Suppose the investment costs $ 1.7bn and will grant $ 1.995 the next year.
= -1.7bn +
= 200mInvestment generates a profit of $ 200m.
But every investment opportunity is related to financing opportunity.
Cash has a certain costs, it has to be borrowed (interest expense) or has opportunity costs
(could invest elsewhere).
Borrow $ 1.9bn now, pay the investment of $ 1.7bn, realize the profit of $ 200m now and
with the mature investment pay back the loan.
=> NPV creates one cash flow in the first period, all following cash flows are 0.
Its a management decision whether to generate equal cash flows over the whole investment
lifetime (annuity) or just realize the profit now (NPV).
=> Simple decision rule: If NPV is positive, the investment makes us better-off. The higher the
NPV the more attractive the investment.
How to take risk into account.
Suppose the conditions above don't change, but the future cash flow is uncertain.
Investors are risk-averse, claim for a compensation for taking the risk.
Interest premium is added on the "normal" interest rate to take risk into account.
If adding an interest premium of 5% the total interest rate is 10%.
= -1.7bn +
= 114mNPV is still positive, but smaller.
Guideline to calculate NPV (example: Monsanto acquisition by Bayer).
1) Assign an expected future cash flow to each possible situation (slump, boom etc.) and
multiply with probability of occurrence. Average of those reveals the expected payoff.
2) Search for a discount rate by looking at stocks with similar risk in the same / similar
industry. (Expected share price current one) over current share price reveals an adequate discount
rate (expected return) for our investment.
3) Discount the future cash flows (average) with this discount rate.
4) Calculate the NPV for this investment.
5) Calculate the expected return for this investment. Difference of expected cash flow
(average) and investment value over purchase price (= NPV over purchase price).
Has to be lower than the discount rate so investors have no better opportunity to invest their
Evaluation key numbers.
Look into the balance sheet or income statement to reveals certain information.
Free Cash Flow = cash flow (tax & investment (= changes in working capital) & CapEx) +
depreciation & amortization.
Income BIT = EBIT financing activities.
Multiple period NPV.
Normally the investment won't pay off in the next year, but e.g. in 5 or 10 years.
Compare different investments with their present value.
Assumption: We want to acquire all Monsanto shares outstanding in 2012 (market
Further assumption: Businesses are sold at 25x of last year's cash flow.
Assumption that money is borrowed for the same interest rate.
Interest rate chosen must be justified (orientated at similar investments with fixed interest
() = -() +
+ [. . . ] +
Given the following data we can calculate the NPV of Monsanto like the following.
Free Cash Flow
Sale of the
(1995 * 25)
Scenario consideration reveals changing conditions.
What if interest rate changes, or business has to be sold for less than the multiple of 25 from
the last cash flow.
Increases in interest rate decrease the NPV because alternative investment become more
Decreases in multiplier decrease the NPV.
This schedule also reveals possible interest premiums as relation to raising risks.
If investors add an interest premium of 5% because of uncertainty, than the investment is no
longer attractive (negative NPV).
Stock prices also contain non-monetary aspects (enthusiasm / cautiousness of investors,
subjective rating of companies operating activities, etc.).
Net income and stock price won't necessarily behave the same way.
=> Reveals possible under- and over-estimations.
Summary of the NPV method.
What is it good for? - Making different investments comparable.
Interest premium is added if investors fear higher risks (will decrease the NPV).
NPV reflects shareholders value principle (Monocity, only money matters).
All possible profit is shifted to the first period of investment (to the present), in all other
periods cash flows are 0.
IRR (internal rate of return) is the interest rate you have a NPV of exactly 0.
Reveals the highest risk security possible.
Imagine the manager wants to create a series of constant cash flows over the investments
The sum of this series of stable payments (or debt paybacks) has to be discounted.
What influences the amount of each regular payment? - PV (= principal), maturity (=
investments useful lifetime) and discount rate.
Capital recovery factor turns present value into an annuity.
(, ) =
(5, 5) =
Suppose the calculated NPV of an investment is $ 21.647, multiplied by the CRF reveals
$ 5.000 which is the total value of each annuity payment over the investments useful lifetime.
Annuity factor converts an annuity payment into its present value.
(, ) =
Suppose you exactly know the annuity payments, than multiply this with the AF and receive
the present value of this investment.
5.000 (annuity payment) * 4.33 (AF) = 21.650 (PV of investment).
Perpetuity (if amount of years is infinity).
. : (, ) =
If T goes to infinity
If annuity payments of $ 5.000 are paid every year until infinity, the investment isn't worth
infinity, only $ 100.000 (AF = 20).
Ratio of amortization and interest expense is constantly decreasing with each payment.
Interest expense is related to carrying amount, amortization decreases it.
