Question

Here are the expected net cash flow estimates (in thousands of dollars):

Year	Project L	Project S
0	($100)	($100)
1	20	80
2	80	60
3	90	30

Depreciation, salvage values, net working capital requirements, and tax effects are all included in these cash flows.

The company's chief financial officer made subjective risk assessments of each project and concluded that both projects have risk characteristics similar those of the firm as a whole. Unilate's required rate of return is 6 percent. You must now determine whether one or both of the projects should go forward.

1. Find the payback periods for Project L and Project S.

2. What is each project's NPV and IRR?  

3. Which project would you select and why?

4. What if project S was riskier than project L and had a required return of 10%. Which project would you select now and why?

Answer 1

Payback period for project L:

Year	Opening Balance	Investment	CF	Closing Balance
0		$               100.00		$               100.00
1	$                  100.00		$                            20.00	$                  80.00
2	$                    80.00		$                            80.00	$                         -

• Closing balance = Opening balance +Investment - CF
• Opening balance = previous year's closing balance
• Closing balance in year 1 was 80 and Cf in year 2 was 80 so the payback period is 2 years
• According to this method, project S is better

Payback period for project K:

Year	Opening Balance	Investment	CF	Closing Balance
0		$               100.00		$               100.00
1	$                  100.00		$                            80.00	$                  20.00
2	$                    20.00		$                            60.00	$                -40.00

Closing balance in year 1 was 20 and CF in year 2 was 60 so sometime during the year, entire investment was recovered. The proportion of the year = 20/60 = 1/3 or 4 months. So the payback period is 1 year 4 months

NPV of the two projects is calculated below:

Year	CF	Discount Factor		Discounted CF
0	$ -100.00	1/(1+0.06)^0=	1	1*-100=	$ -100.00
1	$     20.00	1/(1+0.06)^1=	0.943396226	0.943396226415094*20=	$     18.87
2	$     80.00	1/(1+0.06)^2=	0.88999644	0.88999644001424*80=	$     71.20
3	$     90.00	1/(1+0.06)^3=	0.839619283	0.839619283032302*90=	$     75.57
				NPV = Sum of all Discounted CF	$     65.63

Year	CF	Discount Factor		Discounted CF
0	$ -100.00	1/(1+0.06)^0=	1	1*-100=	-100.00
1	$     80.00	1/(1+0.06)^1=	0.943396226	0.943396226415094*80=	75.47
2	$     60.00	1/(1+0.06)^2=	0.88999644	0.88999644001424*60=	53.40
3	$     30.00	1/(1+0.06)^3=	0.839619283	0.839619283032302*30=	25.19
				NPV = Sum of all Discounted CF	54.06

According to this method, project L is better as it has a higher NPV

IRR is the rate at which the NPV = 0 and can be calculated using a financial calculator or excel

Project L IRR comes to 32.12% rounded to 2 decimal places

Year	CF	Discount Factor		Discounted CF
0	$ -100.00	1/(1+0.321155807484115)^0=	1	1*-100=	$ -100.00
1	$     20.00	1/(1+0.321155807484115)^1=	0.756912996	0.756912995677857*20=	$     15.14
2	$     80.00	1/(1+0.321155807484115)^2=	0.572917283	0.572917283026028*80=	$     45.83
3	$     90.00	1/(1+0.321155807484115)^3=	0.433648537	0.43364853697085*90=	$     39.03
				NPV = Sum of all Discounted CF	$        0.00

Project S has an IRR of 38.80%

Year	CF	Discount Factor		Discounted CF
0	$ -100.00	1/(1+0.387997201618571)^0=	1	1*-100=	-100.00
1	$     80.00	1/(1+0.387997201618571)^1=	0.720462548	0.720462547643382*80=	57.64
2	$     60.00	1/(1+0.387997201618571)^2=	0.519066283	0.519066282556792*60=	31.14
3	$     30.00	1/(1+0.387997201618571)^3=	0.373967816	0.373967816326646*30=	11.22
				NPV = Sum of all Discounted CF	0.00

Project S with higher IRR should be chosen

When different approaches give different selection then we always go with the NPV decision rule which says we should select project L

d) We actually dont need to calculate the NPV as at 6% only the NPV of S was lower so at 10% it will be even lower and we will still go with project L but to verify, we have calculated the NPV as follows:

Year	CF	Discount Factor		Discounted CF
0	$ -100.00	1/(1+0.1)^0=	1	1*-100=	-100.00
1	$     80.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*80=	72.73
2	$     60.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*60=	49.59
3	$     30.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*30=	22.54
				NPV = Sum of all Discounted CF	44.85

As it is lower than that of project L so project L should be selected