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You arrive to the office and begin reviewing a new project for solar-powered widgets

Finance

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

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  • 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