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

A) Statement showing NPV

	Project A			Project B
Year	Cash Flow	PVIF @ 10%	PV	Cash Flow	PVIF @ 10%	PV
0	-8000	1.0000	-8000	-8000	1.0000	-8000
1	2000	0.9091	1818	4000	0.9091	3636
2	3000	0.8264	2479	2000	0.8264	1653
3	5000	0.7513	3757	2500	0.7513	1878
4	1000	0.6830	683	2000	0.6830	1366
NPV(Sum of PV)			737			534

Thus Project A should be selected

B)

i) Let us assume rate to be 8%

Statement showing NPV of project C

	Project C
Year	Cash Flow	PVIF @ 8%	PV
0	-8000	1.0000	-8000
1	2000	0.9259	1852
2	2500	0.8573	2143
3	2000	0.7938	1588
4	4000	0.7350	2940
NPV(Sum of PV)			523

Now, Let us assume rate to be 7%

	Project C
Year	Cash Flow	PVIF @ 7%	PV
0	-8000	1.0000	-8000
1	2000	0.9346	1869
2	2500	0.8734	2184
3	2000	0.8163	1633
4	4000	0.7629	3052
NPV(Sum of PV)			737

Now using interpolation method we can find rate

Rate	NPV
8%	523
7%	737
1% down	214
?	11

1*11/214

=0.0514

Thus rate = 8%- 0.0514%

=7.9485%

II) Project C, Since its has low cost of capital

III) Assuming Cash flow for Year 4 = 3826$

Project C
Year	Cash Flow	PVIF @ 10%	PV
0	-8000	1.0000	-8000
1	2000	0.9091	1818
2	2500	0.8264	2066
3	2000	0.7513	1503
4	3826	0.6830	2613
NPV(Sum of PV)			0

Thus cash flow above 3826$ is required

iv) Project B as sum of it's 3 year cash flow is 8500$ ( 4000+2000+2500)

C) Yes, IRR will be positive for project A , since there are conventional cash flows i.e No negative cash flow after initial period

D) 10% Rate used can be called minimum required rate of return. i.e if one wants to start project , he/she will have to raise funds. the cost of funds suppose is 10%, thus they want project which have atlease 10% return so that they can break even.