1. CTC 475 Review
Is a certain cash flow economically feasible?

2. Methods for Determining if an Alternative is Economically Feasible
CTC 475
Methods for Determining if an Alternative is Economically Feasible

3. Objectives
Know the various methods for determining if an alternative is economically feasible
Be able to use any method for economic feasibility studies

4. Methods for Economic Feasibility Studies
Present Worth (PW)
Annual Worth (AW)
Future Worth (FW)
Internal Rate of Return (IRR)
External Rate of Return (ERR)
Savings/Investment Ratio (SIR) or
Benefit/Cost Ratio (B/C)
Payback Period Method (PBP)
Capitalized Worth Method (CW)

5. Equivalent Methods PW AW FW
IRR
ERR
SIR or B/C

6. Nonequivalent Methods
PBP CW

7. When is an alternative feasible?
PW > 0
AW > 0
FW > 0
IRR > MARR
ERR > MARR
SIR or B/C > 1

8. Net Cash Flows
It’s a good idea to use net cash flows (one cash flow at each period).
It doesn’t matter with respect to whether a project is feasible or not; however, absolute numbers (ERR and SIR) may differ

9. Example (MARR=10%) EOY Cash Flow -$40K 1 $5K 2 $8K 3 $11K 4 $14K 5 6 7
-$40K 1
$5K 2
$8K 3
$11K 4
$14K 5 6 7 8

10. Cash flow breakdown-show on board
Years 1-4: Uniform ($5K) + Gradient ($3K)
n=4
P will occur at t=0
F will occur at t=4
Years 5-8: Uniform ($14K) - Gradient ($3K)
P will occur at t=4
F will occur at t=8

11. Present Worth PW= -40K+5K(P/A10,4)+3K(P/G10,4)
+[14K(P/A10,4)- 3K(P/G10,4)](P/F10,4)
PW= -40K+5K(3.1699)+3K(4.3781)
+[14K(3.1699)-3K(4.3781)]*0.6830
PW= +$10,324
PW>0 ; therefore, cash flow is economically feasible

12. Annual Worth Find A given P AW=PW(A/P10,8) AW=$10,324(.1874) AW=$1,935
AW>0; therefore, cash flow is economically feasible

13. Future Worth FW=PW(F/P10,8) or PW(1.1)8 FW=$10,324(2.1436) FW=$22,130
FW= AW(F/A10,8)
FW=$1,935( )
FW=$22,128
FW>0; therefore, cash flow is economically feasible

14. Future Worth-Alternate Method
FW= -40K(F/P10,8)+[5K+3K(A/G10,4)](F/A10,4)(F/P10,4)
+[14K-3K(A/G10,4)](F/A10,4)
FW=-$85,744+($9,144)(6.7949)+($9,856)(4.6410)
FW=+$22,129

15. Future Worth-Alternate Method “Snail”Method Using Single Sums
FW= -40K(F/P10,8)+5K(F/P10,7)+8K(F/P10,6)+11K(F/P10,5) 14K(F/P10,4)+14K(F/P10,3)+11K(F/P10,2)+8K(F/P10,1)
+5K
FW=-$85,744+$9,744 +$14,172+ $17,716
+$20,497+$18,634+$13,310+$8,800+$5,000
FW=+$22,129

16. IRR-Find i that gives a PW=0
PW= -40K+5K(P/Ai,4)+3K(P/Gi,4)
+[14K(P/Ai,4)- 3K(P/Gi,4)](P/Fi,4)
Interpolate to get an IRR = 16.5%
IRR>MARR
i(%) PW 10
+$10,324 12
+$6,723 15
+$1,994 18
-$2,064

17. ERR: Set FW of + using MARR = FW of – using ERR; solve for ERR
FW(+) = 5K+3K(A/G10,4)](F/A10,4)(F/P10,4)
+[14K-3K(A/G10,4)](F/A10,4) = $107,873
FW(-) = 40K(1+ERR)8
40K(1+ERR)8 = $107,873
(1+ERR)8 =
ERR=13.2%
ERR>MARR
Check: MARR=10%; ERR=13.2%; IRR=16.5%

18. SIR or B/C SIR=PW(+)/PW(-) PW(-)=$40,000 SIR=$50,324/$40,000=1.26
PW(+)=5K(P/A10,4)+3K(P/G10,4)
+[14K(P/A10,4)- 3K(P/G10,4)](P/F10,4)=$50,324
PW(-)=$40,000
SIR=$50,324/$40,000=1.26
SIR>1

19. PBP-Payback Period
If MARR=0 how many periods does it take to get your investment back?
At 1 year; $5K<$40K
At 2 years: $13K<$40K
At 3 years: $24K<$40K
At 4 years: $38K<$40K
At 5 years: $52K>$40K
PBP is 5 years

20. Next lecture
Bonds