Question

Year	Proj Y	Proj Z
0	($2,500,000)	($2,500,000)
1	2,100,000	950,000
2	875,000	863,000
3	—	675,000
4	—	900,250

1. Compare both projects using NPV if the cost of capital is 10%.
2. Compare each project using the IRR approach.
3. Now compare both projects using the equivalent annual annuity (EAA) method.
4. Compare each project using the replication approach.

Answer 1

Using financial calculator to calculate Npv

Project Y

Inputs: C0 = -2,500,000

C1 = 2,100,000. Frequency= 1

C2 = 875,000. Frequency= 1

I = 10%

Npv = Compute

We get , Npv = $132,231.41

Project Z

Inputs: C0 = -2,500,000

C1 = 950,000. Frequency= 1

C2 = 863,000. Frequency= 1

C3 = 675,000. Frequency= 1

C4 = 900,250. Frequency= 1

I = 10%

Npv = compute

We get, Npv= $198,879.86

We choose Project Z , because the Npv is higher than that of project Y .

B) Using financial calculator to calculate Irr

Inputs: C0 = -2,500,000

C1 = 2,100,000. Frequency= 1

C2 = 875,000. Frequency= 1

Irr = compute

We get, IRR = 14.55%

Project Z

Inputs: C0 = -2,500,000

C1 = 950,000. Frequency= 1

C2 = 863,000. Frequency= 1

C3 = 675,000. Frequency= 1

C4 = 900,250 Frequency= 1

Irr = compute

We get, Irr = 13.72%

We choose Project Y, because it has higher irr than that of project Z

C) Project Y

EAA= r x Npv / 1- (1+r)^-n

= 10% × 132,231 / 1 - (1+ 0.1)^-2

= 13,223 / 1 - ( 1.1)^-2

= 13,223 / 1 - 0.8264

= 13,223 / 0.1736

= $76,190

Project Z

EAA = r × NPV / 1 - (1+r)^-4

= 10% × 198,879.86 / 1 - (1+0.1)^ - 4

= 19,888 / 1 - (1.1)^ -4

= 19,888 / 1 - 0.6830

= 19,888 / 0.3170

= $62,740.83

We choose Project Y , because it has higher annuity value.