Question

To recover your investment and earn a MARR of 10% per year, how long will you have to own a business that costs $230,000 to setup, generates $50,000 per year in income and has $15,000 per year in expenses ?

Answer 1

We have to calculate t such that Present value of the entire cash flow is 0 with MARR = 10% = 0.10

Present value of periodic payment is given by :

PV = (P/r)(1 - 1/(1 + r)n)

where PV = Present value, Periodic value = 50,000 - 15,000 = 35000(Note that cost incorred are consider as negative and benefits or income are consider as negative), r = interest rate or MARR = 10% = 0.10, n = time period that we have to calculate.

So, PV = (35000/0.10)(1 - 1/(1 + 0.10)n)

Also note that present value of initial amount is same as initial amount and as they have incrred cost at time 0 and hence will be consider as negative(So, present value of initial cost is -230,000.

So, Net Present value(NPV) = 0 => NPV = -230,000 + (35000/0.10)(1 - 1/(1 + 0.10)n) = 0

=> 1 - 1/(1 + 0.10)n = 23000/35000

=> 1/(1 + 0.10)n = 1 - 23000/35000

=> 1/(1 + 0.10)n = 12//35

=> (1 + 0.10)n = 35/12

Taking log on both sides and using ln(ab) = b*ln(a)

n*ln(1.1) = ln(35/12)

=> n = 11.23

Hence, Total time that will be required is 11.23 years.