Question

Using the information from problem 8 on Alpha & Omega, what is the equivalent annual annuity (EAA) for System B? Enter your answer rounded to two decimal places. Do not enter $ or comma in the answer box. For example, if your answer is $12,300.456 then enter as 12300.46 in the answer box.

Alpha & Omega wants to invest in a new computer system, and management has narrowed the choice to Systems A and B.

System A requires an up-front cost of $100,000, after which it generates positive after-tax cash flows of $70,000 at the end of each of the next 2 years. The system could be replaced every 2 years, and the cash inflows and outflows would remain the same.

System B also requires an up-front cost of $100,000, after which it would generate positive after-tax cash flows of $48,000 at the end of each of the next 3 years. System B can be replaced every 3 years, but each time the system is replaced, both the cash outflows and cash inflows would increase by 10%.

The company needs a computer system for 6 years, after which the current owners plan to retire and liquidate the firm. The company's cost of capital is 14%. What is the NPV (on a 6-year extended basis) of System A? Enter your answer rounded to two decimal places. Do not enter $ or comma in the answer box. For example, if your answer is $12,300.456 then enter as 12300.46 in the answer box.

Answer 1

The replacement chain method is used to compare mutually exclusive Systems with different life span.
Life span of System A = 2 Years
Life span of System B = 3 Years

Required of computer system = 6 Years

This means System A should be repeated 2 more times and System B should be repeated 1 more time.

Calculation of Net Cash Flow for System A if it is repeated 2 more times i.e upto Years 6 :

Year	Working	A NCF (Revenue – Cost)
0		-100000
1		70000
2	70000 – 100000 = -30000	-30000
3		70000
4	70000 – 100000 = -30000	-30000
5		70000
6		70000

Initial Investment at Year 0 will repeat at the end of Year 2 and year 4 i.e on completing of System A and Net Cash Inflows of Year 1,2 will repeat in Year 3,4 and in year 5,6 respectively.

Calculation of NPV for System A

NPV of System A = 36051.95

Calculation of Net Cash Flow for System B if it is repeated 1 more times i.e upto Years 6 :

Year	Working	A NCF (Revenue – Cost)
0		-100000
1		48000
2		48000
3	48000 – (100000 *1.10)	-62000
4	48000 * 1.1	52800
5	48000 * 1.1	52800
6	48000 * 1.1	52800

Initial Investment at Year 0 will repeat at the end of Year 3 i.e on completing of System B and will increase by 10% and Net Cash Inflows of Year 1,2,3 will repeat in Year 4,5,6 respectively and will also increase by 10%.

Calculation of NPV for System B

NPV of System B = 19930.94

Note : Present Value Factor have been calculated as = (1/1+r)n

Where
r= Required rate of Return (Discount rate)
n= No of Periods

Equivalent Annual Annuity assumes the projects/equipments to be annuities and then calculates the cashflow generated by the project over its span.