CAPITAL BUDGETINGthe process of analyzing potential

fixed asset investments  Conceptually, the capital

budgeting process is identical to the decision process used by individuals making investment decisions. These steps are involved:

1. Estimate the cash flows2. Assess the riskiness of the

cash flows.3. Determine the appropriate

discount rate, based on the riskiness of the cash flows and the general level of interest rates

4. Find (a) the PV of the expected cash flows and/or (b) the asset’s rate of return.

5. If the PV of the inflows is greater than the PV of the outflows (the NPV is positive), or if the calculated Rate of Return (the IRR) is higher than the project cost of capital, accept the project.

INDEPENDENT PROJECTSINDEPENDENT PROJECTS

are projects whose cash flows are independent of one another which mean it can accept both projects as long as it passed the criteria

  MUTUALLY EXCLUSIVE MUTUALLY EXCLUSIVE PROJECTSPROJECTS projects whose acceptance of

one impacts adversely the cash flows of the other if one project is taken on the other must be rejected.

NORMAL CASH FLOWS have outflows, or costs, in the first year (or years) followed by a series of inflows.

 NON-NORMAL cash flows

have one or more outflows after the inflow stream has begun.

  

PAYBACK PERIOD PAYBACK PERIOD The expected number of years required

to recover project’s cost.=yr. before full recovery+ Uncovered cost at

start of the year/Cash flow during the year

Payback period (L) = 2 + 30/80 = 2.375 or 2.4 years

Payback period (S) = 1+ 30/5

= 1.6 years 

2)2)RATIONALE FOR THE RATIONALE FOR THE PAYBACK PERIODPAYBACK PERIOD

payback represents a type of “breakeven” analysis: the payback period tells us when the project will break even in a cash flow sense

DIFFERENCE BETWEEN DIFFERENCE BETWEEN REGULAR AND DISCOUNTED REGULAR AND DISCOUNTED PAYBACKPAYBACK In DISCOUNTED PAYBACK PERIOD,

the expected cash flows are discounted by the project’s cost of capital unlike in regular payback period.

MAIN DISADVANTAGE OF MAIN DISADVANTAGE OF DISCOUNTED PAYBACKDISCOUNTED PAYBACK

(4) The main disadvantage in discounted payback is that they ignore cash flows that are paid or received after the payback period.

1.1. DEFINE THE TERM DEFINE THE TERM NET NET PRESENT VALUE (NPV)PRESENT VALUE (NPV). . WHAT IS EACH PROJECT’S WHAT IS EACH PROJECT’S NPV?NPV?

NET PRESENT VALUE (NPV)

SIMPLY THE SUM OF THE PRESENT VALUES OF A PROJECT’S CASH FLOWS:

Npv= -100 + 10 + 60 (1.10)1 (1.10)2 + 80 (1.10)3= -100 + 9.09 + (1.21) 49.59 + (1.331) 60.11

=18.79 NPVL

NPVS= -100 + 70 + 50 (1.10)1 (1.10)2

+ 20(1.10)3

= -100 + 63.64 + 41.32 + 15.03

= -19.99 NPVs

2. WHAT IS THE RATIONALE BEHIND THE NPV METHOD? ACCORDING TO NPV, WHICH PROJECT OR PROJECTS SHOULD BE ACCEPTED IF THEY ARE INDEPENDENT? MUTUALLY EXCLUSIVE?

THE RATIONALE BEHIND THE NPV METHOD IS STRAIGHTFORWARD:

IF A PROJECT HAS NPV = $0, THEN THE PROJECT GENERATES

EXACTLY ENOUGH CASH FLOWS (1) TO RECOVER THE COST OF THE

INVESTMENT AND (2) TO ENABLE INVESTORS TO

EARN THEIR REQUIRED RATES OF RETURN (THE OPPORTUNITY COST OF CAPITAL).

IF NPV = $0, THEN IN A FINANCIAL (BUT NOT AN ACCOUNTING) SENSE, THE PROJECT BREAKS EVEN.

IF THE NPV IS POSITIVE, THEN MORE THAN ENOUGH CASH FLOW IS GENERATED, AND CONVERSELY IF NPV IS NEGATIVE.

IF PROJECTS L AND S ARE INDEPENDENT, THEN BOTH SHOULD BE ACCEPTED, BECAUSE THEY BOTH ADD TO SHAREHOLDERS’ WEALTH, HENCE TO THE STOCK PRICE. IF THE PROJECTS ARE MUTUALLY EXCLUSIVE, THEN PROJECT S SHOULD BE CHOSEN OVER L, BECAUSE S ADDS MORE TO THE VALUE OF THE FIRM.

