Angular Contact
Economy problem I am having problems with?
Danson Iron Works, Inc. manufactures angular contact ball bearings for pumps that operate in harsh environments. If the company invested $2.4 million in a process that resulted in profits of $760,000 per year for 5 years, what rate of return did the company make on its investment?
We can do it with two different methods both resulting in the same result
The company has invested 2,400,000 at present and gained 760,000 per year for 5 years thus the cash flows are as follows
-2400000 760000 760000 760000 760000 760000
The required solution demands finding rate of return in this case the IRR which discounts each of the cash flows at time period t as follows
-2400000 +760000(1+i)^-1 +760000(1+i)^-2 +760000(1+i)^-3 +760000(1+i)^-4 +760000(1+i)^-5 = 0
Here we need to solve for i
The other approach to use is to think of the 2,400,000 as the present worth of an annuity that pays 760,000 for the next 5 years, and we need to find the rate
the equation to use is as follows
PV (1+i)^n + PMT [(1+i)^n -1]/i
here we need to solve for i
The problem with both approaches is the fact that the variable i is not separable from other variables thus we resort to using mathematical techniques such as the Newton Raphson method, or the secant method to find the exact value for i, for coursework in finance the teachers usually accept an approximate value for i that is calculated using linear interpolation method
I will present the answer to the problem using two online calculators
the first one is the IRR calculator that uses cash flows presented in earlier part of my reply http://thinkanddone.com/finance/online-irr-calculator.html and it reports a rate of 17.57%
the second one is the present value of annuity calculator that calculates one of the four values when you provide 3 of the others from payment amount in this case 760000 the number of periods in this case 5 and the present value of annuity in this case 2400000. This calculator here http://thinkanddone.com/finance/present-value-annuity-calculator.htm also reports a rate of 17.57%
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