Question

Suppose your firm would like to earn 10% yearly return from the following two investment projects of equal risk.

                               

Year (t)	Cash flows from Project A (Ct)	Cash flows from Project B (Ct)
0	–$8,000	–$8,000
1	$2,000	$4,000
2	$3,000	$2,000
3	$5,000	$2,500
4	$1,000	$2,000

(a)       If only one project can be accepted, based on the NPV method which one should it be?  Support your answer with calculations.

(b)       Suppose there is another four-year project (Project C) and its cash flows are as follows:

               

C₀ = –$8,000

             C₁ =   $2,000

               C₂ =   $2,500

               C₃ =   $2,000

               C₄ =   $4,000

(i)      Given the above cash flow patterns, at what required rate of return will Project C have the same NPV as Project B?  Briefly explain your answer.

(ii)     If Project C has the same risk as Project B, without calculations, explain which project will you pick?   

(iii)   If cash flow C₄ of Project C is unknown to you (while C₀ – C₃ are known and as above) and the project’s cost of capital is 10%, what amount of C₄ will make Project C worth accepting?

(iv)    If your firm’s investment policy (based on payback method) is such that it only accepts projects whose initial investment can be recouped within three years, will Project B and/or Project C be accepted?   

(c)       Based on the estimated cash flows of Project A, will you expect its internal rate of return (IRR) to be positive?  Briefly explain your answer WITHOUT calculations.

(d)       What kind of rate of return is the 10% interest stated in the question for Projects A and B?  How can it be used in making investment decisions (i.e. its role in investment decision making)?

Answer 1

NPV is given by:

For Project A

NPV = [ 2000 / (1 + 10%)^1] + [ 3000 / (1 + 10%)^2] + [ 5000 / (1 + 10%)^3] + [ 1000 / (1 + 10%)^4] - Initial Investment

NPV = 1818.18 + 2479.34 + 3756.57 + 683.01 - 8000

NPV = $ 737.11

For Project B

NPV = [ 4000 / (1 + 10%)^1] + [ 2000 / (1 + 10%)^2] + [ 2500 / (1 + 10%)^3] + [ 2000 / (1 + 10%)^4] - Initial Investment

NPV = 3636.36 + 1652.89 + 1878.29 + 1366.03 - 8000

NPV = $ 533.57

Since, NPV of Project A > NPV of project B, we should choose Project B

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Answer b)

Answer i)

NPV project C = NPV Project B = $ 533.37

So,

NPV = 533.37 = [ 2000 / (1 + r%)^1] + [ 2500 / (1 + r%)^2] + [ 2000 / (1 + r%)^3] + [ 4000 / (1 + r%)^4] - Initial Investment

533.37 = [ 2000 / (1 + r%)^1] + [ 2500 / (1 + r%)^2] + [ 2000 / (1 + r%)^3] + [ 4000 / (1 + r%)^4] - 8000

8533.37 = [ 2000 / (1 + r%)^1] + [ 2500 / (1 + r%)^2] + [ 2000 / (1 + r%)^3] + [ 4000 / (1 + r%)^4]

Solving for r,

r = 7.95%

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Answer ii) We should choose Project B. It has same NPV at a higher discount rate. If we will decrease the discount rate for Project B, then its NPV will increase. Hence, Project B is better than Project C.

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Answer iii)

For project to accepted, NPV >=0

Hence, for minimum C4, NPV = 0

NPV = 0 = [ 2000 / (1 + 10%)^1] + [ 2500 / (1 + 10%)^2] + [ 2000 / (1 + 10%)^3] + [ C4 / (1 + 10%)^4] - Initial Investment

0 = [ 2000 / (1 + 10%)^1] + [ 2500 / (1 + 10%)^2] + [ 2000 / (1 + 10%)^3] + [ C4 / (1 + 10%)^4] - 8000

8000 = [ 2000 / (1 + 10%)^1] + [ 2500 / (1 + 10%)^2] + [ 2000 / (1 + 10%)^3] + [ C4 / (1 + 10%)^4]

8000 = 1818.18 + 2066.12 + 1502.63 + [ C4 / (1 + 10%)^4]

Solving for C4,

C4 = $ 3825.80

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Answer iv)

For payback period,

For Project B

Year 1 + Year 2 = 4000 + 2000 = $ 6000

Initial investment = $ 8000

Money left to earn = $ 8000 - 6000 = $ 2000

Now, Year 3 = $2500. Hence, we will earn $ 2000 within year 3 and total payback period for Project B < 3 years. Hence, Project B will be accepted.

For Project C

Year 1 + Year 2 = 2000 + 2500 = $ 4500

Initial investment = $ 8000

Money left to earn = $ 8000 - 4500= $ 3500

Now, Year 3 = $2000

Hence, payback period for Project C > 3 years. Hence, it will not be accepted