Question

A recent project nominated for consideration at your company has a four-year cash flow of $20,000; $25,000; $30,000; and $50,000. The cost of the project is $75,000.1.If the required rate of return is 20%, conduct a discounted cash flow calculation to determine the NPV.2.What is the benefit-cost ratio for the project3.Assuming the required rate of return remains 20%, what would the NPV of the above project be if the inflation rate was expected to be 4% in each of the next four years?

Answer 1

Answer:

1. $501.54

2. 1.01

3. -$5,728.56

Explanation:

The computations are shown below:

1. For net present value

Year     Cash flow     Discount factor @20%           Present value  

0          $75,000         1                                               $75,000

1            $20,000        0.8333333333                          $16,666.67

2           $25,000        0.6944444444                       $17,361.11

3           $30,000        0.5787037037                       $17,361.11

4           $50,000        0.4822530864                       $24,112.65

Total of cash inflows                                                   $75,501.54

NPV                                                                              $501.54                                      

The discount factor should be computed below

= 1 ÷ (1 + rate) ^ years

2. The benefit cost ratio would be

= Total Present value ÷ Initial investment

= $75,501.54 ÷ $75,000

= 1.01

3. 1. For net present value

Year     Cash flow     Discount factor @20%           Present value  

0          $75,000         1                                               $75,000

1            $20,000        0.8064516129                     $16,129.03

2           $25,000        0.650364204                    $16,259.11

3           $30,000        0.5244872613                    $15,734.62

4           $50,000        0.4229735978                    $21,148.68

Total of cash inflows                                                 $69,271.44

NPV                                                                            -$5,728.56                                  

The discount factor should be computed below

= 1 ÷ (1 + rate) ^ years

Answer 2

The NPV for question is $501.54, Benefit-Cost Ratio for question 2 is 1.01, while NPV for question 3 is $8,848.40.

Calculations of NPV and Benefit-Cost Ratio

Note: See the attached photo for the calculation of the NPV for numbers 1 and 3.

In the attached photo, the following (formulae) are used in taking care of the inflation:

R = Nominal discount rate = Required rate of return = 20% = 0.20

Inflation = 4% = 0.04

r = Real discount rate = ((1 + nominal discount rate) / (1 + inflation rate)) - 1 = ((1 + 0.20) / (1 + 0.04)) - 1 = 0.153846153846154, or 15.3846153846154%

The answers to the three questions are therefore calculated as follows:

1. From number 1 in the attached photo, we have:

NPV = $501.54

2. Benefit-Cost Ratio can be calculated as follows:

Benefit-Cost Ratio = Addition of Present Values of Cash Flows from Year 1 to 4 in number in the attached photo / Cost of the project

Benefit-Cost Ratio = ($16,666.67 + $17,361.11 + $17,361.11 + $24,112.65) / $75,000

Benefit-Cost Ratio = $75,501.54 / $75,000

Benefit-Cost Ratio = 1.01

3. From number 3 in the attached photo, we have:

NPV = $8,848.40

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