Question

(Equivalent annual cost​ calculation)  The Templeton Manufacturing and Distribution Company of​ Tacoma, Washington, is contemplating the purchase of a new conveyor belt system for one of its regional distribution facilities. Both alternatives will accomplish the same task but the Eclipse Model is substantially more expensive than the Sabre Model and will not have to be replaced for 10​ years, whereas the cheaper model will need to be replaced in just 5 years. The costs of purchasing the two systems and the costs of operating them annually over their expected lives are provided​ below:  

.a.  Templeton typically evaluates investments in plant improvements using a required rate of return of

11

percent.

What are the NPVs for the two​ systems?

b.  Calculate the equivalent annual costs for the two systems.

c.  Based on your analysis of the two systems using both their NPV and​ EAC, which system do you recommend the company​ pick? ​ Why?

a.

The NPV for Eclipse at a discount rate of

1111​%

is

​$nothing.

​(Round to the nearest​ dollar.)

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Data Table

Year	Eclipse		Sabre
0	​$(1 comma 500 comma 0001,500,000​)		​$(900 comma 000900,000​)
1	​(22 comma 00022,000​)		​(45 comma 00045,000​)
2	​(31 comma 00031,000​)		​(45 comma 00045,000​)
3	​(31 comma 00031,000​)		​(58 comma 00058,000​)
4	​(31 comma 00031,000​)		​(58 comma 00058,000​)
5	​(41 comma 00041,000​)		​(85 comma 00085,000​)
6	​(41 comma 00041,000​)
7	​(41 comma 00041,000​)
8	​(41 comma 00041,000​)
9	​(41 comma 00041,000​)
10	​(41 comma 00041,000​)

Answer 1

(a)-Net Present Value (NPV) of the two systems

Net Present Value (NPV) - Eclipse

Period	Annual Cash Flow ($)	Present Value factor at 11%	Present Value of Cash Flow ($)
1	-22,000	0.900901	-19,819.82
2	-31,000	0.811622	-25,160.30
3	-31,000	0.731191	-22,666.93
4	-31,000	0.658731	-20,420.66
5	-41,000	0.593451	-24,331.50
6	-41,000	0.534641	-21,920.27
7	-41,000	0.481658	-19,747.99
8	-41,000	0.433926	-17,790.99
9	-41,000	0.390925	-16,027.92
10	-41,000	0.352184	-14,439.56
TOTAL		5.889232	-2,02,325.95

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$2,02,325.95 - $15,00,000

= -$17,02,325.95

Net Present Value (NPV) – Sabre

Period	Annual Cash Flow ($)	Present Value factor at 11%	Present Value of Cash Flow ($)
1	-45,000	0.900901	-40,540.54
2	-45,000	0.811622	-36,523.01
3	-58,000	0.731191	-42,409.10
4	-58,000	0.658731	-38,206.40
5	-85,000	0.593451	-50,443.36
TOTAL		3.695897	-2,08,122.41

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$2,08,122.41 - $900,000

= -$11,08,122.41

(b)-Equivalent Annual Costs (EAC) for the two systems.

Equivalent Annual Cost (EAC) - Eclipse

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 11%, 10 Years]

= -$17,02,325.95 / 5.889232

= -$2,89,057.38 (Negative)

Equivalent Annual Cost (EAC) - Sabre

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 11%, 5 Years]

= -$11,08,122.41 / 3.695897

= -$2,99,825.02 (Negative)

(c)-DECISION

Templeton Manufacturing and Distribution Company should select the Eclipse Model, since it has the lower Equivalent Annual Cost (EAC) of -$2,89,057.38 as compared to the lower Equivalent Annual Cost (EAC) of Sabre of -$2,99,825.02.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.