Question

You are a manager in hospital and need to make a decision of 2 choice investment. Both are X-ray Machine and Biopsy, both cost $750.000, and both estimated lifetime 5 years. Net Cash Inflow as below:

Year	X-Ray	Biopsy
1	375.000	75.000
2	150.000	75.000
3	300.000	525.000
4	150.000	600.000
5	75.000	675.000

You need to:

1. Calculated the NPV from each investment with rate 12%

2. Calculated payback period from each investment. The hospital only accepted having payback period in 3 years maximum.

3. Is 3 years payback period is rational ? Explain..

Answer 1

Solution: (1)

Year	X-Ray Net Cash Inflow	Biopsy Net Cash Inflow	Discount Factor @ 12 %	X-Ray Present Value of Net Cash Inflow	Biopsy Present Value of Net Cash Inflow
1	$ 375.000	$ 75.000	0.893	$ 334,875	$ 66,975
2	150.000	75.000	0.797	119,550	59,775
3	300.000	525.000	0.712	213,600	373,800
4	150.000	600.000	0.636	95,400	381,600
5	75.000	675.000	0.567	42,525	382,725
Total				805,950	1,264,875
NPV= Present Value of Cash inflows – Initial Investment				=$ 805,950- $750.000	= $ 1,264,875-$750.000
NPV (Answer)				$ 55,950	$ 514,875
Decision				Rejected	Selected
Reason					NPV is greater than X Ray.

Solution: (2)

Year	X-Ray Net Cash Inflow	Biopsy Net Cash Inflow	X-Ray Cumulative Net Cash Inflow	Biopsy Cumulative Net Cash Inflow
1	$ 375.000	$ 75.000	$ 375.000	$ 75.000
2	150.000	75.000	525,000	150,000
3	300.000	525.000	825,000	675,000
4	150.000	600.000	975,000	1,650,000
5	75.000	675.000	1,050,000	2,325,000
Payback period			2.75 Years	3.125 Years
Decision			Selected	Rejected
Reason			As the maximum payback period considered in hospital is 3 years.

Payback period

= A+ B/C

Where, A = Year corresponding to the cumulative amount nearest to initial cost

B= Difference between cumulative amount nearest to initial cost and initial cost

C= Net cash flow of year next to Year corresponding to the cumulative amount nearest to initial cost

X-Ray Payback period

= 2 + ($ 750,000 - $ 525,000) / $ 300,000

= 2 + $ 225,000 / $ 300,000

= 2 + 0.75

= 2.75 years (Answer)

Biopsy Payback period

= 3 + ($ 750,000 - $ 675,000) / $ 600,000

= 3 + $ 75,000 / $ 600,000

= 3 + 0.125

= 3.125 Years (Answer)

Answer (3):

No, 3 years payback period is not rational here in the given case, as both the projects do have constant cash inflows. Also in Biopsy cash inflows in later years are higher than initial ones. So, deciding payback period only on the basis of cash inflows in initial years is not a rational decision.