Sexton Inc. is considering Projects S and L, whose cash flows are shown below. T

Question

Sexton Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under certain conditions choosing projects on the basis of the IRR will not cause any value to be lost because the project with the higher IRR will also have the higher NPV, so no value will be lost if the IRR method is used.

WACC: 11.50%

Year 0 1 2 3 4

CFS -$2,050 $ 750 $ 760 $ 770 $ 780

CFL -$4,300 $1,500 $1,518 $1,536 $1,554

Explanation / Answer

Computation of NPV of CFS :-

Computation of IRR of CFS :-

IRR :- stands for internal rate of return, it is the rate of return hidden inside the project.

at IRR , NPV=0, it is bacause

at irr, PV of outflows = PV of inflows

let the IRR be x

then, PV of outflows = 2050

   PV of inflows = 750/(1+x) + 760/(1+x)2 + 770/(1+x)3 + 780/(1+x)4

hence at IRR

2050 = 750/(1+x) + 760/(1+x)2 + 770/(1+x)3 + 780/(1+x)4

guess approach will be applied to calculate x

let x = be 17% then , 750/(1.17) + 760/(1+1.17)2 + 770/(1.17)3 + 780/(1.17)4 = 2093.228

let x = 19% then, 750/(1.19) + 760/(1+1.19)2 + 770/(1.19)3 + 780/(1.19)4 = 2012.829

at 17% = inflow =2093.228

at 19% = inflow = 2012.829

at x% = infow= 2050

hence, using slope methid, 17-19/19-x = (2093.228-2012.829)/(2012.829-2050)

   -2/19-x = 80.399/ -37.171

-2/19-x = -2.16295

-2/-2.16295 = 19-x

0.9246= 19-x

x = 19-0.9246 =18.06 approx = IRR of CFS

     

Computation of NPV of CFL :-

at irr, PV of outflows = PV of inflows

let the IRR be x

then, PV of outflows = 4300

   PV of inflows = 1500/(1+x) + 1518/(1+x)2 + 1536/(1+x)3 + 1554/(1+x)4

hence at IRR

4300 = 1500/(1+x) + 1518/(1+x)2 + 1536/(1+x)3 + 1554/(1+x)4

guess approach will be applied to calculate x

using the above used method,we get x=15.58%=IRR of CFl

hence

NPVof cfs is lower than CFL

but IRR of CFS is higher than CFL

do if we choose project based on IRR than we will choose CFS

and the value we loose because of choosing CFS is value lost in NPV =294.09-379.81=85.72

Year CFS PV Factor@11.50% PV=CFS*PV Factor@11.50% 0 ($2,050) 1 -2050 1 750 1/(1.115)1=0.896860987 672.64574 2 760 1/(1.115)2=0.804359629 611.31332 3 770 1/(1.115)3=0.721398771 555.47705 4 780 1/(1.115)4=0.646994413 504.65564 NPV $ 294.09

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