Question

Barney Googal owns a garage and is contemplating purchasing a tire retreading machine for $26,820. After estimating costs and revenues, Barney projects a net cash inflow from the retreading machine of $4,200 annually for 10 years. Barney hopes to earn a return of 8% on such investments

(For calculation purposes, use 5 decimal places as displayed in the factor table provided.)
What is the present value of the retreading operation? (Round answer to 2 decimal places, e.g. 25.25.)

Should Barney Googal purchase the retreading machine?

Answer 1

Present value of retreading operation = $28182

Should barney googal purchase the retreading machine? = YES.

solution :

Present value of retreading operation = present value cash inflows - present value of cash outflows.

Present value of cash inflows = annual cash inflows × present value of annuity factor at 8% for 10 years.

Present value of annuity factor at 8% for 10 years =

= [1-(1+r)^-n ]/r

Where, r = rate of interest = 0.08, n = number of years = 10.

= [1-(1+0.08)^-10 ]/0.08

= [1-1/(1.08)¹⁰ ]/0.08

= [1-1/(2.1589]/0.08

= [1-0.4632]/0.08

= 0.5368/0.08

= 6.71

Therefore,

Present value of cash inflows = $4200 × 6.71 = $28182

Present value of cash outflows (initial investment) = $26820

Present value of retreading operation (present value of cash inflows) = $28182.

As the net present value of retreading operation is $1362 ($28182 - $26820), barney googal should purchase the machine. The positive net present value indicates that the machine generates returns in excess of 8%, which is profitable to the company.