In: Finance
Machine |
0 |
1 |
2 |
3 |
4 |
NPV |
Annuity Factor |
EAA |
A |
+20 |
+6 |
+6 |
? |
? |
? |
||
B |
+15 |
+4 |
+5 |
+6 |
? |
? |
? |
|
C |
+10 |
+5 |
+6 |
+7 |
+8 |
? |
? |
? |
Equivalent annual cashflow is used in capital budgeting to compare the investments which are having unequal lengh of project life. It shows the NPV of an investment as series of equal cashflows for the length of the investment. NPV doesnt take into consideration the length of the investment. Equivalent annual cashflow provides a way to factor in the length of the investment.
As all three machines cost same to purchase,
For Machine A,
NPV= 20+6/1.06+6/1.06^2= 31
Annuity factor= (1-(1/(1+r)^t))/r= (1-(1/(1+6%)^2))/6%= 0.11
EAA= NPV/Annuity Factor= 31/0.11= 16.91
For Machine B,
NPV= 15+4/1.06+5/1.06^2+6/1.06^3= 28.26
Annuity factor= (1-(1/(1+r)^t))/r= (1-(1/(1+6%)^3))/6%= 0.16
EAA= NPV/Annuity Factor= 28.26/0.16= 10.57
For Machine C,
NPV= 10+5/1.06+6/1.06^2+7/1.06^3+8/1.06^4= 32.27
Annuity factor= (1-(1/(1+r)^t))/r= (1-(1/(1+6%)^4))/6%= 0.21
EAA= NPV/Annuity Factor= 32.27/0.21= 9.31
Machine | 0 | 1 | 2 | 3 | 4 | NPV | Annuity Factor | EAA |
A | 20 | 6 | 6 | 31 | 0.11 | 16.91 | ||
B | 15 | 4 | 5 | 6 | 28.26 | 0.16 | 10.57 | |
C | 10 | 5 | 6 | 7 | 8 | 32.27 | 0.21 | 9.31 |