Question

Kosovski Company is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and are not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the IRR will cause $0.00 value to be lost. WACC: 7.75% Year 0 1 2 3 4 CFS -$1,050 $675 $650 CFL -$1,050 $360 $360 $360 $360 I WANT ANSWER BUT NO USE EXCEL THANKS

Answer 1

Computation of IRR using Trial and Error method:

Project S:

Computation of NPV at discount rate of 17 %

Year	PV Factor Computation	PV Factor @ 17 % (F)	Cash Flow (CS)	PV (CS x F)
0	1/ (1+0.17) ^0	1	-$1,050	-$1,050
1	1/ (1+0.17) ^1	0.85470085470086	675	576.9230769
2	1/ (1+0.17) ^2	0.73051355102637	650	474.8338082
			NPV1	$1.7568851

As NPV is positive, let’s compute NPV at discount rate of 18 %.

Year	PV Factor Computation	PV Factor @ 18 % (F)	Cash Flow (CS)	PV (CS x F)
0	1/ (1+0.18) ^0	1	-$1,050	-$1,050
1	1/ (1+0.18) ^1	0.84745762711864	675	572.0338983
2	1/ (1+0.18) ^2	0.71818442976156	650	466.8198793
			NPV2	-$11.1462224

IRRS = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

= 17 % + [$ 1.7568851 x (18 % - 17%)/ ($ 1.7568851 – (-$ 11.1462224))]

= 17 % + [($ 1.7568851 x 1 %)/ ($ 1.7568851 + $ 11.1462224)]

= 17 % + ($ 0.017568851/ $ 12.9031075)

= 17 % + 0.0013615984

= 17 % + 0.14 % = 17.14 %

Project L:

Computation of NPV at discount rate of 13 %

Year	PV Factor Computation	PV Factor @ 13 % (F)	Cash Flow (CL)	PV (CL x F)
0	1/ (1+0.13) ^0	1	-$1,050	-$1,050
1	1/ (1+0.13) ^1	0.88495575221239	360	318.5840708
2	1/ (1+0.13) ^2	0.78314668337380	360	281.9328060
3	1/ (1+0.13) ^3	0.69305016227770	360	249.4980584
4	1/ (1+0.13) ^4	0.61331872767938	360	220.7947420
			NPV1	$20.8096772

As NPV is positive, let’s compute NPV at discount rate of 14 %.

Year	PV Factor Computation	PV Factor @ 14 % (F)	Cash Flow (CL)	PV (CL x F)
0	1/ (1+0.14) ^0	1	-$1,050	-$1,050
1	1/ (1+0.14) ^1	0.87719298245614	360	315.7894737
2	1/ (1+0.14) ^2	0.76946752847030	360	277.0083102
3	1/ (1+0.14) ^3	0.67497151620202	360	242.9897458
4	1/ (1+0.14) ^4	0.59208027737019	360	213.1488999
			NPV2	-$1.0635704

IRR L = R1 + [NPV1 x (R2 – R1)/ (NPV1 – NPV2)]

= 13 % + [$ 20.8096772 x (14 % - 13%)/ ($ 20.8096772 – (-$ 1.0635704))]

= 13 % + [($ 20.8096772 x 1 %)/ ($ 20.8096772 + $ 1.0635704)]

= 13 % + ($ 0.208096772/ $ 21.8732476)

= 13 % + 0.009513757

= 13 % + 0.95 % = 13.95 %

Project S is preferable based on IRR rule decision as it has higher IRR.

Computation of NPV of both projects:

Year	PV Factor Computation	PV Factor @ 7.75 % (F)	Cash Flow (CS)	PV S (CS x F)	Cash Flow (CL)	PV L (CL xF)
0	1/ (1+0.0775)0	1	-$1,050	-$1,050	-$1,050	-$1,050
1	1/ (1+0.0775)1	0.92807424593968	675	626.4501160	360	581.39221903
2	1/ (1+0.0775)2	0.86132180597650	650	559.8591739	360	482.21891474
3	1/ (1+0.0775)3	0.79937058559304	0	0	360	0
4	1/ (1+0.0775)4	0.74187525345061	0	0	360	0
			NPV S	$136.3092899	NPV L	$13.61113377

NPV of Project S is $136.31 and that of Project L is $13.61

Choosing project on the basis of IRR will cause no value to forgone, as the preferred project S has higher NPV. There is no conflicting result between NPV and IRR decision rule for the two mutually exclusive projects.