Could you please indicate the steps taken that found the NPV and IRR Below is th

Question

Could you please indicate the steps taken that found the NPV and IRR

Below is the problem and what I have completed so far. I am at a loss at this point

Tom Osborne, the CFO of Huskers Private Equity Fund, is reviewing an acquisition opportunity for the fund. Mr. Osborne is considering whether Huskers should buy the firm XYZ. XYZ is currently for sale at the book value of its equity (i.e. $30,000 to be paid immediately). Huskers investment guidelines require that each investment should earn at least 40% per year. Investment horizon in XYZ is 7 years. At the end of the 7th year (i.e. t=7 or year 2021), Huskers expects to sell XYZ at a price that is 8 times the firm's free cash-flow in 2021. Using the assumptions given below, answer the following questions:

1- What is the NPV of this acquisition given Huskers required return of 40%?

2- What is the IRR of the proposed investment?

3- Should Mr. Osborne recommend buying XYZ?

- Annual revenue growth rates will be -10%, 20%, 20%, 40%, 75%, 30%, 20% during the next seven years respectively.

- COGS will be 75% of the annual revenues.

- Depreciation expense will be 10% of gross PP&E.

- XYZ will make $25,000 per year in additional capital investments during the next seven years.

- Interest rate on debt is 10% and the annual interest expense is computed as 10% of the average of the current year’s and the previous year's interest bearing debt balance (= long-term debt).

- Minimum cash balance should be at least $5000 every year.

- XYZ will pay the maximum dividends as long as there is no equity issuance during the fiscal year. In other words, there cannot be a dividend payment during a fiscal year if XYZ needs equity funding during that fiscal year. Dividend payments out of XYZ is a cash inflow for Huskers.

- Accounts receivable will be 60% of annual revenues.

- Accounts payable will be 60% of annual revenues.

- No new debt will be issued. Long-term debt is due seven years from now (i.e. t=7 or year 2021). The principal amount of $20,000 will be paid as of the 2021 fiscal year end.

- XYZ will issue equity as needed. Since Huskers is the sole owner of XYZ, XYZ's equity issuance is funded by Huskers (i.e. from Huskers' perspective any equity issuance by XYZ is a cash outflow or equivalently additional investment contribution in XYZ ). Huskers' investment guidelines permit contributing at most $100,000 in XYZ during the next 7 years (including the $30,000 acquisition price). Any dividends that are paid out reduce the total amount contributed.

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Workings

2014 2015 2016 2017 2018    2019    2020 2021 Revenue $      50,000.00 $      45,000.00 $    54,000.00 $    64,800.00 $    90,720.00 $ 158,760.00 $ 206,388.00 $ 247,665.60 COGS (Excludes depreciation expense) $      36,750.00 $      33,750.00 $    40,500.00 $    48,600.00 $    68,040.00 $ 119,070.00 $ 154,791.00 $ 185,749.20 Depreciation expense $        5,000.00 $        7,500.00 $    10,000.00 $    12,500.00 $    15,000.00 $    17,500.00 $    20,000.00 $    22,500.00 EBIT $        8,250.00 $        3,750.00 $       3,500.00 $       3,700.00 $       7,680.00 $    22,190.00 $    31,597.00 $    39,416.40 Interest expense $        2,000.00 $        2,100.00 $       2,310.00 $       2,541.00 $       2,795.10 $       3,074.61 $       3,382.07 $       3,720.28 EBT $        6,250.00 $        1,650.00 $       1,190.00 $       1,159.00 $       4,884.90 $    19,115.39 $    28,214.93 $    35,696.12 Taxes (20%) $        1,250.00 $            330.00 $          238.00 $          231.80 $          976.98 $       3,823.08 $       5,642.99 $       7,139.22 Net income $        5,000.00 $        1,320.00 $          952.00 $          927.20 $       3,907.92 $    15,292.31 $    22,571.94 $    28,556.90 Dividends $                     -   Assets 2014 Cash $      10,000.00 $        5,000.00 $       5,000.00 $       5,000.00 $       5,000.00 $       5,000.00 $       5,000.00 $       5,000.00 Accounts receivable $      30,000.00 $      27,000.00 $    32,400.00 $    38,880.00 $    54,432.00 $    95,256.00 $ 123,832.80 $ 148,599.36 Gross PP&E $      50,000.00 $      75,000.00 $ 100,000.00 $ 125,000.00 $ 150,000.00 $ 175,000.00 $ 200,000.00 $ 225,000.00 Less accumulated depreciation $      10,000.00 $      17,500.00 $    27,500.00 $    40,000.00 $    55,000.00 $    72,500.00 $    92,500.00 $ 115,000.00 Net PP&E $      40,000.00 $      57,500.00 $    72,500.00 $    85,000.00 $    95,000.00 $ 102,500.00 $ 107,500.00 $ 110,000.00 Total assets $      80,000.00 $      89,500.00 $ 109,900.00 $ 128,880.00 $ 154,432.00 $ 202,756.00 $ 236,332.80 $ 263,599.36 Liabilities and Equity Accounts payable $      30,000.00 $      27,000.00 $    32,400.00 $    38,880.00 $    54,432.00 $    95,256.00 $ 123,832.80 $ 148,599.36 Long-term debt $      20,000.00 $      22,000.00 $    24,200.00 $    26,620.00 $    29,282.00 $    32,210.20 $    35,431.22 $    38,974.34 Common stock $      20,000.00 Retained earnings $      10,000.00 $      11,320.00 $    12,272.00 $    13,199.20 $    17,107.12 $    32,399.43 $    54,971.38 $    83,528.27 Total L+E $      80,000.00 $      60,320.00 $    68,872.00 $    78,699.20 $ 100,821.12 $ 159,865.63 $ 214,235.40 $ 271,101.97

Explanation / Answer

For calculating the NPV and IRR of any project or investment , we need to know the cash inflow and out flow during the entire span of the project . The Cash flow should take into account cash from initial investment, regular operation, Debt taken and repayed, terminal flows etc. Please remember that the cash flows should not have any non cash expenditure like depreciation. And this is the reason the Expert has added back depreciation after the after tax profit. After which he has deducted the further investments from this operating cash flow and also any debt repayment. After performing all these steps , when you have cash in/out flow from each year, you need to remember that they are all future value and need to be brought tp present value to make a decesion. Hence you need to multiply cash flows from each year to their respective discounting rate to atain PV of all cash flow.

Steps for NPV Calculation Only

NPV = PV of all Cash inflows - PV of all Cash outflows

Use this formula to get the NPV of the project.

Steps for IRR calculation

IRR is the discount rate at which all inflows equal to out flows and the NPV is Zero,

i.e. PV of cash inflow - PV of all Cash outflows = 0

Hence to get the IRR you need to take the future value s of the cash flows and by method of trial and error, apply different discount rates to the cash flow to attain an NPV of 0. For example , if the NPV at any disc rate is positive then you need to keep increasing the disc rate to reach a point where the NPV become Zero, i.e. no profit no loss situation. Vice versa if the NPV at any disc rate is negative you need to try with a lower discount rate to reach an NPV of 0.

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