A planned factory expansion project has an estimated initial cost of $800,000.Using a discount rate of 20%,the present value of future cost savings from the expansion is $843,000.To yield exactly a 20% internal rate of return,the actual investment cost cannot exceed the $800,000 estimate by more than which of the following? (Ignore income taxes in this problem.)
A) $1,075.
B) $20,000.
C) $43,000.
D) $160,000.

Question

Quizplus · Accepted Answer

To calculate the internal rate of return (IRR), we need to set the initial cost equal to the present value of future cost savings and solve for the discount rate that makes the two values equal. 
$800,000 = $843,000/(1+IRR)^n 
Solving for IRR, we get 20%. 
To find the maximum additional investment cost that still yields a 20% IRR, we need to find the present value of the cost savings at a 20% discount rate that equals the additional investment cost. 
PV = Additional Investment Cost / (1+IRR)^n 
PV = X / (1.20)^n 
X = PV * (1.20)^n 
X = $843,000 - $800,000 * (1.20)^n 
We want to find X when n=0, or today. 
X = $843,000 - $800,000 * (1.20)^0 = $843,000 - $800,000 = $43,000 
So the actual investment cost cannot exceed the $800,000 estimate by more than $43,000. The correct answer is (C).

A Planned Factory Expansion Project Has an Estimated Initial Cost