Answer:(1) payback period Product A 2.83 years, Product B 2.92 years (2) NPV Product A $26,464, Product B $45,672, (3) IRR Product A 25%, Product B 20%, (4) Profitability index Product A 1.15, Product B 1.12, (5) Simple rate of return Product A 15.3%, Product B 14.2%
Explanation:
To calculate the pay back period
Product A. Product B
Sales 250,000. 350,000
Less:
Variable cost 120,000. 170,000
Depreciation. 34,000. 76,000
Fixed operating cost 70,000. 50,000
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Net income. 26,000. 54,000
Add: Depreciation. 34,000. 76,000
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Net cash inflow. 60,000. 130,000
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Pay back period = initial investment / Annual cash inflow
For product A
Initial investment = $170,000, Annual cash inflow =$60,000
=170,000/60,000
=2.83 years
For product B
Initial investment =$380,000, Annual cash inflow =$130,000
=380,000/130,000
=2.92 years
To calculate NPV for each product
For product A
Initial investment = $170,000, Annual cash inflow =$60,000
Discount Factor = 16% for 5 years
DF = 1 - (1 + i) ∧-n / i
= 1 - (1 + 0.16)∧-5 / 0.16
= 1- (1.16)∧-5 / 0.16
= 1- 0.4761 / 0.16
= 0.5239/0.16
=3.2744
PV of cash inflow = 60,000 × 3.2744 = $196,464
NPV of Product A = PV of cash inflow - PV of cash outflow
= $196,464 - 170,000
= $26,464
For product B
Initial investment =$380,000, Annual cash inflow =$130,000
DF = 16% for 5years = 3.2744
PV of cash inflow = $130,000 × 2.2744 = $425,672
NPV of Product B = PV of cash inflow - PV of cash outflow
$425,672 - $380,000
=$45,672
To calculate the IRR
DF = 25% for 5years using the formula 1 - (1 + i )∧-n / i
= 1 - (1 + 0.25)∧-5 / 0.25
= 1 - (1.25)∧-5 / 0.25
= 1 - 0.3277 / 0.25
= 0.6723/ 0.25
=2.6892
PV of cash inflow =$60,000 × 2.6892 = $161,352
NPV of Product A = PV of cash inflow - PV of cash outflow
= $161,352 - $170,000
=-$8,648
For product B
DF = 20% for 5 years using the above formula
1 - ( 1 + 0.2)∧-5 / 0.2
= 1 - (1.2)∧-5 / 0.2
=1 - 0.4019 / 0.2
= 0.5981/0.2
=2.9905
PV of cash inflow =$130,000 × 2.9905 = $388,765
NPV of Product B = PV of cash inflow -PV of cash outflow
= $388,765 -$380,000
=$8,765
Therefore IRR Product A =25%, Product B =20%
To calculate the profitability index
PI = PV of cash inflow / initial investment
For product A
= PV of cash inflow = $196,464, initial investment = $170,000
= $196,464 / $170,000
=1.15
For product B
PV of cash inflow =$425,672, initial investment = $380,000
= $425,672/$380,000
=1.12
To calculate simple rate of return
Simple rate of return = Annual income / initial investment
For product A
Annual income =$26,000, initial investment =$170,000
=$26,000 / $170,000
=0.1529 × 100
= 15.29
=15.3% Approximately
For product B
Annual income =$54,000, initial investment =$380,000
=$54,000/ $380,000
=0.142 × 100
= 14.2%
Payback period choose Product A
NPV choose Product B
IRR choose Product A
PI choose Product A
Simple rate of return choose Product A