Robot Economic Analysis

Introduction

This note is a full worked example (Example 8). It uses the Payback Method and the ROI method on one robot cell.

Problem

A company wants to set up a robot cell for a new product. The product will last 5 years.

• the cell has two robots, one production machine and one conveyor belt
• each robot costs \60{,}000$ and has a service life of 10 years
• the machine costs \20{,}000$andtheconveyorcosts$$10{,}000$
• at the end of 5 years, each robot has a salvage value of \22{,}500$
• one operator is paid \10$ per hour and spends 2 hours per day on the cell
• other operating and maintenance costs are \20{,}000$ per year
• revenue is \100{,}000$ per year
• $MARR=35\%$ and there are 250 days of operation each year

Find the payback period and the rate of return.

Solution

1. Initial investment

Item	Unit cost	Quantity	Total
Robot	\60{,}000$	2	\120{,}000$
Machine	\20{,}000$	1	\20{,}000$
Conveyor	\10{,}000$	1	\10{,}000$
Total			\150{,}000$

2. Operating cost

$$\text{Direct labour}=10\times 2\times 250=\$5,000\text{ per year}$$ $$\text{Total annual cost}=5,000+20,000=\$25,000$$

3. Payback period

$$n=\frac{150,000}{100,000-25,000}=2.0\text{ years}$$

4. Rate of return

The salvage value is 2\times22{,}500=\45{,}000$.

$$EUAC=-150,000\left(\frac{A}{P},i,5\right)+100,000-25,000+45,000\left(\frac{A}{F},i,5\right)=0$$

Try $i=40\%$, with $(A/P)=0.49136$ and $(A/F)=0.09136$:

$$EUAC=-150,000(0.49136)+75,000+45,000(0.09136)=+5,407.2$$

Try $i=45\%$, with $(A/P)=0.53318$ and $(A/F)=0.08318$:

$$EUAC=-150,000(0.53318)+75,000+45,000(0.08318)=-1,233.9$$

By interpolation, $i=44.07\%$. This is more than the MARR of $35\%$, so the project is good.