CFA Level I Question

Multiply every term by (1 + r)2. You’ll get a quadratic equation for which you can use the quadratic formula.
 
I get 8.53266% using the CF worksheet. Nothing wrong with the quadratic formula, but if I treat this as cash outflows of -10 at time 0 and -100 at time 1 to get an accumulated value of $120.312, the IRR function saves oodles of time!!!
 
Step 1: Multiply by (1+r)2 (thats squared, I cannot write it properly on here, sorry) as proposed by S2000magician
Step 2: You now have 10r2 + 120r + 110 = 120.31 which can be written as 10(r2 + 12r + 11) = 10(12.03)
Step 3: Divide by 10 to get r2 + 12r + 11 = 12.03 We have a quadratic equation here. To solve algebraically, you need ot turn it to a true quadratic equation. We do it by adding 25 to both sides of the equation so equilibrium holds - r2 + 12r + 36 = 37.03
Step 4: Transform left side to (r+6)2 and apply a SQRT to both sides
r + 6 = 6.085
r = 0.085 or 8.5%
This is close to a IRR calculation which is done by trial and error, its just that Excel or the TI calculator are fast at it (and the TI calculator is annoyingly slow when you want to be fast with it). If you cannot convert to an equation that can be solved, you have to put some value for r and see where the equation goes. Then another and after some trial and error you`d get to the actual result, or very close to it.
 
Scanspeak wrote: Step 1: Multiply by (1+r)2 (thats squared, I cannot write it properly on here, sorry)
Click to expand...
Sure you can: we have superscripts in the ribbon, above.
(1+r)2
 
Scanspeak wrote:
Step 1: Multiply by (1+r)2 (thats squared, I cannot write it properly on here, sorry) as proposed by S2000magician
Step 2: You now have 10r2 + 120r + 110 = 120.31 which can be written as 10(r2 + 12r + 11) = 10(12.03)
Step 3: Divide by 10 to get r2 + 12r + 11 = 12.03 We have a quadratic equation here. To solve algebraically, you need ot turn it to a true quadratic equation. We do it by adding 25 to both sides of the equation so equilibrium holds - r2 + 12r + 36 = 37.03
Step 4: Transform left side to (r+6)2 and apply a SQRT to both sides
r + 6 = 6.085
r = 0.085 or 8.5%
This is close to a IRR calculation which is done by trial and error, its just that Excel or the TI calculator are fast at it (and the TI calculator is annoyingly slow when you want to be fast with it). If you cannot convert to an equation that can be solved, you have to put some value for r and see where the equation goes. Then another and after some trial and error you`d get to the actual result, or very close to it.
Click to expand...
Newton-Raphson or hacksaw!!!!
 
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