Question

A company is analyzing two mutually exclusive projects, S and L, with the following cash flow:

0                     1                      2 3 4           

Project S       -$1,000              $870                $250               $25                  $25      

Project L       -$1,000              $0                    $250               $400                $845    

The company’s WACC is 8.5%. What is the IRR of the better project?(Hint: The better project may or may not be the one with the higher IRR.)

**SHOW WORK**

Answer 1

Present value of inflows=cash inflow*Present value of discounting factor(rate%,time period)

S:

Present value of inflows=870/1.085+250/1.085^2+25/1.085^3+25/1.085^4

=$1051.82

NPV=Present value of inflows-Present value of outflows

=$1051.82-$1000

=$51.82(Approx)

L:

Present value of inflows=250/1.085^2+400/1.085^3+845/1.085^4

=$1135.26

NPV=Present value of inflows-Present value of outflows

=$1135.26-$1000

=$135.26(Approx)

Hence L is better having higher NPV.

Hence

Let irr be x%
At irr,present value of inflows=present value of outflows.

1000=250/1.0x^2+400/1.0x^3+845/1.0x^4

Hence x=irr=12.70%(Approx).