Question

A new project will cost $80,000 initially and will last for 7 years, at which time its salvage value will be $2,500. Annual revenues are anticipated to be $15,000 per year. The initial cost is believed to be accurate, but the estimates of annual revenue and salvage value are subject to error.

For a MARR of 12 percent/year, what values in the equation below relates Revenue (X) and Salvage (Y) for the project to be feasible using an annual worth analysis.
------- + ------ X<=Y
Also, plot a two-factor sensitivity graph (critical to be shown in Excel submission). Include a line that separates the favorable and unfavorable regions as well as a box showing the 15 percent error region.

Answer 1

Step-by-step explanation:

The equation relating Revenue (X) and Salvage (Y) for the project to be feasible using an annual worth analysis is:

X + (Y - $2,500)/[(1 + 0.12)^7] >= $80,000

This equation shows that the present value of the annual revenues (X) and salvage value (Y) must be greater than or equal to the initial cost of the project ($80,000), taking into account the time value of money with a MARR of 12 percent/year and the salvage value at the end of the project.

To plot a two-factor sensitivity graph, we can use Excel to calculate the present value of the annual revenues and salvage value for different combinations of X and Y. We can then create a table or matrix of the present values and use conditional formatting to color code the cells based on whether the project is favorable (green) or unfavorable (red). The dividing line between the favorable and unfavorable regions corresponds to the equation above, while the 15 percent error region corresponds to a range of values for X and Y that are 15 percent above or below the estimated values.

The sensitivity graph shows how the feasibility of the project varies with changes in the estimates of annual revenue and salvage value. By exploring different scenarios, we can identify the range of revenue and salvage values that are most critical for the project's success and assess the level of uncertainty associated with these estimates. This analysis can inform decision-making and help stakeholders to understand the risks and opportunities associated with the project.

Answer 2

Hi gautamshubhi98, it is my pleasure to assist you in answering this question in-depth step by step today.

Okay, to determine the values that relate Revenue (X) and Salvage (Y) for the project to be feasible, we can use the annual worth analysis equation:

AW = P(A/P, i, n) - X(A/F, i, n) - Y

Where:

P = initial cost = $80,000

A = annual revenue = $15,000

X = revenue factor

Y = salvage value factor

i = MARR = 12% per year

n = project life = 7 years

Substituting the values into the equation, we get:

AW = 80,000(A/P, 12%, 7) - X(A/F, 12%, 7) - Y

To find the values of X and Y, we need to set the equation equal to zero (since the project is feasible when the annual worth is zero):

0 = 80,000(A/P, 12%, 7) - X(A/F, 12%, 7) - Y

Solving for X, we get:

X = 80,000(A/P, 12%, 7) - Y / (A/F, 12%, 7)

Substituting the values into the equation, we get:

X = 12,879.77 - 1,289.55Y

Therefore, the values that relate Revenue (X) and Salvage (Y) for the project to be feasible are:

X <= 12,879.77 - 1,289.55Y

To create a two-factor sensitivity graph, we can plot Revenue (X) on the y-axis and Salvage (Y) on the x-axis. The equation X = 12,879.77 - 1,289.55Y represents the boundary between the favorable and unfavorable regions. The 15% error region can be represented by a box centered at the point (2,500, 15,000) with a width of 2,500 and a height of 3,750 (15,000 x 0.15 = 2,250, which we round up to 2,500 for simplicity).