Explain the concept of equivalent annual cash flow. Given the following cash flows from operating three...

Explain the concept of equivalent annual cash flow.

Given the following cash flows from operating three machines and a 6% cost of capital, which machine has the higher value using the equivalent annual annuity method. All three machines cost the same to purchase.

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	?	?	?

Solutions

Expert Solution

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

jeff jeffy answered 1 year ago

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