000
Projects:
Project
A
B
C
D
Step 1: Rank by PI (highest to lowest): A & B (tied) → C & D
(tied).
Step 2: Select within $1,000:
Option 1: A ($500) + B ($300) + D ($200)
= $1,000 → Total NPV = $370
Option 2: A ($500) + C ($400) + D ($200) = $1,100 (❌
Over budget)
Option 3: B ($300) + C ($400) + D ($200)
= $900 → Total NPV = $270 (Less optimal)
Best Choice: A + B + D (NPV = $370).

Example 2: Multi-Period Rationing

Budget: Year 0: $800, Year 1: $500
Projects:

Project

X
Y
Z
Constraints:
Year 0: X + Y + Z ≤ $800
Year 1: X + Y + Z ≤ $500
Optimal Combination:
X ($500) + Y ($300) → Year 0: $800, Year 1: $300
→ Total NPV = $400
Cannot add Z (exceeds Year 1 budget).
Key Takeaways
1. PI Ranking: Ensures highest returns per dollar
spent.
2. Budget Constraints: Multi-period rationing requires
checking limits for each year.
3. ICAP Focus: Exam questions often test optimal
project selection under rationing.
Practice Problem:
Budget: $1,500
Projects:
Project
P
Q
R
S
What’s the best combination?
*(Answer: P + S = $1,400 → NPV $560; or P + Q + R = $1,500
→ NPV $535. Choose P + S for higher NPV.)*
Need further clarification? 😊
Explain APV & EIRR in detail
Adjusted Present Value (APV) and Equivalent IRR
(EIRR) – Detailed Explanation with Examples

1. Adjusted Present Value (APV)

What it is: A valuation method that separates the value of a
project into:
1. Base Value (Unlevered NPV) – As if fully financed by
equity.
2. Value of Financing Effects (Tax shields, subsidies,
etc.).
Formula:
APV=NPVUnlevered+PV(Financing Benefits)APV=NPVUnlever
ed+PV(Financing Benefits)
​

Components of APV
1. Unlevered NPV:

Discount Free Cash Flows (FCF) at the unlevered cost

of equity (r₀).
 Ignores debt (pure equity assumption).
2. Financing Benefits:

Tax Shield (PV of Interest Tax Savings):

Tax Shield=Debt×Tax Rate×Cost of DebtTax Shield=Debt×
Tax Rate×Cost of Debt
Subsidies/Grants: Present value of any government
incentives.

Example: APV Calculation

Project:
Initial Investment: $1,000
FCF (Year 1-3): $400, $500, $600
Unlevered Cost of Equity (r₀): 12%
Debt: $500 at 6% interest
Tax Rate: 30%
Step 1: Calculate Unlevered NPV
NPVUnlevered=4001.12+5001.122+6001.123−1000= ∗∗$227
.65∗∗NPVUnlevered=1.12400+1.122500+1.123600
​ ​ ​ ​

−1000=∗∗$227.65∗∗
Step 2: Calculate Tax Shield
Annual Interest = $500 × 6% = $30
Annual Tax Savings = $30 × 30% = $9
PV of Tax Shield (assuming perpetuity):
PV(Tax Shield)=90.06=∗∗$150∗∗PV(Tax Shield)=0.069 ​

=∗∗$150∗∗
Step 3: Compute APV
APV=227.65+150=∗∗$377.65∗∗APV=227.65+150=∗∗$377
.65∗∗
Conclusion: Debt financing adds $150 in value due to tax
savings.

2. Equivalent IRR (EIRR)

What it is: A modified IRR used in public sector
projects where:
Cash flows include social benefits/costs (not just
financial).
Discount rate adjusts for public opportunity cost.
Key Differences from IRR
 Feature

Purpose

Cash Flows

Discount Rate

Example: EIRR Calculation

Public Highway Project:
Initial Cost: $10M
Annual Benefits (Social + Financial):

Year 1: $2M (reduced traffic)

Year 2: $3M (toll revenue)
Year 3: $4M (economic growth)
Social Discount Rate (SDR): 5%
Step 1: Find EIRR (where NPV = 0)
0=−10+2(1+EIRR)
+3(1+EIRR)2+4(1+EIRR)30=−10+(1+EIRR)2+(1+EIRR)23
​ ​

+(1+EIRR)34 ​

Solve numerically (or Excel):

EIRR ≈ 10.5%
Step 2: Compare to SDR (5%)
Since EIRR (10.5%) > SDR (5%), the project is socially
viable.

When to Use APV vs. EIRR?