Suppose the example above: $ 5.000 over 5 years with a discount rate of 5%.
year Interest expense amortization Remaining PV
Value of NPV and annuity is the same, just the distribution of this money over the
investment's useful lifetime has changes.
Management decision whether constant cash flows are preferred or receiving the profit at the
beginning and paying back an older debt.
Back to the Monsanto example.
CRF (5%, 5 years) = 0,231
c (Monsanto) = CRF (5%, 5 years) * NPV
(Monsanto) = 0,231 * 6,647 = 1.535.
=> Regular payments of 1.535 each year have the same value as getting 6.647 at the beginning of
Creation of a financing plan if we have to take several bank loans to ensure a regular annuity
If taking loans for one year each, the compounded interest effect is prevented and by taking
the surplus of generated payments this is more attractive than taking one single big loan.
Company X and company Y have the same annuity payment, but company X's projects has a
useful lifetime which exceeds the one of company Y by one year.
Even though both companies have the same annuity payment, they have different maturities and
therefore can't be compared.
Make them comparable by extending the maturity of company Y by one year without cash
flow and spread the annuity over the whole time span.
Calculate the annuity by multiplying NPV with CRF, but for 5 years.
() = -30.023 +
= (5; 5)
() = 0.231 5.442 = 1.257.
Only investments with same maturity are comparable.
General overview of the 3 valuation models.
NPV shifts profits to the first period.
Annuity spreads profits equally over all periods of the investment.
Future Value shifts profits to the end of the investment's useful lifetime.
=> Shift profits to the best point in time Management decision.
NPV, FV and Annuity are consistent (except of negative interest numbers).
Internal Rate of Return (IRR).
Maximum discount rate ensuring a positive NPV.
No longer interested in monetary decision, interested in percentage value.
Breaking-up the assumption of one interest rate in the whole market available for every
market participant; looking at project-based interest rate.
IRR of two investment alternatives can not be used to compare each other.
Comparing by NPV is possible, but IRR isn't subject to the interest assumption, but the
NPV function computes IRR for different NPV, slope is typically negative; IRR is the
intersection with the x-axis.
When the opportunity costs of investors are below the IRR, the investment has a positive
NPV and becomes attractive.
Visual display of different IRR.
Even though the IRR is misleading, with a graphical approach we can examine which of the
both investments is better.
Given a market interest rate of 5% Monsanto is a better investment than company X despite
X has a higher IRR.
Intersection of both NPV functions reveals the turning point. Because 5% market interest rate is
left of the intersection, it lays in the Monsanto dominated area.
Ambiguity IRR pitfalls.
Regular investment project: Only one
negative cash flow at the beginning of the
investment (investment costs).
Irregular investment project: Several
negative cash flows over the whole useful
lifetime of the investment (e.g., for expansion
IRR reveals two intersections with the x-
axis, question is which is the "true IRR".
When the sign of cash flows is turned
(within the investment new money is needed negative sign), there are different solutions to solve
IRR can't be applied to this situation.
=> Simply use NPV for decision making.
Summary / Conclusions.
Comparison of market interest rate and IRR enables to analyze the better investment project.
IRR can't be used for irregular investment projects.
IRR compared for different investment projects is not a qualified criterion.
IRR assumes that cash flows are reinvested in the project, but only possible at market
Calculate value of future cash flows for now.
(, ) =
Calculate annuity payment by PV.
(, ) =
Calculate PV by annuity payment.
= 0Maximum discount rate ensuring a positive NPV.
Loan issued over capital markets; most important asset class together with stocks.
Coupon payments = interest revenue per year.
Bond structure: Invest the principal, receive cash flows over the bonds useful lifetime and
receive principal at maturity.
Zero-bond is special, has no coupon payments.
Invest in bonds: Fixed cash flows that we can use for planning profit from price changes in
Bond price should be set at NPV, but is influenced by supply and demand; expectations of
changing market conditions.
Assumption that all investors are rational and bond price reflects NPV.
Changes in the market interest rate influences the value of bonds.
Generate profit if bonds coupon is higher than market interest or by trading the bond.
Two major kinds of risk.
Market risk: Risk that changes in market interest rate influences bonds value.
Credit risk: PD + distance to default (DtD) influence the discount rate of the bond.
Given a certain bond with principal = 100, discount rate = 1%, coupon = 1.875%
Today: December 1 , 2016; maturity: January 24, 2021; coupon payment: 24. January
Comparison of maturity and interest rate, needed to be offered to meet investors opportunity
costs compared to risk-free assets (German government bonds).
Excerpt out of 27 pages
- Quote paper
- Mike G. (Author), 2017, Foundations of Finance. A lecture summary, Munich, GRIN Verlag, https://www.grin.com/document/366705