Question

Consider the following cash flow profile and assume MARR is 10%/year.

A) No project is acceptable
B) Both projects are acceptable
C) Project X is acceptable, Project Y is not
D) Project Y is acceptable, Project X is not

Answer 1

The Net Present Value (NPV) of the cash flow profile, with a 10% Minimum Acceptable Rate of Return (MARR), approximates to $36.16. It considers yearly cash flows of $28 and an initial investment of -$85.

NPV Formula:

`\[ NPV = \sum_(t=0)^(n) (NCF_t)/((1 + r)^t) \]`

Where:

`\(NCF_t\)` represents the net cash flow at the end of year \(t\).

`\(r\)` is the discount rate (MARR).

`\(n\)` is the last year of cash flows.

Calculation Steps:

Year 0:

Cash Flow: -\$85 (Initial investment)

There is no discounting for Year 0.

Years 1 to 6:

Cash Flow: $28 per year

Discount each cash flow to its present value:

`\[ (28)/((1 + 0.10)^t) \]`

Now, let's compute the NPV step by step:

`\[ NPV = -85 + (28)/((1 + 0.10)^1) + (28)/((1 + 0.10)^2) + (28)/((1 + 0.10)^3) + (28)/((1 + 0.10)^4) + (28)/((1 + 0.10)^5) + (28)/((1 + 0.10)^6) \]`

Solving each term:

`\[ NPV = -85 + 25.45 + 23.14 + 21.04 + 19.13 + 17.39 + 15.81 \]`

`\[ NPV = \$36.16 \]`

Therefore, after computing the present value of each cash flow and summing them, the Net Present Value (NPV) of the cash flow profile, considering a MARR of 10% per year, is approximately $36.16 .

complete the question

Consider the following cash flow profile and assume MARR is 10%/year.

| EOY | NCF |

| 0 | -$85 |

| 1 | $28 |

| 2 | $28 |

| 3 | $28 |

| 4 | $28 |

| 5 | $28 |

| 6 | $28 |