Question

1. A company considers the following investment projects. Both projects involve the purchase of machinery with a life span of five (5) years.

• Project A would generate annual cash flows of $150,000; the machinery would cost $350,000 and have a scrap value of $45,000.
• Project B would generate annual cash flows of $250,000; the machinery would cost $800,000 and would have a scrap value of $350,000.

The company’s discount rate is 12%. Assume that the annual cash flows arise on the anniversaries of the date of purchase.

Calculate the net present value and payback for each project and state which project the company should accept and why.

Answer 1

NPV for both the projects is calculated as follows:

Project A
Year	FCF	Discount rate factor	Discount rate	DCF
0	-350000	1/1.12^0	1	-350000
1	150000	1/1.12^1	0.892857143	133928.5714
2	150000	1/1.12^2	0.797193878	119579.0816
3	150000	1/1.12^3	0.711780248	106767.0372
4	150000	1/1.12^4	0.635518078	95327.71176
5	150000	1/1.12^5	0.567426856	85114.02836
			NPV	190716.4304

Project B
Year	FCF	Discount rate factor	Discount rate	DCF
0	-800000	1/1.12^0	1	-800000
1	250000	1/1.12^1	0.892857143	223214.2857
2	250000	1/1.12^2	0.797193878	199298.4694
3	250000	1/1.12^3	0.711780248	177945.062
4	250000	1/1.12^4	0.635518078	158879.5196
5	250000	1/1.12^5	0.567426856	141856.7139
			NPV	101194.0506

According to NPV rule, the project with highest positive NPV should be selected. So project A should be selected.

Payback period calculation is as follows:

• Project A:
  • Cost = 350000
  • Annual CF = 150000
  • 
  • 
  • So payback period for project A = 2.33 years as it is assumed that the CF is earned uniformly throughout the year
• Project B:
  • Cost = 800000
  • Annual CF = 250000
  • 
  • 
  • So payback period for project B = 3.2 years as it is assumed that the CF is earned uniformly throughout the year
• As the payback period of project A is lower than that of project B, therefore it should be selected.