# A B C Investment 800000 100000 900000 Cost 90000 130000 100000 Revenue 300000 500000 350000...

## Question:

 A B C Investment 800000 100000 900000 Cost 90000 130000 100000 Revenue 300000 500000 350000 Life 4 7 5

A) Is this cost based or revenue based project.

B) Layout cash flows, value for years depending on the answer to A part.

C) Assume repeatability, use Annual Worth (AW) to calculate the best option.

## Equivalent Annual Worth:

The equivalent annual worth or equivalent annuity is a mechanism used for evaluating a capital budget out of all the available investment alternatives. The other methods which may also be used are net present value method, internal rate of return method, cash payback period method etc.

Investment A

The net operating income is given by:

• = Revenue - annual cost
• = $300,000 -$90,000
• = $210,000 Assuming discount rate of 10% (or 0.10), the net present value of all the cash flows is given by: • {eq}= \dfrac{\$210,000}{1.10^1} + \dfrac{\$210,000}{1.10^2} + ..... + \dfrac{\$210,000}{1.10^4} - $800,000 {/eq} • = -$134,328.30

The equivalent annual cost (A) can be figured out by equating the net present value with the sum of present value of all annuities as shown below:

{eq}-$134,328.30 = \dfrac{A}{1.10^1} + \dfrac{A}{1.10^2} +.....+ \dfrac{A}{1.10^4} {/eq} On solving the above equation we get, annuity (A) =$42,376.70

Investment B

The net operating income is given by:

• = Revenue - annual cost
• = $500,000 -$130,000
• = $370,000 Assuming discount rate of 10% (or 0.10), the net present value of all the cash flows is given by: • {eq}= \dfrac{\$370,000}{1.10^1} + \dfrac{\370,000}{1.10^2} + ..... + \dfrac{\370,000}{1.10^7} - $100,000 {/eq} • = -$1,701,315

The equivalent annual cost (A) can be figured out by equating the net present value with the sum of present value of all annuities as shown below:

{eq}$1,701,315 = \dfrac{A}{1.10^1} + \dfrac{A}{1.10^2} +.....+ \dfrac{A}{1.10^7} {/eq} On solving the above equation we get, annuity (A) =$349,459.46

Investment C

The net operating income is given by:

• = Revenue - annual cost
• = $350,000 -$100,000
• = $250,000 Assuming discount rate of 10% (or 0.10), the net present value of all the cash flows is given by: • {eq}= \dfrac{\$250,000}{1.10^1} + \dfrac{\$250,000}{1.10^2} + ..... + \dfrac{\$250,000}{1.10^5} - $900,000 {/eq} • = -$47,696.70

The equivalent annual cost (A) can be figured out by equating the net present value with the sum of present value of all annuities as shown below:

{eq}-$47,696.70 = \dfrac{A}{1.10^1} + \dfrac{A}{1.10^2} +.....+ \dfrac{A}{1.10^5} {/eq} On solving the above equation we get, annuity (A) =$12,582.30

• Since the equivalent annual worth is the highest for the investment B, it should be selected among all the available projects.