working out if an investment is economic. (question inside)

Quote:

Originally Posted by kelly_m

if an investment returned $1000 every year for the first 4 years and returned $1200 yearly after that for 5 years. which after the return becamse $2000 forever. The investment requires three instalments of the same size; immediately, in two years time and five years time. the interest rate is constant and 10%
What is the maximum size of instalments before the investment becomes uneconomic?

Can some one tell me what formulae to use for what part of this question as i am completely stumped. any help GREATLY APPRECIATED.

Let each installment be X, then present value of the installments:

$ A=X + 1.1^{-2}X + 1.1^{-5}X \approx 2.447~X $

Present value of the payments is:

$ B=1000 ( 1 + 1.1^{-1} + 1.1^{-2} + 1.1^{-3}) + 1200 \times 1.1^{-4} (1+1.1^{-1} + 1.1^{-2}+1.1^{-3}+1.1^{-4})$
................. $+ 2000 \times 1.1^{-9} (1 + 1.1^{-1} + 1.1^{-2} +...) $

... $= 1000 \frac{1-1.1^{-4}}{1-1.1^{-1}} + 1200\times 1.1^{-4} \frac{1-1.1^{-5}}{1-1.1^{-1}}+ 2000\times 1.1^{-9} \frac{1}{1-1.1^{-1}}\approx 16234.69 $

So the break even point is:

$ X \approx 16234.69/2.447 \approx 6634.53 $

RonL