Question

ABC Company is evaluating whether to invest in two projects. ABC Co. has the funds to invest in both. The first project is a $250,000 investment in pollution abatement equipment. The cash savings from implementing this equipment will be $24,000 per year for 25 years. The second project is a robot that will stack the finished goods product on pallets for shipment. Currently, the product is being stacked manually. The robot will cost $1,000,000. The cash inflows for project 2 are Tear 1: $230,000; Year 2: $180,000; Year 3: $150,000; and Years 4-10: $100,000. Evaluate the investments using each of the capital budgeting methods (IRR, NPV and the Payback Period). The cost of capital for ABC Co. is 8%. Discuss your findings and recommendations. Consider some of the following in your review:

1. Were your recommendations the same for each method? Why or why not?
2. How would you determine which method is most appropriate for different circumstances?
3. Are there any non-financial considerations? If so, what?

Answer 1

For 1st project

NPV = -250000 + 24000/1.08+ 24000/1.08^2+...+24000/1.08^25

=-250000+24000/0.08*(1-1/1.08^25)

=6194.63

IRR (r) is the rate at which NPV =0

So,

-250000+24000/r*(1-1/(1+r)^25) =0............................ (1)

Using hit and trial method ,

let r = 10% =0.1, the Left hand side of the equation (1) becomes =-32151.04

r = 9% =0.09, the Left hand side of the equation (1) becomes =-14258.09

r = 8.5% =0.085, the Left hand side of the equation (1) becomes = -4379.42

r = 8.3% =0.083, the Left hand side of the equation (1) becomes = -236.62

r = 8.2% =0.082, the Left hand side of the equation (1) becomes = 1877.69

So, r lies between 8.2% and 8.3%', Using linear approximation method

r = 0.082 +(1877.69-0)/(1877.69-(-236.62))*(0.083-0.082) =0.08288 or 8.288%

payback period = 250000/24000 = 10.42 years or 11 years

For 2nd project

NPV =-1000000+230000/1.08+180000/1.08^2+150000/1.08^3+(100000/1.08^4+..+100000/1.08^10)

=-1000000+486358.79 + 100000/0.08*(1-1/1.08^7)*1/1.08^3

=-100342.77

IRR (r) is the rate at which NPV =0

So,

-1000000+230000/(1+r)+180000/(1+r)^2+150000/(1+r)^3+ 100000/r*(1-1/(1+r)^7)*1/(1+r)^3 =0...... (1)

Using hit and trial method ,

let r = 7% =0.07, the Left hand side of the equation (1) becomes =-65456.53

r = 6% =0.06, the Left hand side of the equation (1) becomes =-28169.11

r = 5% =0.05, the Left hand side of the equation (1) becomes = 11737.25

r = 5.5% =0.055, the Left hand side of the equation (1) becomes = -8557.79

r = 5.3% =0.053, the Left hand side of the equation (1) becomes = -523.52

r = 5.2% =0.052, the Left hand side of the equation (1) becomes = 3535.25

So, r lies between 5.2% and 5.3%', Using linear approximation method

r = 0.052 +(3535.25-0)/(3535.25-(-523.52))*(0.053-0.052) =0.05287 or 5.287%

payback period can be calculated as the year in which cumulative cashflows is positive

Cumulative Cashflows upto year 3 = -1000000+230000+180000+150000 =-440000

No. of years beyond 3 years required = 440000/100000 = 4.4 or 5

So, payback period = 5+3 = 8 years

So,

NPV of project 1 is positive and negative for project 2,So accept Project 1 and reject project 2

IRR of project 1 is more than cost of capital and less than cost of capital for project 2, So accept Project 1 and reject project 2

Payback period of project 1 is 11 years whereas that for project 2 is 8 years . Hence project 2 should be accepted according to this criteria

NPV and IRR give the same decision but payback period is giving a different decision (This is because life of both projects are different)  

NPV is the most appropriate decision making criteria as it is consistent with the shareholder's wealth maximisation criteria

There may be non-financial considerations like some projects may be compulsory from legal and statutory point of view, or from social point of view, these projects may have to be undertaken even with negative NPV