Question

Mary Inc. is considering mutually exclusive Projects A and B, whose cash flows are shown below. If the decision is made by choosing the project with the higher IRR, will there be any value loss due to the IRR-based decision? If there is a loss, how much value will be forgone? The WACC is assumed to be 9.5%.

WACC: Year	9.5%	0	1	2	3	4
CFA		−$2,020	$730	$730	$740	$740
CFB		−$4,100	$1,400	$1,500	$1,520	$1,530

Please do not use excel.

Answer 1

IRR is the internal rate of return(discount Rate) where the present values of the cash inflows & outflows of the project ,are exactly equal,ie. NPV of the cash flows=0

Formula for IRR=

CF(0)=(CF1/(1+r)^1)+(CF2/(1+r)^2)+(CF3/(1+r)^3)+(CF4/(1+r)^4)

So,

IRR(A)=

2020=(730/(1+r)^1)+(730/(1+r)^2)+(740/(1+r)^3)+(740/(1+r)^4)

Solving for r , in an online eqution solver,we get

IRR=16.85%

IRR(B)=

4100=(1400/(1+r)^1)+(1500/(1+r)^2)+(1520/(1+r)^3)+(1530/(1+r)^4)

IRR=16.49%

CF(A) has the highest IRR of 16.85%

IRR(A) 16.85%> IRR(B)16.49%

So, going by the IRR criterion,

Project (A) will be chosen

Now, if we discount the cash flows for its value/NPV at the WACC of 9.5%

NPV (A)=

-2020+(730/(1+0.095)^1)+(730/(1+0.095)^2)+(740/(1+0.095)^3)+(740/(1+0.095)^4)=

334

NPV (B)=

-4100+(1400/(1+0.095)^1)+(1500/(1+0.095)^2)+(1520/(1+0.095)^3)+(1530/(1+0.095)^4)=

651

So, going by the NPV criteria , decision is to SELECT

Project B for its greater NPV,

ie. NPV( B) 651 > NPV(A) 334

So, If we go by the IRR decision & select Project A,

Value forgone =651-334=

317