Question

Using information from Question 5, determine the better option at interest rate 10% using Present Worth Analysis. Please solve using Excel if possible.

Question 5: Consider the following two alternatives that have no salvage value:

	A	B
Initial Cost Uniform Annual Benefits Useful life, in years	$15,000 $3,000 8	$5,100 $1,800 4

Answer 1

Hi,

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Question:

Answer:

Here, i will determine the better option through NPV method. Net present value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows over a period of time.

As per the qusetion:

For Project A:

Initial Cost = $15000

Uniform annual benefits = $3000

Useful Life = 8 years

Interest rate = 10%

NPV = Cash flow 0 + Cash flow1/(1+r)^1 + Cash flow2/(1+r)^2 + Cash flow3/(1+r)^3 + Cash flow4/(1+r)^4 + Cash flow5/(1+r)^5 + Cash flow6/(1+r)^6 + Cash flow7/(1+r)^7 + Cash flow8/(1+r)^8

= - $15000 + $3000/(1+10%)^1 + $3000/(1+10%)^2 + $3000/(1+10%)^3 + $3000/(1+10%)^4 + $3000/(1+10%)^5 + $3000/(1+10%)^6 + $3000/(1+10%)^7 + $3000/(1+10%)^8

= - $15000 + $3000/(1+ 0.1)^1 + $3000/(1+ 0.1)^2 + $3000/(1+ 0.1)^3 + $3000/(1+ 0.1)^4 + $3000/(1+ 0.1)^5 + $3000/(1+ 0.1)^6 + $3000/(1+ 0.1)^7 + $3000/(1+ 0.1)^8

=  - $15000 + $3000/(1.1)^1 + $3000/(1.1)^2 + $3000/(1.1)^3 + $3000/(1.1)^4 + $3000/(1.1)^5 + $3000/(1.1)^6 + $3000/(1.1)^7 + $3000/(1.1)^8

=  - $15000 + $3000/1.1 + $3000/1.21 + $3000/1.331 + $3000/1.4641+ $3000/1.61051 + $3000/1.771561 + $3000/1.9487171 + $3000/2.14358881

= - $15000 + 2727.27 + 2479.33 + 2253.94 + 2049.04 + 1862.76 + 1693.42 + 1539.47 + 1399.52

= - $15000 + $160004.75

NPV of project A = $10004.75

For Project A:

Initial Cost = $5100

Uniform annual benefits = $1800

Useful Life = 4 years

Interest rate = 10%

NPV = Cash flow 0 + Cash flow1/(1+r)^1 + Cash flow2/(1+r)^2 + Cash flow3/(1+r)^3 + Cash flow4/(1+r)^4

= - $5100 + $1800/1.1 + 1800/1.21 + $1800/1.331 + $1800/1.4641

= - $5100 + 1636.36 + 1487.60 + 1352.36 + 1229.42

= - $5100 + $5705.74 = $605.74

NPV of project B = $605.74

Here, NPV of project "A" is better than project "B" so, Project "A" is better than project "B" . So, Project "A" is  the better option.

Thank You