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)?

Please answer all parts with clear steps. thanks so much

Answer 1

Part a) NPV of A is calculated below:

Year	CF	Discount Factor		Discounted CF
0	$ -8,000.00	1/(1+0.1)^0=	1	1*-8000=	$ -8,000.00
1	$   2,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*2000=	$    1,818.18
2	$   3,000.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*3000=	$    2,479.34
3	$   5,000.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*5000=	$    3,756.57
4	$   1,000.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*1000=	$        683.01
				NPV = Sum of all Discounted CF	$        737.11

NOV of B is below:

Year	CF	Discount Factor		Discounted CF
0	$ -8,000.00	1/(1+0.1)^0=	1	1*-8000=	$ -8,000.00
1	$   4,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*4000=	$    3,636.36
2	$   2,000.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*2000=	$    1,652.89
3	$   2,500.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*2500=	$    1,878.29
4	$   2,000.00	1/(1+0.1)^4=	0.683013455	0.683013455365071*2000=	$    1,366.03
				NPV = Sum of all Discounted CF	$        533.57

NPV of A is higher so it should be selected

Part b)

i) Basically Projects B and C have the same CFs only the timing is reversed, therefore both will have an equal NPV if the discount rate =0, for any other discount rate, the projects will have different NPVs because, if we calculate the payback period of both, we will get to know that under project B the initial investment is recovered sooner as it has higher CFs at the beginning.

ii) As explained above, even if the risk is same, the recovery is sooner in Project B so it is better to pick that.

iii) Using goal-seek, we need to determine the 4th CF which makes the NPV = 0 at 10% discount rate, so any CF greater than that, the project is worth accepting. The same has been done below:

Year	CF	Discount Factor		Discounted CF
0	$ -8,000.00	1/(1+0.1)^0=	1	1*-8000=	$ -8,000.00
1	$    2,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*2000=	$    1,818.18
2	$    2,500.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*2500=	$    2,066.12
3	$    2,000.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*2000=	$    1,502.63
4	$    3,825.80	1/(1+0.1)^4=	0.683013455	0.683013455365071*3825.8=	$    2,613.07
				NPV = Sum of all Discounted CF	$            0.00

Therefore the CF4 should be greater than  $3,825.80 for it to be acceptable

iv) Payback period is calculated below:

Project B:

Year	Opening Balance	Investment	CF	Closing Balance
0		$            8,000.00		$            8,000.00
1	$              8,000.00		$                      4,000.00	$            4,000.00
2	$              4,000.00		$                      2,000.00	$            2,000.00
3	$              2,000.00		$                      2,500.00	$              -500.00
4	$                -500.00		$                      2,000.00	$          -2,500.00

We see that the closing balance at the end of year 2 was 2000 and the CF for year 3 was 2500 so in 2000/2500 = 2.8 years the initial investment is recovered. If the cutoff is set at 3 years then project B is acceptable

Project C:

Year	Opening Balance	Investment	CF	Closing Balance
0		$            8,000.00		$            8,000.00
1	$              8,000.00		$                      2,000.00	$            6,000.00
2	$              6,000.00		$                      2,500.00	$            3,500.00
3	$              3,500.00		$                      2,000.00	$            1,500.00
4	$              1,500.00		$                      4,000.00	$          -2,500.00

We see that the closing balance at the end of year 3 was 1500 So the initial investment will be recovered in coming years if it is recovered at all so Project C doesn't meet the criteria of 3 years.

Part c) If we don't use any discounting, the sum of inflows > the outflow, therefore the IRR should be positive because it is the discount rate used to have a 0 NPV, that is the sum of all CFs, positive and negative can only be 0 if the discount rate > 0% and therefore the IRR will have to be > % or positive.

Part d) 10% is the required rate, or the discount rate for projects, which means that the project will have to have a minimum return of 10% because of the risks associated with it for the project to be worth it. Therefore, we use this return to discount the CFs and see if NPV is positive, if that is the case then our actual return is greater than 10% so we have met the criteria and have earned greater return than the risk. Or we can even say that the IRR is greater because that is the return which is used to reinvest the CFs