Question

In: Accounting

You are considering the following capital investment. You can buy a shoelace manufacturing machine for 7...

You are considering the following capital investment. You can buy a shoelace manufacturing machine for 7 million dollars. The machine would be depreciated using straight-line depreciation over 7 years. Assume first that the revenue from shoelace sales would be 3.2 million dollars per year, and variable costs would be 2 million per year. Assuming your firm has a beta of 1.2 and is all equity financed, and that the expected return on the market is 8% that the risk-free rate is 1%, and your firm has a marginal tax rate of 21%, is this a good investment?

1.b) How much is the option to sell the machine after 5 years for 3 million dollars (and exit the business) worth to you

1,c) If you can sell shoelaces at $2 and have variable costs of $0.50, how many shoelaces do you need to sell to have an accounting breakeven?

1.d) How many do you need to sell to have positive EVA/NPV?

Solutions

Expert Solution

1) ($ millions)
Year Cash inflow Cash outflow Net Cashflow Depreciation Net profit Tax @21% Cashflow after tax PVF @ 9.40 % Discounted Value  
(a) (b) (c ) (d=b-c) (e ) (f=d-e) (g=f x 21%) (h=d-g) (i) (J=h x i)
               -                            -                   7.00                    -7.00                          -                 -7.00                     -                 -7.00      1.00               -7.00
                1                      1.20                     -                        1.20                     1.00                 0.20                0.04                 1.16      0.91                 1.06
                2                      1.20                     -                        1.20                     1.00                 0.20                0.04                 1.16      0.84                 0.97
                3                      1.20                     -                        1.20                     1.00                 0.20                0.04                 1.16      0.76                 0.88
                4                      1.20                     -                        1.20                     1.00                 0.20                0.04                 1.16      0.70                 0.81
                5                      1.20                     -                        1.20                     1.00                 0.20                0.04                 1.16      0.64                 0.74
                6                      1.20                     -                        1.20                     1.00                 0.20                0.04                 1.16      0.58                 0.68
                7                      1.20                     -                        1.20                     1.00                 0.20                0.04                 1.16      0.53                 0.62
Net Present Value               -1.25
It is not recommend to invest in this project as having negative Net Present Value. So it is not a good investment.
Working Notes:
(i)Net cash inflow: ($ millions)
(1) Sales Variable cost Net Cash Inflow
1-7 year                      3.20                 2.00                      1.20
(ii) Annual Depreciation = $ 7 million/7 = $ 1 million
(iii) Cost of capital = Risk free rate + Beta (Market rate - Risk free rate)
        Cost of capital = 1% + 1.2 (8% -1%)
        Cost of capital = 9.4 %
1b) Present worth for $ 3 million of machine shall be recover after 5 year is ($ 3 million x .64) = $ 1.92 millions
1c) Contribution = Sales - Variable cost
       Contribution = $ 2 - $ .50 = $ 1.50 per shoelaces
        Breakeven Sales in unit = Fixed cost / Contribution per unit
        Breakeven Sales in unit = $ 7 millions / $ 1.50 per shoelaces
        Breakeven Sales in unit = $ 46,66,667 shoelaces
1d) EVA = Net operating profit after tax - (Invested Capital x Cost of capital)
        then Net operating profit after should be more that ($ 7 million x 9.4%) = $ 6,58,000

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