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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
Expert Solution
-
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
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