Mutually Exclusive Projects

EXERCISE 01

Project	Year 0	Year 1	Year 2	Year 3
A	-1000	400	600	800
B	-1500	500	700	1000

The required return is 10%.

A.Calculate the NPVs and select the project.

A.

Discount each future cash flow at 10% for its own maturity. The initial investment at time 0 is not discounted.

NPV_A=-1{,}000+\frac{400}{1.10}+\frac{600}{1.10^2}+\frac{800}{1.10^3}=460.56

NPV_B=-1{,}500+\frac{500}{1.10}+\frac{700}{1.10^2}+\frac{1{,}000}{1.10^3}=284.37

Choose A: it has the higher NPV.

Both NPVs are positive. Because the projects are mutually exclusive, select the one that creates more value.

Mutually Exclusive Projects

EXERCISE 02

Project A requires €10,000 now and pays €20,000 in one year. Project B requires €20,000 now and pays €35,000 in one year. The projects are mutually exclusive, have the same risk and face a 10% discount rate; financing is available.

A.Rank the projects by IRR and by NPV.
B.Which project should be selected?

A.

NPV_A=-10{,}000+\frac{20{,}000}{1.10}\approx8{,}181.82

NPV_B=-20{,}000+\frac{35{,}000}{1.10}\approx11{,}818.18

IRR_A=20{,}000/10{,}000-1=100\%

IRR_B=35{,}000/20{,}000-1=75\%

Project	IRR	NPV (€)
A	100%	8,181.82
B	75%	11,818.18

IRR=\frac{CF_1}{I_0}-1

B.

\Delta NPV=-10{,}000+\frac{15{,}000}{1.10}\approx3{,}636.36

IRR_{B-A}=15{,}000/10{,}000-1=50\%

Choose B: it creates more value in euros despite the lower percentage return. The incremental investment B − A costs €10,000 and returns €15,000; its 50% IRR exceeds the 10% hurdle rate.

Project A; Project B — NPV (€) against Discount rate (%)

Mutually Exclusive Projects

EXERCISE 03

Alfa requires €50,000 today and returns €60,000 next year. B requires €10,000 and returns €15,000 next year. The required return is 10%.

A.Rank the projects by NPV and IRR.

A.

NPV_A=-50{,}000+\frac{60{,}000}{1.10}\approx4{,}545.45

NPV_B=-10{,}000+\frac{15{,}000}{1.10}\approx3{,}636.36

IRR_A=60{,}000/50{,}000-1=20\%

IRR_B=15{,}000/10{,}000-1=50\%

Project	NPV	IRR
Alfa	4,545.45	20%
B	3,636.36	50%

For mutually exclusive projects without capital rationing, choose Alfa: it adds more value. B has the greater percentage return.

Mutually Exclusive Projects

EXERCISE 04

Alfa and Beta are mutually exclusive, have equal lives and comparable risk. Alfa costs €20 and Beta €200. Assume funding is available.

Project	NPV	PI	IRR
Alfa	16	1.80	41.04%
Beta	52	1.26	22.11%

A.Choose the project and explain the ranking.

A.

\Delta NPV=NPV_B-NPV_A

\Delta NPV=52-16

Choose Beta: €36 more value.

The higher PI and IRR of Alfa do not override the greater absolute NPV when projects are mutually exclusive and capital is not rationed.

Mutually Exclusive Projects

EXERCISE 05

A.If equal-life project A has a larger NPV than B, must A always be selected?

A.

Choose the higher positive NPV when the projects are mutually exclusive, risks are valued appropriately and financing is available. For independent projects, both may be accepted if both have positive NPV. With capital rationing or different constraints, the optimal combination can differ. If both NPVs are negative and neither is mandatory, reject both.