TransITRI is a transportation company with a recent need of a new construction equipment at a first cost of $78,000 (Equation (1)), zero salvage value, and a cash flow before taxes (CFBT) per year t that follows Equation (2).                                            CFBT = $30,000 – 3,000t (for t = 1, 2, … T)                                       (1)                                            CFBT = - $78,000 (for t =0)                                                                  (2)Calculate the PW if the economic life of similar machinery is 8 years, while the MARR is 16%, 20%, and 24%

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Asked Dec 11, 2019
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TransITRI is a transportation company with a recent need of a new construction equipment at a first cost of $78,000 (Equation (1)), zero salvage value, and a cash flow before taxes (CFBT) per year t that follows Equation (2).

                                            CFBT = $30,000 – 3,000t (for t = 1, 2, … T)                                       (1)

                                            CFBT = - $78,000 (for t =0)                                                                  (2)

Calculate the PW if the economic life of similar machinery is 8 years, while the MARR is 16%, 20%, and 24%

 

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Expert Answer

Step 1

Present worth can be calculated by taking the difference of present value of cash inflow and present value of cash outflow.

The below table shows the calculation of present worth at 16%:

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D. 1 MARR 2 Discount factor 0.16 =(1+B1)^-1 Discount factor Cashflow Present worth 4 Time =$B$2^A5 =B5"CS |-78000 6 =AS+1 7 =A6+1 8 =A7+1 9 =A8+1 10 =A9+1 11 =A10+1 12 =A11+1 13 =A12+1 =$B$2^A6 =30000-3000*A6 =B6"C6 =30000-3000*A7 =$B$2^A7 =B7"C7 =30000-3000*A8 =$B$2^A8 =B8"C8 |=30000-3000*A9 =$B$2^A9 =89"C9 =810 C10 =$B$2^A10 =30000-3000*A10 =30000-3000*A11 =$B$2^A11 =B11"C11 =B12 C12 =30000-3000 A12 =$B$2^A12 =$B$2^A13 =30000-3000*A13 =B13"C13 =SUM(DS:D13) 14 Net Present Worth

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Step 2

The resultant figures are shown below:

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1 MARR 16% 2 Discount factor 0.86207 4 Time Cashflow Discount factor Present worth -$78,000.00 -$78,000.00 $27,000.00 $23,275.86 0.862068966 $24,000.00 $17,835.91 2. 0.743162901 $21,000.00 $13,453.81 0.640657674 $18,000.00 $9,941.24 0.552291098 $15,000.00 $7,141.70 10 0.476113015 $12,000.00 $4,925.31 0.410442255 11 $9,000.00 $3,184.47 $1,830.15 0.35382953 12 $6,000.00 13 0.305025457 $3,588.44 14 Net Present Worth 15 7.

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Step 3

The below table shows the calculati...

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1 MARR 2 Discount factor 0.2 =(1+B1)^-1 3 Cashflow Discount factor 4 Time Present worth |-78000 =$B$2^A5 =B5*CS 6 =A5+1 7 A6+1 =$B$2^A6 =30000-3000*A6 =86*C6 =$B$2^A7 =87°C7 |=30000-3000*A7 8 =A7+1 9 =A8+1 |=30000-3000*A8 =$B$2^A8 =B8"C8 =$B$2^A9 =$B$2^A10 =30000-3000*A9 =89*C9 10 =A9+1 =30000-3000*A10 =B10*C10 =$B$2^A11 -30000-3000*A11 =B11*C11 11 =A10+1 =$B$2^A12 12 =A11+1 =30000-3000*A12 =B12*C12 =$B$2^A13 13 =A12+1 =30000-3000*A13 =B13"C13 14 Net Present Worth =SUM(D5:D13) 15

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