1. Lecture No. 9 Combined NPV & IRR
Financial Management
Lecture No. 9
Combined NPV & IRR
Copyright: M. S. Humayun

2. NPV - Net Present Value
The Most Important Mathematical Skill in this course is understanding the NPV equation and calculating NPVas reliably as possible. NPV is the Most Important Criterion.
The project or investment offering the highest NPVgets the highest rank.
NPV calculation is Uncertain because based on lots of Estimates:
Estimate the Life (n) of project or investment … uncertain
Net Annual After-Tax Cash Flow Forecasts (CF) … difficult to estimate and often wrong
Investment Forecast (I)… timing not exactly predictable
Estimated Discount Rate (Required Rate of Return or “i”) … changes with the markets and risk-level from one year to the next so you can use a different value of “i” for each year in the NPV equation. n
NPV = -Io CFt / (1+i)t = -Io + CF1/(1+i) + CF2/(1+i) 2 + CF3 /(1+i) 3 +..
t =1
Copyright: M. S. Humayun

3. NPV, Value, & Wealth
NPV is the basis of estimating the Intrinsic Value of working Assets (in the form of Investments or Projects) based on the Net Cash Flows that the working Assets will generate over their life.
NPV has a crucial connection with the Objective of Financial Management
If a company invests in Projects with Positive NPV then:
the company’s EVA rises by the same value
the company’s MVA or market value rises
the company Shareholders’ Wealth rises
Copyright: M. S. Humayun

4. NPV (Savings Certificate Example)
You invest Rs 100,000 in a Savings Certificate. After 1 Year you receive a coupon payment (or profit) of Rs 12,000 and you also reclaim you investment (principal).
Step 1: Identify the Variables: Io = Rs 100,000 CF1=Rs 12,000 Life = n=1year Required Rate of Return = i =10% (assumed). Annual compounding. CF I1 = Rs 100,000 (Don’t forget that you get back your principal investment after 1 Year. This is a positive cash flow and must be discounted back to the present just like any other future cash flow).
Step 2: Solve the NPV Equation
NPV = Io CF1 / (1+ i) CF I1 / (1+ i)
= -100, ,000/(1+0.10) ,000/(1+0.10)
= -100, , ,909
= + Rs 1,818 NPV positive so investment acceptable
NOTE: PV = NPV + Io = 1, ,000 = Rs 101,818
Copyright: M. S. Humayun

5. NPV Cash Flow Diagram Savings Certificate Example
CFI1 = Rs 100,000
Rs 90,909
Rs 10,909
CF1= Rs 12,000
NPV = Rs 1,818
i = 10%
Yr 0 (Today)
Yr 1
Io = Rs 100,000
Copyright: M. S. Humayun

6. IRR - Internal Rate of Return
Very Important & Most Common Calculation - Uses Trial & Error
NPV = 0 = -Io CFt / (1+IRR)t = -Io + CF1/(1+IRR) + CF2/(1+IRR)
Represents the Break-even Return on Investment
IRR is a Forecasted Return (derived from the project’s forecasted cash flows)
UNLIKE the Required Return (like the Discount Rate “i” used in NPV which is based on market or risk data)
IRR remains constant (same) for each and every year over the life of the project
UNLIKE the Required Return (or Discount Rate) “i” used in NPV which can be changed independently for each year
IRR Criteria can give project rankings from NPV Criteria because the “i” has different meanings for NPV and for IRR.
Copyright: M. S. Humayun

7. IRR (Numerical Example)
Same Savings Certificate Example as before. Except this time, we do not assume any value for “i” as we had done in the NPV calculation. We set the NPV = 0 and solve the equation for “i” (or IRR).
NPV = 0 = -Io [CF1 / (1+IRR)] + [ CFI1 / (1+IRR)]
0 = -100, [ (CF1 + CFI1) / (1+IRR) ]
0 = -100, [(12, ,000) / (1+IRR)]
IRR= (112,000 / 100,000) (no need for trial & error)
= = 0.12 = 12 % per annum
Copyright: M. S. Humayun

