Question

A company is analyzing a pressing machine to acquire. The purchasing price of this machine is $300,000. This machine will be used towards pressing 1,000 products every 6 months, which each will be sold for $50. Its operating and maintenance cost will be $7000 in the first semi-annual and it increases by $500 every six months (semi-annual) after that till the end of its useful life, which year 7. The salvage value at the end of year 7 will be $20,000. If the interest rate is 7% per year, compounded quarterly, do you recommend the company to purchase this pressing machine? Provide your detailed calculations.

Answer 1

Formula used:

(P/F, i%,n) = (1 + i)^-n

(P/A, i%,n) = ((1 + i)^n-1)/(i(1 + i)^n)

(P/G, i%,n) = {((1 + i)^n-1)/((i^2)(1 + i)^n) - n/(i((1 + i)^n))}

I = 7% / 4 = 1.75% per quarter

Effective interest rate per semiannual period = (1 + 0.0175)^2 -1

= (1.0175)^2 -1

= 0.03530625 ~ 3.53%

t = 7*2 = 14 semiannual periods

NPW of machine = -300000 + (1000*50 - 7000)*(P/A,3.53%,14) - 500*(P/G,3.53%,14) + 20000*(P/F,3.53%,14)

= -300000 + (1000*50 - 7000)*(((1 + 0.0353)^14-1)/(0.0353*(1 + 0.0353)^14)) - 500*{((1 + 0.0353)^14-1)/((0.0353^2)(1 + 0.0353)^14) - 14/(0.0353 *((1 + 0.0353)^14))} + 20000*((1 + 0.0353)^-14)

= -300000 + 43000*(((1.0353)^14-1)/(0.0353*(1.0353)^14)) - 500*{((1.0353)^14-1)/((0.0353^2)(1.0353)^14) - 14/(0.0353 *((1.0353)^14))} + 20000*((1.0353)^-14)

= -300000 + 43000*10.898575 - 500*64.720998 + 20000*0.615280

= 148583.83

As NPW is positive, this machine should be purchased