Problem II (50 Points) Using payback, ARR, NPV, and IRR to make capital investme
ID: 2587377 • Letter: P
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Problem II (50 Points) Using payback, ARR, NPV, and IRR to make capital investment decisions Water Country is considering purchasing a water park in Atlanta, Georgia, for $1,200,000. The new facility will generate annual net cash inflows of $400,000 for eight years. Engineers estimate that the facility will remain useful for eight years and have no residual value. The company uses straight-line depreciation, and its stockholders demand an annual return of 12% on investments of this nature. 1. Compute the payback period. Amount invested Expected annual net cash inflow Payback 2. Compute the Accounting Rate of Return Total net cash inflows during operating life of facility Average annualOperating life net cash inflowof facility Total depreciation during = Cost - Residual value operating life of facilityExplanation / Answer
Cost of Water Park
$ 1,200,000
Annual Cash Net Inflow
$ 400,000
Period of Inflow
8 years
Straight Line Method Depreciation
= 1200000 / 8
$ 150,000
Expected Annual Returns
12%
1. Payback Period
Payback =
Amount Invested
Expected Annual Net Cash Inflow
=
$ 1,200,000
$ 400,000
=
3
years
2. Accounting Rate of Return
Total Net Cash inflows during operating life of facility
= Average annual net cash flow x Operating life facility
= 400,000 x 8
$ 3,200,000
Total Depreciation during operating Life of Facility
= Cost - Residual Value
= 1,200,000 - 0
$ 1,200,000
Total Net Cash inflows during operating life of facility
$ 3,200,000
Less : Total Depreciation during operating Life of Facility
$ 1,200,000
Total Operating Income during operating life in years
$ 2,000,000
Divide by : Facility operating life in years
$ 8
Average annual Operating income from facility
$ 250,000
Average amount Invested
= Amount Invested + Residual Value
2
= 1,200,000 / 2
$ 600,000
ARR
= Average annual Operating income from facilty
Average amount Invested
= 250,000 / 600,000
41.67%
3. Net Present Value
Time
Annual Net Cash Flow
Annuity PV Factor (I = 12% , n=8)
Present Value
1-8
PV of Annuity
$ 400,000
4.9676
$ 1,987,056
0
Initial Investment
$ 1,200,000
NPV of Facility
$ 787,056
4. Compute Internal Rate of Return
Annuity PV Factor
= Initial Investment / Amount of each net cash flow
(I = ?%, n=8)
=1,200,000 / 400,000
3
Annuity PV Factor
3
IRR
29%
Cost of Water Park
$ 1,200,000
Annual Cash Net Inflow
$ 400,000
Period of Inflow
8 years
Straight Line Method Depreciation
= 1200000 / 8
$ 150,000
Expected Annual Returns
12%
1. Payback Period
Payback =
Amount Invested
Expected Annual Net Cash Inflow
=
$ 1,200,000
$ 400,000
=
3
years
2. Accounting Rate of Return
Total Net Cash inflows during operating life of facility
= Average annual net cash flow x Operating life facility
= 400,000 x 8
$ 3,200,000
Total Depreciation during operating Life of Facility
= Cost - Residual Value
= 1,200,000 - 0
$ 1,200,000
Total Net Cash inflows during operating life of facility
$ 3,200,000
Less : Total Depreciation during operating Life of Facility
$ 1,200,000
Total Operating Income during operating life in years
$ 2,000,000
Divide by : Facility operating life in years
$ 8
Average annual Operating income from facility
$ 250,000
Average amount Invested
= Amount Invested + Residual Value
2
= 1,200,000 / 2
$ 600,000
ARR
= Average annual Operating income from facilty
Average amount Invested
= 250,000 / 600,000
41.67%
3. Net Present Value
Time
Annual Net Cash Flow
Annuity PV Factor (I = 12% , n=8)
Present Value
1-8
PV of Annuity
$ 400,000
4.9676
$ 1,987,056
0
Initial Investment
$ 1,200,000
NPV of Facility
$ 787,056
4. Compute Internal Rate of Return
Annuity PV Factor
= Initial Investment / Amount of each net cash flow
(I = ?%, n=8)
=1,200,000 / 400,000
3
Annuity PV Factor
3
IRR
29%
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