3. WOULD THE NPVs CHANGE 3. WOULD THE NPVs CHANGE IF THE COST OF CAPITAL IF THE COST OF CAPITAL CHANGED?CHANGED?  THE NPV OF A PROJECT IS THE NPV OF A PROJECT IS DEPENDENTDEPENDENT ON THE COST OF ON THE COST OF CAPITAL USED. THUS, IF THE COST CAPITAL USED. THUS, IF THE COST OF CAPITAL CHANGED, THE NPV OF OF CAPITAL CHANGED, THE NPV OF EACH PROJECT WOULD CHANGE. EACH PROJECT WOULD CHANGE. NPV DECLINES AS k INCREASES, AND NPV DECLINES AS k INCREASES, AND NPV RISES AS k FALLS.NPV RISES AS k FALLS.

f. 1. DRAW NPV PROFILES FOR f. 1. DRAW NPV PROFILES FOR PROJECTS L AND S. AT WHAT PROJECTS L AND S. AT WHAT DISCOUNT RATE DO THE PROFILES DISCOUNT RATE DO THE PROFILES CROSS? CROSS?

NOTE THE FOLLOWING POINTS:1. THE Y-INTERCEPT IS THE PROJECT’S NPV

WHEN k = 0%. THIS IS $50 FOR L AND $40 FOR S.2. THE X-INTERCEPT IS THE PROJECT’S IRR.

THIS IS 18.1 PERCENT FOR L AND 23.6 PERCENT FOR S.

3. NPV PROFILES ARE CURVES RATHER THAN STRAIGHT LINES. TO SEE THIS, NOTE THAT THESE PROFILES APPROACH COST = -$100 AS k APPROACHES INFINITY.

4. FROM THE FIGURE BELOW, IT APPEARS THAT THE CROSSOVER RATE IS BETWEEN 8 AND 9 PERCENT. THE PRECISE VALUE IS APPROXIMATELY 8.7 PERCENT. ONE CAN CALCULATE THE CROSSOVER RATE BY (1) GOING BACK

•IT APPEARS THAT THE CROSSOVER RATE IS BETWEEN 8 AND 9 PERCENT. •THE PRECISE VALUE IS APPROXIMATELY 8.7 PERCENT. ONE CAN CALCULATE THE CROSSOVER RATE BY •(1) GOING BACK TO THE DATA ON THE PROBLEM, FINDING THE CASH FLOW DIFFERENCE FOR EACH YEAR, •(2) ENTERING THOSE DIFFERENCES INTO THE CASH FLOW REGISTERS, AND •(3) PRESSING THE IRR BUTTON TO GET THE CROSSOVER RATE, 8.68% 8.7%.

F. 2. LOOK AT YOUR NPV PROFILE GRAPH WITHOUT REFERRING TO THE ACTUAL NPVs AND IRRs. WHICH PROJECT OR PROJECTS SHOULD BE ACCEPTED IF THEY ARE INDE-PENDENT? MUTUALLY EXCLUSIVE? EXPLAIN. ARE YOUR ANSWERS CORRECT AT ANY COST OF CAPITAL LESS THAN 23.6 PERCENT?

•THE NPV PROFILES SHOW THAT THE THE NPV PROFILES SHOW THAT THE IRR AND NPV CRITERIA LEAD TO THE IRR AND NPV CRITERIA LEAD TO THE SAME ACCEPT/REJECT DECISION FOR SAME ACCEPT/REJECT DECISION FOR ANY ANY INDEPENDENTINDEPENDENT PROJECT. PROJECT. CONSIDER PROJECT L,IT INTERSECTS CONSIDER PROJECT L,IT INTERSECTS THE X-AXIS AT ITS IRR, 18.1 PERCENT. THE X-AXIS AT ITS IRR, 18.1 PERCENT. ACCORDING TO THE IRR RULE, L IS ACCORDING TO THE IRR RULE, L IS ACCEPTABLE IF k IS LESS THAN 18.1 ACCEPTABLE IF k IS LESS THAN 18.1 PERCENT. PERCENT. ALSO, AT ANY k LESS THAN 18.1 ALSO, AT ANY k LESS THAN 18.1 PERCENT, L’S NPV PROFILE WILL BE PERCENT, L’S NPV PROFILE WILL BE ABOVE THE X-AXIS, SO ITS NPV WILL BE ABOVE THE X-AXIS, SO ITS NPV WILL BE GREATER THAN $0. GREATER THAN $0.

THUS, FOR ANY INDEPENDENT THUS, FOR ANY INDEPENDENT PROJECT, NPV AND IRR LEAD PROJECT, NPV AND IRR LEAD TO THE SAME ACCEPT/REJECT TO THE SAME ACCEPT/REJECT DECISION.DECISION.NOW ASSUME THAT L AND S NOW ASSUME THAT L AND S ARE MUTUALLY EXCLUSIVE. IN ARE MUTUALLY EXCLUSIVE. IN THIS CASE, A CONFLICT MIGHT THIS CASE, A CONFLICT MIGHT ARISE. FIRST, NOTE THAT IRRARISE. FIRST, NOTE THAT IRRSS = 23.6% > 18.1% = IRR= 23.6% > 18.1% = IRRLL..

