Question

Sentinel Company is considering an investment in technology to improve its operations. The investment will require an initial outlay of $257,000 and will yield the following expected cash flows. Management requires investments to have a payback period of 3 years, and it requires a 8% return on investments. (PV of $1, FV of $1, PVA of $1, and FVA of $1) (Use appropriate factor(s) from the table provided.)

Period	Cash Flow
1		$	48,700
2			52,100
3			76,600
4			95,600
5			125,800

Required:
1. Determine the payback period for this investment.
2. Determine the break-even time for this investment.
3. Determine the net present value for this investment.

Answer 1

Correct Answer:

Requirement 1: Payback period: = 3.83 years.

Working:

Payback period = year before full recovery + (unrecovered amount at the start to the period / cash flow during the next period.

Year	Net Cash Flow	Cumulative Cash Flow
0	$ (2,57,000.00)	$ (2,57,000.00)
1	$      48,700.00	$ (2,08,300.00)
2	$      52,100.00	$ (1,56,200.00)
3	$      76,600.00	$     (79,600.00)
4	$      95,600.00	$      16,000.00
5	$   1,25,800.00	$   1,41,800.00

Year before full recovery = 3 years

Unrecovered amount at the start of the next period = $ 79,600

Cash flow during the next period = $ 95,600

Payback period = 3 + (79600/95600)

= 3 + 0.832636

= 3.83 years

Requirement 2: break-even time for the investment (Discounted payback period) = 4.42 years

Break-even time for the investment (Discounted payback period) = year before full recovery + (unrecovered discounted amount at the start to the period / discounted cash flow during the next period.

Year	Net Cash Flow	discount rate @ 8%	Discounted cash flow	Cumulative Cash Flow
0	$ (2,57,000.00)	1	$     (2,57,000.00)	$   (2,57,000.00)
1	$      48,700.00	0.925925926	45,092.59	$   (2,11,907.41)
2	$      52,100.00	0.85733882	44,667.35	$   (1,67,240.05)
3	$      76,600.00	0.793832241	60,807.55	$   (1,06,432.51)
4	$      95,600.00	0.735029853	70,268.85	$      (36,163.65)
5	$   1,25,800.00	0.680583197	85,617.37	$       49,453.71

Break-even time for the investment = 4 +( 36163.65/85617.37)

= 4 + 0.42238687

= 4.42 years

Requirement 3: Net present value: $ 49,453.71

Net present value = total present value of all future cash inflows – cash outflow

Year	Net Cash Flow	discount rate @ 8%	Present value fo cash flow (outflow)
0	$ (2,57,000.00)	1	$     (2,57,000.00)
1	$      48,700.00	0.925925926	$           45,092.59
2	$      52,100.00	0.85733882	$           44,667.35
3	$      76,600.00	0.793832241	$           60,807.55
4	$      95,600.00	0.735029853	$           70,268.85
5	$   1,25,800.00	0.680583197	$           85,617.37
	Net Present value		$           49,453.71

End of answer.

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