Question

A recently hired chief executive officer wants to reduce future production costs to improve the company’s earnings, thereby increasing the value of the company’s stock. The plan is to invest $86,000 now and $56,000 in each of the next 4 years to improve productivity. By how much must annual costs decrease in years 5 through 14 to recover the investment plus a return of 10% per year?

The annual cost decreases by $ ?

Answer 1

PW of costs is given by

PW(C)=-86000-56000*(P/A,0.10.4)

Let us calculate the interest factor

PW(C)=-86000-56000*(P/A,0.10.4)=-86000-56000*3.169865=-$263,512.44

Let the annual cost saving from year 5 to 14 be x

Present worth of cost savings is given as

PW(B)=x*(P/F,0.10,4)*(P/A,0.10,10)

Let us calculate the interest factors

(P/F,0.10,4)=1/(1+0.10)^4=0.683013

So,

PW(B)=x*0.683013*6.144567

NPV of project should at least be equal to 0. So,

x*0.683013*6.144567-263512.44=0

x=263512.44/(0.683013*6.144567)=$62,788.61

Cost should at atleast decrease by $62788.61 per year for year 5 to year 14 to justify the project.