Metric

APV
 EIRR

ICAP Exam Tips

1. APV: Expect questions on tax shield
calculations and WACC vs. unlevered cost of equity.
2. EIRR: Focus on social vs. financial cash
flows and SDR.
Practice Problem:
A project has:
Unlevered NPV = $200
Debt = $1,000, Interest = 7%, Tax Rate = 25%
Calculate APV.
*(Answer: Tax Shield = $1,000 × 7% × 25% =
$17.5/year → PV at 7% = $17.5/0.07 = $250 → APV =
$200 + $250 = $450)*
Need further clarification? 😊
too complex. again teach PV & EIRR but in easy and
understanding way
**
too complex. again teach APV & EIRR but in easy and
understanding way
APV & EIRR Made Super Simple
1. APV (Adjusted Present Value) – Like a Discounted Burger
Meal
What it is: A way to value a project by separating its core
value (burger) from financing perks (free fries).
How it works:
1. Burger Value (Unlevered NPV):

Calculate project’s cash flows without debt (like a

burger’s base price).
Discount at equity cost (no debt).
2. Free Fries (Tax Shield):

Debt gives tax savings (like a coupon).

Calculate savings: Debt × Interest Rate × Tax Rate.
Example:
Project cost: $100
Cash flows (no debt): $120 → Burger Value = $20
profit
Debt: $50 at 5%, Tax: 20%

Yearly tax save: $50 × 5% × 20% = $0.50

Free Fries Value: $0.50 / 5% = $10 (forever savings)
APV = Burger ($20) + Fries ($10) = $30

2. EIRR (Equivalent IRR) – Social Project’s True Return

What it is: IRR for government projects where benefits aren’t
just cash (e.g., schools, roads).
How it works:
1. Include social benefits (e.g., reduced pollution,
jobs).
2. Use Social Discount Rate (SDR) (like a charity’s low
return expectation).
Example:
Build a park for $1,000.
Benefits:

Year 1: $300 (visitors)

Year 2: $500 (tourism boost)
Year 3: $400 (healthier community)
EIRR = The "break-even" rate making total benefits =
$1,000.

Turns out to be 8% (vs. SDR of 4% → Good project!).

Key Differences

Use

Focus

Math
APV Tip: Debt makes projects cheaper (like a discount).
EIRR Tip: If EIRR > SDR, the project helps society.

Real-Life Analogy
APV = Ordering a meal with a coupon (burger + free
fries).
EIRR = Donating to a food bank (less cash return, but
big social impact).
Need an even simpler breakdown? 😊
 6/28/2025 12/3/2025 158

NPV= PV of Future Cash Flow- Initial Investment

NPV= 227.6483847

IRR using Interpolation Method

Npv @ LR 20% Npv @ HR 25%

27.78 -52.8

IRR using interpolation method

21.72%

MIRR (Terminal Value of cashinflow/PV of Outflow)^1/n - 1

(FV of Cash Inflow Compounded @ Revinvestment Rate/PV of cash outflow discounted @ Finance Rate) ^ 1/n -1

n= Project Life in Years

Answer
16%
 16%

Answer:
Years Cash Inflow Remaining Cost
1000
1 300 700
2 400 300
3 500 -200 0.6
4 600

So, recovery period is 2.6 years.

Answer:
Profitabilty Index= PV of cash inflows/ Initial Investment
1.22765
If PI > 0 than accept the Project

Cost NPV PI
$600 $240 1.4
$500 $175 1.35
$400 $120 1.3
$800 $320 1.4

First we are
going to rank
these projects
in sequence of
Highest to
lowest PI

Cost NPV PI
$600 $240 1.4
$800 $320 1.4
$500 $175 1.35
 $400 $120 1.3

PQR
1500 535
PS
1400 560

Unlevered NPV + PV (Financing Benefits)

Answer :
Unlevered NPV

Formula= FCF discounted @ cost of equity Less Initial Inv

182.8079446
PV (Financing Benefits)

Tax Benefits= 9
PV of tax benefits= 150
332.807944606414
Cost NPV PI
500 200 1.4
300 120 1.4
200 60 1.3
 Key
Calculation Result
Assumption

Reinvests
Solves for
~22% at 22% (unre
NPV=0
alistic)

Reinvests
Uses explicit
16.50% at 6% (realis
rates
tic)
 Change
New NPV
vs. Base
▼ $800
$1,200
(40% ↓)
▲ $800
$2,800
(40% ↑)
Sales Volume Price/Unit NPV

20% 10% $150K

0% 0% $100K
-15% -5% $60K
Initial Cost NPV PI
$500 $200 1.4
$300 $120 1.4
$400 $100 1.25
$200 $50 1.25

Cost
Cost (Year 0) NPV
(Year 1)
$500 $200 $250
$300 $100 $150
$400 $300 $200
Cost NPV PI
$600 $240 1.4
$500 $175 1.35
$400 $120 1.3
$800 $320 1.4
IRR EIRR
Public
Private projects
projects

Includes
Financial only social
impacts

Social
Discount
WACC/ROI
Rate
(SDR)

Key
Best For Advantag
e

Separate
Leveraged s project
buyouts, M&A risk &
financing
 Captures
Government non-
infrastructure financial
benefits
 APV EIRR
Governm
Companies with
ent/social
debt
projects

Tax savings Non-cash

from loans benefits

IRR +
NPV + Tax
Social
Shield
Benefits
ate) ^ 1/n -1