Question

Wizard Inc. has to choose between two mutually exclusive projects. If it chooses project A, Wizard Inc. will have the opportunity to make a similar investment in three years. However, if it chooses project B, it will not have the opportunity to make a second investment. The following table lists the cash flows for these projects. If the firm uses the replacement chain (common life) approach, what will be the difference between the net present value (NPV) of project A and project B, assuming that both projects have a weighted average cost of capital of 14%?

	Cash Flow
Project A
Year 0:	–$12,500	Year 0:	–$40,000
Year 1:	8,000	Year 1:	8,000
Year 2:	14,000	Year 2:	15,000
Year 3:	13,000	Year 3:	14,000
		Year 4:	13,000
		Year 5:	12,000
		Year 6:	11,000

A.) $14,947

B.) $13,286

C.) $10,795

D.) $16,608

E.) $9,965

Wizard Inc. is considering a four-year project that has a weighted average cost of capital of 11% and a NPV of $75,682. Wizard Inc. can replicate this project indefinitely. What is the equivalent annual annuity (EAA) for this project?

A.) $24,394

B.) $26,833

C.) $29,273

D.) $21,955

E.) $20,735

Answer 1

Given the following,

Years	Project A	Projec B
0	-12500	-40000
1	8000	8000
2	14000	15000
3	13000	14000
4		13000
5		12000
6		11000

For Project A in year 3, Cash flow = 13000-12500 = 500 (since 12500 invested once again for replacement chain involves cash outflows)

Now the values of project A and project B are as follows,

Years	Project A	Projec B
0	-12500	-40000
1	8000	8000
2	14000	15000
3	500	14000
4	8000	13000
5	14000	12000
6	13000	11000

and

WACC = 14% = 0.04

Calculating NPV for project A and project B,

For project A:

NPV for A = CF0/(1+r)^0 + CF1/(1+r)^1 +CF2/(1+r)^2 +CF3/(1+r)^3+CF4/(1+r)^4 + CF5/(1+r)^5 + CF6/(1+r)^6

CF0/(1+r)^0 = -12,500

CF1/(1+r)^1 = 8000/(1+0.14) = 8000*(1/1.14) = 8000*0.8772 = 7017.54

CF2/(1+r)^2 = 14000/(1+0.14)^2 = 14000/ (1.14)^2 = 14000*0.7695 = 10772.55

CF3/(1+r)^3 = 500/(1+0.14)^3 = 500/ (1.14)^3 = 500*0.6750 = 337.4858

CF4/(1+r)^4 = 8000/(1+0.14)^4 = 8000/ (1.14)^4 = 14000*0.5921 = 4736.642

CF5/(1+r)^5 = 14000/(1+0.14)^5 = 14000/ (1.14)^5 = 14000*0.5194 = 7271.161

CF6/(1+r)^6 = 13000/(1+0.14)^6 = 13000/ (1.14)^6 = 14000*0.4556 = 5922.625

NPV = -12500 + 7017.54 + 10772.55 + 337.4858 + 4736.642 + 7271.161 + 5922.625

NPV = 23558

Therefore, NPV for project A = 23558

For project B:

NPV for B = CF0/(1+r)^0 + CF1/(1+r)^1 +CF2/(1+r)^2 +CF3/(1+r)^3 + CF4/(1+r)^4 + CF5/(1+r)^5 + CF6/(1+r)^6

CF0/(1+r)^0 = -40000

CF1/(1+r)^1 = 8000/(1+0.14) = 8000*(1/1.14) = 8000*0.8772 = 7017.54

CF2/(1+r)^2 = 15000/(1+0.14)^2 = 15000/ (1.14)^2 = 15000*0.7695 = 11542.01

CF3/(1+r)^3 = 14000/(1+0.14)^3 = 14000/ (1.14)^3 = 14000*0.6750 = 9449.601

CF4/(1+r)^4 = 13000/(1+0.14)^4 = 13000/ (1.14)^4 = 13000*0.5921 = 7697.044

CF5/(1+r)^5 = 12000/(1+0.14)^5 = 12000/ (1.14)^5 = 12000*0.5194 = 6232.424

CF6/(1+r)^6 = 11000/(1+0.14)^6 = 11000/ (1.14)^6 = 11000*0.4556 = 5011.452

NPV = -40000 + 7017.54 + 11542.01 + 9449.601 + 7697.044 + 6232.424 + 5011.452

NPV = 6950.078

Therefore, NPV for project B = 6950.078

Difference between NPV's of both projects = 23558 - 6950 = 16608

Thus, the difference between NPV of A and B is D) $16,608

b) Equivalent annual annuity(EAA) is given by the following formula,

EAA = NPV/ (1-(1/(1+r)^n)/r)

where

NPV = $75682

r = 11% = 0.11

n = number of periods = 4

Substituting these we get,

EAA = 75682/ (1-(1/(1+0.11)^4)/0.11)

= 75682/ (1-(1/1.11)^4)/0.11

= 75682/ (1-(0.9009)^4)/0.11

= 75682/ (1-0.6587)/0.11

= 75682/ (0.3413)/0.11

= 75682/ 3.1024

= 24394.30

Therefore EAA for this project is A) $24394