Question

Larson Manufacturing is considering purchasing a new​ injection-molding machine for ​$210,000 to expand its production capacity. It will cost an additional ​$15,000 to do the site preparation. With the new​ injection-molding machine​ installed, Larson Manufacturing expects to increase its revenue by ​$100,000 per year. The machine will be used for four ​years, with an expected salvage value of ​$78,000. At an interest rate of 8​%, would the purchase of the​ injection-molding machine be​ justified?

The present worth of the project is ​$_______. ​ (Round to the nearest​ dollar.)

Would the purchase of the injection-molding machine be justified?

yes or no?

Answer 1

Present value of a cash flow after n years at interest rate r is given by:

$\small PV = \frac{FV}{(1+r)^n}$

Present worth of the project:

$\small = \frac{100000}{(1+0.08)^1}+\frac{100000}{(1+0.08)^2}+\frac{100000}{(1+0.08)^3}+\frac{100000}{(1+0.08)^4}+\frac{78000}{(1+0.08)^4}$

$\small = 92592.59+85733.88+79383.22+73502.99+57332.33 \approx 388545$

Present cost = 210000+15000 = 225000

Yes, the purchase of the​ injection-molding machine is​ justified.