Your company is deciding whether to invest in a new machine. the new machine will increase cash flow by $328,000 per year. you believe the technology used in the machine has a 10-year life; in other words, no matter when you purchase the machine, it will be obsolete 10 years from today. the machine is currently priced at $1,850,000. the cost of the machine will decline by $120,000 per year until it reaches $1,250,000, where it will remain.

The best profit will be if the machine is purchased today (t=0). This will yield a 2,630,000 profit

Explanation:

we need to construct a formula for profit:

revenue: 328,000 x (10 - t )

being t the year of purchase, more we delay the purchase, less revenue we generate.

the machine will decrease during 5 year at 120,000 per year:

cost:   1,250,000 - 120,000 (5 -t)

Now, we can construct profit formula and check at which point is better:

proft:             revenues - cost

Profit: 328,000 x (10-t) - (1,250,000 - 120,000(5-t))

Proft: 328,000 x 10 - 328,000t - (1,250,000 - 120,000x5 - 120,000t=

Profit: 3,280,000 - 328,000t - 1,250,000 + 600,000 + 120,000t

Profit: 2,630,000 -208,000t

As the time increase, our profit will decrease as the formula show that time is having a negative effect on profit.

The company should invest in the new machine.

Explanation:

We use spreadsheets to get the present value of this investment

See document attached.

We use a cash flow to solve this problem.

At moment 0 we have the investment cost , in this case $1,850,000. From period 1 to period 10, we have incomes o benefits of $328,000.

We add the residual cost at the end of the project.  

Then, we calculate the Net cash flow that is the difference between benefits and cost.

We use all the result (positive and negative) in Net cash flow to get the present value.  

Net Present Value (NPV)2680000

Internal Rate of Return (IRR)16,23%

Present value is positive , so the company should invest in the new machine.