investmentworth investment worth. investment worth marr suppose a company can earn 12% / annum in u....
TRANSCRIPT
InvestmentInvestment WorthWorth
Investment Worth
MARRSuppose a company can earn 12% / annum in U. S. Treasury bills
No way would they ever invest in a project earning < 12%
Def: The Investment Worth of all projects are measured at the Minimum AttractiveRate of Return (MARR) of a company.
MARR
MARR is company specific utilities - MARR = 10 - 15% mutuals - MARR = 12 - 18% new venture - MARR = 20 - 30%
MARR based on firms cost of capital Price Index Treasury bills
Investment Worth Alternatives
NPW(MARR) > 0 Good Investment
Investment Worth Alternatives
NPW(MARR) > 0 Good Investment
EUAW(MARR) > 0 Good Investment
Investment Worth Alternatives
NPW(MARR) > 0 Good Investment
EUAW(MARR) > 0 Good Investment
IRR > MARR Good Investment
Present WorthExample: Suppose you buy and sell a piece of equipment.
Purchase Price $16,000 Sell Price (5 years) $ 4,000 Annual Maintenance $ 3,000 Net Profit Contribution $ 6,000
MARR 12%
Is it worth it to the company to buy the machine?
Present Worth
16,000
6,000
3,000
50
4,000
NPW = -16 + 3(P/A,12,5) + 4(P/F,12,5)
16,000
3,000
50
4,000
Present Worth
16,000
6,000
3,000
50
4,000
NPW = -16 + 3(P/A,12,5) + 4(P/F,12,5)
= -16 +3(3.6048) + 4(.5674)
16,000
3,000
50
4,000
Present Worth
16,000
6,000
3,000
50
4,000
NPW = -16 + 3(P/A,12,5) + 4(P/F,12,5)= -16 +3(3.6048) + 4(.5674)= -2.916= -$2,916
16,000
3,000
50
4,000
Annual Worth
Annual Worth (AW or EUAW)
AW(i) = PW(i) (A/P, i%, n) = [ At (P/F, i%, t)](A/P, i%, n)
AW(i) = Annual Worth of Investment
AW(i) > 0 **OK Investment**
Annual Worth; Example
Repeating our PW example, we have
AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5)
3,000
50
4,000
16,000
Annual Worth; Example
Repeating our PW example, we have
AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5)= -16(.2774) + 3 + 4(.1574)
3,000
50
4,000
16,000
Annual Worth; Example
Repeating our PW example, we have
AW(12)= -16(A/P,12,5) + 3 + 4(A/F,12,5)= -16(.2774) + 3 + 4(.1574)= -.808= -$808
3,000
50
4,000
16,000
Alternately
AW(12) = PW(12) (A/P, 12%, 5) = -2.92 (.2774) = - $810 < 0 NO
GOOD
3,000
50
4,000
16,000
Internal Rate of ReturnInternal Rate-of-ReturnIRR - internal rate of return is that
return for which NPW(i*) = 0 i* = IRR
i* > MARR **OK Investment**
Internal Rate of ReturnInternal Rate-of-ReturnIRR - internal rate of return is that
return for which NPW(i*) = 0 i* = IRR
i* > MARR **OK Investment**
Alt:
PWrevenue(i*) = PWcosts(i*)
Internal Rate of ReturnExample
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)3,000
50
4,000
16,000
Internal Rate of ReturnExample
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
i PW(i)
12 -2.9210 -2.146 -0.374 0.645 0.12
3,000
50
4,000
16,000
Internal Rate of ReturnExample
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
i* = 5 1/4 %
i* < MARR
i PW(i)
12 -2.9210 -2.146 -0.374 0.645 0.12
3,000
50
4,000
16,000
Summary
NPW > 0 Good Investment
Summary
NPW > 0 Good Investment
EUAW > 0 Good Investment
Summary
NPW > 0 Good Investment
EUAW > 0 Good Investment
IRR > MARR Good Investment
Summary
NPW > 0 Good Investment
EUAW > 0 Good Investment
IRR > MARR Good Investment
Note: If NPW > 0 EUAW > 0IRR > MARR
Internal Rate of ReturnInternal Rate-of-ReturnIRR - internal rate of return is that return
for which NPW(i*) = 0 i* = IRR
i* > MARR **OK Investment**
Alt:FW(i*) = 0 = At(1 + i*)n - t
PWrevenue(i*) = PWcosts(i*)
Internal Rate of ReturnExample
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
i PW(i)
12 -2.9210 -2.146 -0.374 0.645 0.12
3,000
50
4,000
16,000
Internal Rate of ReturnExample
PW(i) = -16 + 3(P/A, i, 5) + 4(P/F, i, 5)
i* = 5 1/4 %
i* < MARR
i PW(i)
12 -2.9210 -2.146 -0.374 0.645 0.12
3,000
50
4,000
16,000
Spreadsheet Example
1
2
3
45678910111213
A B C D E F
ExamplePeriod Cash Flow
0 (16,000)1 3,0002 3,0003 3,0004 3,0005 7,000 MARR = 12.0%
NPV = (2,916) = NPV(E9,C5:C9)+ C4PMT = (809) = -PMT(E9,5,C10)IRR = 5.2% = IRR(C4:C9,E9)