Question

Ranking Investment Proposals: Payback Period, Accounting Rate of Return, and Net Present Value
Presented is information pertaining to the cash flows of three mutually exclusive investment proposals:

	Proposal X	Proposal Y	Proposal Z
Initial investment	$98,000	$98,000	$98,000
Cash flow from operations
Year 1	90,000	49,000	98,000
Year 2	8,000	49,000
Year 3	49,000	49,000
Disinvestment	0	0	0
Life (years)	3 years	3 years	1 year

(a) Select the best investment proposal using the payback period, the accounting rate of return on initial investment, and the net present value criteria. Assume that the organization's cost of capital is 10 percent.

• Round accounting rate of return four decimal places.

• Round net present value to the nearest whole number.

• Use negative signs with your answers, when appropriate.

	Proposal X	Proposal Y	Proposal Z	Best proposal
Payback period (years)	Answer	Answer	Answer	AnswerXYZX,YX,ZY,Z
Accounting rate of return	Answer	Answer	Answer	AnswerXYZX,YX,ZY,Z
Net present value	Answer	Answer	Answer	AnswerXYZX,YX,ZY,Z

(b) Factors explaining the differences in rankings include all of the following except:

Net present value considers the timing of cash flows while payback considers only total cash flows.

The net present value method considers the cost of capital while the payback method does not discount future cash flows.

The accounting rate of return considers profitability while payback only considers the time required to recover the investment.

While the accounting rate of return explicitly considers the cost of the asset as part of annual depreciation the net present value method considers the cost of the asset as part of the initial investment.

** JUST NEED THE ACCOUNTING RATE OF RETURN - IT IS NOT 50%

Answer 1

1)

Proposal X

Net Present value = PV of Cash Inflow - PV of Cash outflow

= 90000*PVF(10%, n year) + 8000*PVF(10%, n year)+ 49000*PVF(10%, nyear) - 98000

= 90000*.909+8000*.826+49000*.751 - 98000

= $27217

Payback Period

= 1+ (8000 /8000)

= 2 years

Accounting rate of return = Average Income / Average Investment

Average Income = (90000+8000+49000)/3 = 49000

ARR = 49000/ 98000

= 50%

Proposal Y

Net Present value = PV of Cash Inflow - PV of Cash outflow

= 49000*.909+49000*.826+49000*.751 - 98000

= $ 23814

Payback Period = Initial Investment / Cash inflow per period

= 98000/ 49000 = 2 years

Accounting rate of return = Average Income / Average Investment

Average Income = (49000+49000+49000)/3 = 49000

ARR = 49000/ 98000

= 50%

Proposal Z

Net Present value = PV of Cash Inflow - PV of Cash outflow

= 98000*.909 - 98000

= - 8918

Payback Period = Initial Investment / Cash inflow per period

= 98000/ 98000 = 1 year

Accounting rate of return = Average Income / Average Investment

= 98000/ 98000 = 100%

Proposal X should be accepted.

2) Net present value considers the timing of cash flows while payback considers only total cash flows.