Dr. Ramirez runs a busy OB-Gyne practice. An updated ultrasound machine would ge

Question

Dr. Ramirez runs a busy OB-Gyne practice. An updated ultrasound machine would generate new revenues of $12,000 per year. Because of rapidly changing technology, she estimates that she will need to replace the machine at the end of 3 years, and the scrap or trade in value will be $1,000 at that time. To break even, what is the highest amount Dr. R should pay for another ultrasound, to the nearest $100? She will be giving up 3% annual earnings on the cash that she would use to pay for the machine.

Explanation / Answer

Annual cash inflows = $12000

Salvage value after 3 years = $1000

Time (n)= 3 years

Discount rate (R) = 3%

Now,

Present value of cash inflows = 12000*(1-1/(1+R)^n)/R + 1000/(1+R)^n

Present value of cash inflows = 12000*(1-1/1.03^3)/.03 + 1000/1.03^3

Present value of cash inflows = $34858.48 or $34900 approx. (to the nearest $100)

Thus, she will pay $34900 for the machine to achieve break even.

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