G.G. 1.1. WHAT IS THE WHAT IS THE UNDERLYING CAUSE OF UNDERLYING CAUSE OF RANKING CONFLICTS RANKING CONFLICTS BETWEEN NPV AND IRR?BETWEEN NPV AND IRR?

FOR NORMAL PROJECTS’ NPV FOR NORMAL PROJECTS’ NPV PROFILES TO CROSS, ONE PROJECT PROFILES TO CROSS, ONE PROJECT MUST HAVE BOTH A HIGHER MUST HAVE BOTH A HIGHER VERTICAL AXIS INTERCEPT AND A VERTICAL AXIS INTERCEPT AND A STEEPER SLOPE THAN THE OTHER. STEEPER SLOPE THAN THE OTHER.

A PROJECT’S VERTICAL AXIS A PROJECT’S VERTICAL AXIS INTERCEPT TYPICALLY DEPENDS ON INTERCEPT TYPICALLY DEPENDS ON (1) THE (1) THE SIZESIZE OF THE PROJECT AND OF THE PROJECT AND (2) THE (2) THE SIZE AND TIMING PATTERN OF SIZE AND TIMING PATTERN OF THE CASH FLOWSTHE CASH FLOWS--LARGE PROJECTS, --LARGE PROJECTS, AND ONES WITH LARGE DISTANT AND ONES WITH LARGE DISTANT CASH FLOWS, WOULD GENERALLY BE CASH FLOWS, WOULD GENERALLY BE EXPECTED TO HAVE RELATIVELY HIGH EXPECTED TO HAVE RELATIVELY HIGH VERTICAL AXIS INTERCEPTS. VERTICAL AXIS INTERCEPTS.

THE SLOPE OF THE NPV PROFILE THE SLOPE OF THE NPV PROFILE DEPENDS ENTIRELY ON THE DEPENDS ENTIRELY ON THE TIMING TIMING PATTERN OF THE CASH FLOWSPATTERN OF THE CASH FLOWS--LONG---LONG-TERM PROJECTS HAVE STEEPER NPV TERM PROJECTS HAVE STEEPER NPV PROFILES THAN SHORT-TERM ONES. PROFILES THAN SHORT-TERM ONES. THUS, WE CONCLUDE THAT NPV THUS, WE CONCLUDE THAT NPV PROFILES CAN CROSS IN TWO PROFILES CAN CROSS IN TWO SITUATIONS: (1) WHEN MUTUALLY SITUATIONS: (1) WHEN MUTUALLY EXCLUSIVE PROJECTS DIFFER IN EXCLUSIVE PROJECTS DIFFER IN SCALE SCALE (OR SIZE)(OR SIZE) AND (2) WHEN THE PROJECTS’ AND (2) WHEN THE PROJECTS’ CASH FLOWS DIFFER IN TERMS OF THE CASH FLOWS DIFFER IN TERMS OF THE TIMING PATTERNTIMING PATTERN OF THEIR CASH FLOWS OF THEIR CASH FLOWS (AS FOR PROJECTS L AND S).(AS FOR PROJECTS L AND S).

G.G. 2.2. WHAT IS THE WHAT IS THE “REINVESTMENT RATE “REINVESTMENT RATE ASSUMPTION,” AND ASSUMPTION,” AND HOW DOES IT AFFECT HOW DOES IT AFFECT THE NPV VERSUS IRR THE NPV VERSUS IRR CONFLICT?CONFLICT?

THE UNDERLYING CAUSE OF THE UNDERLYING CAUSE OF RANKING CONFLICTS IS THE RANKING CONFLICTS IS THE REINVESTMENT RATE REINVESTMENT RATE ASSUMPTION. ASSUMPTION.

ALL DCF METHODS IMPLICITLY ASSUME ALL DCF METHODS IMPLICITLY ASSUME THAT CASH FLOWS CAN BE REINVESTED AT THAT CASH FLOWS CAN BE REINVESTED AT SOME RATE, REGARDLESS OF WHAT IS SOME RATE, REGARDLESS OF WHAT IS ACTUALLY DONE WITH THE CASH FLOWS. ACTUALLY DONE WITH THE CASH FLOWS. DISCOUNTING IS THE REVERSE OF COM-DISCOUNTING IS THE REVERSE OF COM-POUNDING. POUNDING. SINCE COMPOUNDING ASSUMES SINCE COMPOUNDING ASSUMES REINVESTMENT, SO DOES DISCOUNTING.REINVESTMENT, SO DOES DISCOUNTING. NPV AND IRR ARE BOTH FOUND BY NPV AND IRR ARE BOTH FOUND BY DISCOUNTING, SO THEY BOTH IMPLICITLY DISCOUNTING, SO THEY BOTH IMPLICITLY ASSUME SOME DISCOUNT RATE. ASSUME SOME DISCOUNT RATE.

