Question

Markman & Sons is considering Projects S and L. These projects are mutually exclusive, equally risky, and not repeatable and their cash flows are shown below. 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, i.e., no conflict will exist.
NO EXCEL

r:	10.00%
Year	0	1	2	3	4
CFS	?$1,025	$650	$450	$250	$50
CFL	?$1,025	$100	$300	$500	$700

Answer 1

For project S , NPV = 650/1.1+450/1.1^2+250/1.1^3+50/1.1^4 - 1025/1.1^0 = 159.79;

For project L, NPV = 100/1.1+300/1.21+500/1.331+700/1.4641-1025/1.1^0 = 167.61

Now let us calculate the Intermal Rate of Return (IRR) of project L. IRR = R1 + NPV1(R2-R1)/NPV1-NPV2

Let R1 =6% , R2 = 14%; NPV1 = 100/1.06 + 300/1.1236+500/1.191016+700/1.26247696 - 1025 = 286.34.

Hence NPV1=286.34 ; NPV2 = 100/1.14+300/1.2996+500/1.481544+700/1.68896016 -1025 = 45.51

Hence NPV2 = 45.51 Hence, IRR = 0.06+ 286.34*(0.14-0.06)/286.34-45.51 = 15.51%

Therefore, IRR for project L = 15.51%.

Let us now consider project S; Here NPV1 = 650/1.06 + 450/1.1236+250/1.191016+50/1.26247696 - 1025

= 613.21+400.5+209.9+39.6-1025= 238.21 = NPV1 ; NPV2 = 650/1.14+450/1.2996+250/1.481544+50/1.68896016 -1025 = 570.18+346.26+168.74+29.6-1025=89.78=NPV2 ; IRR of project S = 0.06 + 238.21(0.08)/148.43 = 18.84%

Hence PROJECT S has higher IRR OF 18.84% . At IRR rate NPV = 0. AT 10% rate of return NPV of project was = 159.79. Therefore 159.79 value will be foregone if project with higher IRR is considered.