Question

Faleye Consulting is deciding which of two computer systems to purchase. It can purchase state-of-the-art equipment (System A) for $19,000, which will generate cash flows of $7,000 at the end of each of the next 6 years. Alternatively, the company can spend $14,000 for equipment that can be used for 3 years and will generate cash flows of $7,000 at the end of each year (System B). If the company’s WACC is 5% and both “projects” can be repeated indefinitely, which system should be chosen, and what is its EAA? Do not round intermediate calculations. Round your answer to the nearest cent.

Choose project A or B whose EAA = S

Answer 1

Question:

Faleye Consulting is deciding which of two computer systems to purchase. It can purchase state-of-the-art equipment (System A) for $19,000, which will generate cash flows of $7,000 at the end of each of the next 6 years. Alternatively, the company can spend $14,000 for equipment that can be used for 3 years and will generate cash flows of $7,000 at the end of each year (System B). If the company’s WACC is 5% and both “projects” can be repeated indefinitely, which system should be chosen, and what is its EAA? Do not round intermediate calculations. Round your answer to the nearest cent.

Choose project A or B whose EAA = S

Solution:

1. Calculation of NPV & EAA for System A:

Given:

Initial Investment or Purchase Price of A = $ 19,000

Cash Flow per year = $ 7,000

Number of Years n = 6 Years

WACC = 5 %

To Calculate:

EAA i.e. Equivalent Annual Annuity

Formula:

Equivalent Annual Annuity EAA = r × NPV / 1- (1 + r) ^ -n

Where:

r= Interest Rate or WACC

NPV = Net Present Value of Project

n= Number of Years

So, to calculate EAA, first of all we have to calculate the NPV of Project A whose formula is as follows:

Formula:

NPV = ∑ CFn / (1 + WACC) ^ n – Initial Investment

Where,

CFn = Cash Flow of the n Year

WACC = Interest Rate

n= Number of Years

Tabulation of the Calculation of NPV of System A:

Years	Cash Flow	Present Value = CFn / (1 + WACC) ^ n	Present Value Amount in $
1.	$7,000	7000 / (1 + 0.05) ^ 1 = 7000 / 1.05 ^ 1	6666.67
2.	$7,000	7000 / (1 + 0.05) ^ 2 = 7000 / 1.05 ^ 2	6349.21
3.	$7,000	7000 / (1 + 0.05) ^ 3 = 7000 / 1.05 ^ 3	6046.86
4.	$7,000	7000 / (1 + 0.05) ^ 4 = 7000 / 1.05 ^ 4	5758.92
5.	$7,000	7000 / (1 + 0.05) ^ 5 = 7000 / 1.05 ^ 5	5484.68
6.	$7,000	7000 / (1 + 0.05) ^ 6 = 7000 / 1.05 ^ 6	5223.51
Total	Present Value of Cash Flows	$ 35,529.85
Less: Initial Purchase Price	-$ 19,000.00
Net Present Value of System A	$ 16,529.85

Now we find the EAA of Project A:

Equivalent Annual Annuity

EAA = r × NPV / 1- (1 + r) ^ -n

On putting the values in the formula, we get,

= (0.05 × 16,529.85) / (1 – (1 + 0.05) ^-6)

= 826.49 / 1- (1.05) ^-6

= 826.49 / 1- 0.7462

= 826.49 / 0.2538

= $ 3256.46

Equivalent Annual Annuity EAA of Project A = $ 3256.46

2. Calculation of NPV & EAA for System B:

Given:

Initial Investment or Purchase Price of B = $ 14,000

Cash Flow per year = $ 7,000

Number of Years n = 3 Years

WACC = 5 %

To Calculate:

EAA i.e. Equivalent Annual Annuity

Formula:

Equivalent Annual Annuity EAA = r × NPV / 1- (1 + r) ^ -n

Where:

r= Interest Rate or WACC

NPV = Net Present Value of Project

n= Number of Years

So, to calculate EAA, first of all we have to calculate the NPV of Project B whose formula is as follows:

Formula:

NPV = ∑ CFn / (1 + WACC) ^ n – Initial Investment

Where,

CFn = Cash Flow of the n Year

WACC = Interest Rate

n= Number of Years

Tabulation of the Calculation of NPV of System B:

Years	Cash Flow	Present Value = CFn / (1 + WACC) ^ n	Present Value Amount in $
1.	$7,000	7000 / (1 + 0.05) ^ 1 = 7000 / 1.05 ^ 1	6666.67
2.	$7,000	7000 / (1 + 0.05) ^ 2 = 7000 / 1.05 ^ 2	6349.21
3.	$7,000	7000 / (1 + 0.05) ^ 3 = 7000 / 1.05 ^ 3	6046.86
Total	Present Value of Cash Flows	$ 19,062.74
Less: Initial Purchase Price	-$ 14,000.00
Net Present Value of System B	$ 5,062.74

Now we find the EAA of Project B:

Equivalent Annual Annuity

EAA = r × NPV / 1- (1 + r) ^ -n

On putting the values in the formula, we get,

= (0.05 × 5,062.74) / (1 – (1 + 0.05) ^-3)

= 253.137 / 1- (1.05) ^-3

= 253.137 / 1- 0.8638

= 253.137 / 0.1362

= $ 1858.57

Equivalent Annual Annuity EAA of Project B = $ 1858.57

Ans:

Methods	Project A	Project B	Analytical Decision
Net Present Value NPV	$ 16,529.85	$ 5,062.74	"Project A should be Chosen" Project A is better than B in NPV: NPV of A > NPV of B = $ 16,529.85 > $ 5,062.74
Equivalent Annual Annuity EAA	$ 3256.46	$ 1858.57	"Project A should be Chosen" Project A is better than B in EAA: EAA of A > EAA of B $ 3256.46 > $ 1858.57

Project A should be chosen because its Net Present Value is greater than that of Project B. Also according to EAA criteria Project A should be chosen as EAA of Project A is also greater than EAA of Project B.