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Homework answers / question archive / You arrive to the office and begin reviewing a new project for solar-powered widgets
You arrive to the office and begin reviewing a new project for solar-powered widgets. Compute the NPV, IRR, PI, and cash flows for the following project:
The firm is considering expanding into a new product line of solar-powered widgets. It is estimated that the firm will sell 100,000 solar-powered widgets per year for the next 10 years and that the widgets will sell for $75 each. The appropriate WACC is 12%.
Variable costs |
$25 each |
Annual fixed costs |
$1,500,000 |
Initial robot production expenditure |
$10,000,000 At the end of the project the value is $0. The robots are recycled and are not sold for cash. |
Robot depreciation |
straight-line method for 10 years, no residual value |
Change in net working capital investment |
One-time $500,000 initial investment in inventory to be recovered at the end of the project in 10 years |
Marginal tax rate |
25% |
Question 1: The IRR of the project is:
A) 9.32%
B) 25.13%
C) 19.22%
D) 13.38%
Question 2: The initial cash outlay in year 0 is:
A) -250,000
B) -10,000,000
C) -10,250,000
D) -9,750,000
Question 3: The Profitability Index (PI) of the project is:
A) .59
B) 1.68
C) .41
D) 1.59
Question 4: The terminal cash flows for year 10 is:
A) 3,125,000
B) 2,875,000
C) 10,250,000
D) 13,125,000
Question 5: The annual net cash flows for years 1-9 are:
A) 1,875,000
B) 2,375,000
C) 2,875,000
D) 937,500
Question 6: NPV of the project is:
A) +5,130,045
B) +6,074,885
C) -6,075,003
D) -1,237,800
Statement showing NPV , annual cash flow , initial investment and terminal cash flow
Particulars | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |
Selling price per unit | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | ||
Less : Variable cost per unit | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | ||
Contribution per unit | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | ||
Total unit sold | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | ||
Total contribution | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | ||
Less : Fixed cost | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | ||
Less : Depreciation | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | ||
PBT | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | ||
Tax @ 25% | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | ||
PAT | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | ||
Add: Depreciation | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | ||
Annual cash flow | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | ||
Initial Robot production cost | -10000000 | |||||||||||
Changes in cash due to change in WC | -250000 | 250000 | ||||||||||
Total cash flow | -10250000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 3125000 | |
PVIF @ 12% | 1.000 | 0.893 | 0.797 | 0.712 | 0.636 | 0.567 | 0.507 | 0.452 | 0.404 | 0.361 | 0.322 | |
PV | -10250000.00 | 2566964.29 | 2291932.40 | 2046368.21 | 1827114.48 | 1631352.21 | 1456564.47 | 1300503.99 | 1161164.28 | 1036753.82 | 1006166.36 | 6074884.52 |
Thus NPV = 6074885 $
Initial investment = 10250000 $
Annual cash flow = 2875000 $
Termianl cash flow = 3125000 $
PI = PV of cash inflow/PV of cash outflow
= 16324885 / 10250000
= 1.59
IRR is rate at which NPV is 0, assuem r = 25.13%
Particulars | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | NPV = sum of PV |
Selling price per unit | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | 75 | ||
Less : Variable cost per unit | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | 25 | ||
Contribution per unit | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | 50 | ||
Total unit sold | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | 100000 | ||
Total contribution | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | 5000000 | ||
Less : Fixed cost | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | 1500000 | ||
Less : Depreciation | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | ||
PBT | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | 2500000 | ||
Tax @ 25% | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | 625000 | ||
PAT | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | 1875000 | ||
Add: Depreciation | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | 1000000 | ||
Annual cash flow | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | ||
Initial Robot production cost | -10000000 | |||||||||||
Changes in cash due to change in WC | -250000 | 250000 | ||||||||||
Total cash flow | -10250000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 2875000 | 3125000 | |
PVIF @ 25.13% | 1.0000 | 0.7991 | 0.6386 | 0.5104 | 0.4078 | 0.3259 | 0.2605 | 0.2081 | 0.1663 | 0.1329 | 0.1062 | |
PV | -10250000.00 | 2297530.25 | 1836050.52 | 1467263.16 | 1172550.09 | 937032.80 | 748821.28 | 598413.76 | 478216.94 | 382162.74 | 331958.59 | 0 |
Thus IRR = 25.13%
Ans)
1) B) 25.13%
2) C) -10,250,000
3) D) 1.59
4) A) 3,125,000
5) C) 2,875,000
6) B) +6,074,885