Question

Consider a $20,000 investment with a 5 year life. The salvage

value is $4,000, and the minimal acceptable return is 8%. The

investment produces annual benefits of $10,000 at an operating

cost of $3,000. Suppose there is considerable uncertainty as to

whether the new machinery will survive 5 years of continuous

use.

Find the Break-Even Point, in terms of life(years), at which the

project just becomes economically viable.

Answer 1

20000 is the year 0 investment.

Year 1: incremental net benefit is 10000-3000=7000. The present value is 7000/(1+8%)^1=$6481.48

Year 2: incremental net benefit is 10000-3000=7000. The present value is 7000/(1+8%)^2=$6001.37

Year 3: incremental net benefit is 10000-3000=7000. The present value is 7000/(1+8%)^3=$5556.83

At end of year 3, cumulative cash inflows is $6481.48+$6001.37+$5556.83=$18039.68

Still the firm needs, 20000-18039.68=$1960.32

Year 4: incremental net benefit is 10000-3000=7000. The present value is 7000/(1+8%)^4=$5145.21

So, $1960.32/ $5145.21 = 0.38 of 4th year is required to breakeven.

Therefore total of 3+0.38=3.38 years required