G.G. 3.3. WHICH METHOD IS WHICH METHOD IS THE BEST? WHY?THE BEST? WHY?INHERENT IN THE NPV INHERENT IN THE NPV CALCULATION IS THE ASSUMPTION CALCULATION IS THE ASSUMPTION THAT CASH FLOWS CAN BE THAT CASH FLOWS CAN BE REINVESTED AT THE PROJECT’S REINVESTED AT THE PROJECT’S COST OF CAPITAL, WHILE THE IRR COST OF CAPITAL, WHILE THE IRR CALCULATION ASSUMES CALCULATION ASSUMES REINVESTMENT AT THE IRR RATEREINVESTMENT AT THE IRR RATE

WHETHER NPV OR IRR GIVES BETTER WHETHER NPV OR IRR GIVES BETTER RANKINGS DEPENDS ON WHICH HAS THE RANKINGS DEPENDS ON WHICH HAS THE BETTER REINVESTMENT RATE BETTER REINVESTMENT RATE ASSUMPTION. ASSUMPTION. NORMALLY, THE NPV’S ASSUMPTION IS NORMALLY, THE NPV’S ASSUMPTION IS BETTER.BETTER. THE REASON IS AS FOLLOWS: THE REASON IS AS FOLLOWS: A PROJECT’S CASH INFLOWS ARE A PROJECT’S CASH INFLOWS ARE GENERALLY USED AS SUBSTITUTES FOR GENERALLY USED AS SUBSTITUTES FOR OUTSIDE CAPITAL, THAT IS, PROJECTS’ OUTSIDE CAPITAL, THAT IS, PROJECTS’ CASH FLOWS REPLACE OUTSIDE CAPITAL CASH FLOWS REPLACE OUTSIDE CAPITAL AND, HENCE, SAVE THE FIRM THE COST OF AND, HENCE, SAVE THE FIRM THE COST OF OUTSIDE CAPITALOUTSIDE CAPITAL  

. THEREFORE, IN AN . THEREFORE, IN AN OPPORTUNITY COST OPPORTUNITY COST SENSE, A PROJECT’S SENSE, A PROJECT’S CASH FLOWS ARE CASH FLOWS ARE REINVESTED AT THE REINVESTED AT THE COST OF CAPITAL.COST OF CAPITAL.

Internal rate in returnInternal rate in returnInternal rate return is the

discount rate that equates the present value of a project’ expected cash flow to the present value of the project’s costs. It’s the rate that forces a project’s NPV to equal zero.

-100+ 10/(.17)^1+10/(1.17)^2+10/(1.17)^3=0

IRR (L) = 17%

-100+70/(1.18)^1+50/(1.18)^2+30/(1.18)^3=0

IRR (S) = 18%

IRR RELATED TO YTM ON IRR RELATED TO YTM ON BONDBOND

are computed in the same manner, and there is an assumption that the cash in flow from the various projects is utilized thereafter.

LOGIC BETWEEN IRR LOGIC BETWEEN IRR METHODMETHODThe IRR on a project is the

expected rate of return. If the internal rate of return exceeds the cost of capital, and this surplus accrues to the firm’s stockholders. Therefore taking on a project whose IRR exceeds its cost of capital increases shareholder’s wealth.

Would the project’s IRR Would the project’s IRR change if the cost of capital change if the cost of capital changed?changed?

No, IRR is not dependent on the cost of capital. But the project’s acceptance can change if the IRR is lower than its cost of capital.

Modified IRR is the discount rate at which the present value of a project’s cost is equal to the present value of it’s terminal value, where the terminal value is found as the sum of the future values of the cash inflows, compounded at the firm’s cost of capital.

MIRR (L)= 16%MIRR (S) = 17%

  What are the MIRRs’s What are the MIRRs’s advantages and disadvantage advantages and disadvantage vis-a-vis the NPVvis-a-vis the NPV

NPV gives a direst measure of the dollar benefit of the project to shareholders.The NPV provides no information in the cash flow forecasts or the amount of capital at risk. The MIRR has all the virtues of IRR but it incorporates a better investment rate assumption, and it avoids the multiple rate of return problem.

P’S NPV,IRR, MIRRP’S NPV,IRR, MIRRNPV=$0.35 IRR= 25%MIRR= 6%

It has a nonnormal cash flow.No because it’s NPV is negative.

And the company wouldn’t get back their investment if that project is accepted.