8. Graphical IRR Estimation Using “NPV PROFILE”
Savings Certificate Investment
Using a low and a high value for “i”, plot two points on the graph and extend the NPV line. Where it cuts the x-axis is the IRR.
Use this Graphical Technique when:
The investment or project life is longer than 2 years
The IRR equation can not be easily solved algebraically in terms of “i” (or IRR)
Comparing the NPV’s of 2 or more investments, to study how sensitive the NPV’s of the different investments are to the discount rate “i”
IRR=12% pa
NPV (Rupees)
Copyright: M. S. Humayun

9. Ranking 2 Different Investments Which Investment is Better?
Let us rank 2 Mutually Exclusive & Independent Investments using NPV and IRR criteria.
Mutually Exclusive means that you can invest in ONE of the investments and NOT both.
Independent means that the cash flows of the two investments are not linked to each other
One Investment is the Savings Certificate (which we described earlier) and the second investment is a Bank Deposit of Rs 100,000 at 10% interest compounded annually for two years.
Copyright: M. S. Humayun

10. NPV & IRR Numerical Comparing the 2 Investments
Bank Deposit Example
FV = PV (1+i)n = 100,000 x (1.10)2 = 121,000
NPV = -100, ,000/(1.1) + 11,000/(1.1) ,000/(1.1)2 = 100, , ,736 = + Rs 826
IRR: NPV = 0 = -100, ,000/(1+IRR) + 111,000/(1+IRR)2 … by trial & error IRR = 10.5%
Compare the Investment 1 (Savings Certificate) to Investment 2 (Bank Deposit): Savings Certificate Bank Deposit
NPV (i=10% pa) + Rs 1, Rs 826
IRR % pa 10.5% pa
Savings Certificate appears to be a better investment because it offers both a higher NPV and a higher IRR.
Copyright: M. S. Humayun

11. Graphical Comparison of 2 Investments “CROSS-OVER IRR”
NPV Profiles of Investments Intersect at the Cross Over Point
Slope of Bank Deposit investment is steeper because larger cash flows (Rs 111,000) are taking place later in time (2 years instead of 1 year for Saving Certificates). Size of the Discounting Factor grows exponentially with time so NPV graph falls much faster.
The IRR at this Point is 8.8%. At this Point the NPV of both investments is equal at about +Rs 2,950
When IRR is less than 8.8% (Cross Over IRR) then the NPV of Bank Deposit is higher !
NPV (Bank Deposit)
Cross Over Point
NPV (Saving Certificate)
Copyright: M. S. Humayun

12. Investment Criteria IRR Interpretation - How High is High
Investment Criteria IRR Interpretation - How High is High? Macro Aspects
Inflation
An IRR which is considered low for a medium inflation country like Pakistan may be considered high for a low inflation country like USA, Japan, Singapore where inflation is below 5%.
Risk Free Rate of Return
Recall our discussion from earlier lecture on Interest Rates and Money Markets.
In Pakistan, we use the Government T-Bill rate which varies from 7% to 12% per annum depending on the Money Market. The IRR on investment should be higher than this. We will talk more about this after we study RISK.
Copyright: M. S. Humayun

13. Investment Criteria IRR Interpretation (Micro Aspects)
ROA & ROE
If the Investor has an existing running business that generates cash-flows, then any new project that matches or exceeds the returns of the existing business is worth considering.
Problem: ROA & ROE are Financial Accounting Ratios based on Net Income (not cash) & Historical Cost or Book Value (not market value) whereas IRR is based on Cash and Forecasted Market Value.
Weighted Average Cost of Capital (WACC) or Hurdle Rate
If the Investoras an existing operating business that runs on borrowed money (or financing) then the Investor (the borrower) bears the cost of interest, say 18% pa in Pakistan. Obviously, the rate of cash generation should exceed the rate of interest payment. The IRR of a new project should exceed the WACC. We will discuss this in detail when we study Capital Structuring.
When IRR is above the WACC, the excess return represents surplus that increases shareholders’ wealth.
Copyright: M. S. Humayun