California Mining is evaluating the introduction of new ore production process. Two alternatives are available, Production Process A has an initial cost of $25,000, a 4-year life, and a $5,000 net salvage value, and the use of Process A will increase net cash flow by $13,000 per year for each of the 4 years that the equipment is in use. Production Process B also requires an initial investment of $25,000, will also last 4 years, and its expected net salvage value is zero, but Process B will increase net cash flow by $15, 247 per year. Management believes that a risk adjusted discount rate of 12 percent should be used for Process A. If California Mining is to be indifferent (same NPV for Process A and B) between the two processes, what risk-adjusted discount rate must be used to evaluate B?

Question

California Mining is evaluating the introduction of new ore production process. Two alternatives are available, Production Process A has an initial cost of $25,000, a 4-year life, and a $5,000 net salvage value, and the use of Process A will increase net cash flow by $13,000 per year for each of the 4 years that the equipment is in use. Production Process B also requires an initial investment of $25,000, will also last 4 years, and its expected net salvage value is zero, but Process B will increase net cash flow by $15, 247 per year. Management believes that a risk adjusted discount rate of 12 percent should be used for Process A. If California Mining is to be indifferent (same NPV for Process A and B) between the two processes, what risk-adjusted discount rate must be used to evaluate B?

Answer 1

A: inputs: CF0 = -25000; CF1 = 13000; Nj = 3; CF2 = 18000; I = 12

Output: NPVA = 17663.13

B: Inputs: CF0 = -42663.13 (-25,000 + -17,663.13); CF1 = 15247; Nj = 4
Output: IRR = 16.0% = K.

Answer 2

To determine the risk-adjusted discount rate that California Mining must use to evaluate Process B to be indifferent between Process A and Process B, we need to calculate the net present value (NPV) of both processes using the given information and then solve for the discount rate.

Let's start by calculating the NPV for Process A:
Initial Cost = $25,000
Net Salvage Value = $5,000
Net Cash Flow per year = $13,000
Number of years = 4
Risk-Adjusted Discount Rate for Process A = 12%

To calculate NPV, we use the formula:
NPV = (-Initial Cost) + (Net Cash Flow / (1 + Discount Rate)^Year) + (Net Salvage Value / (1 + Discount Rate)^Year)

For Process A:
NPV_A = (-$25,000) + ($13,000 / (1 + 0.12)^1) + ($13,000 / (1 + 0.12)^2) + ($13,000 / (1 + 0.12)^3) + ($13,000 / (1 + 0.12)^4) + ($5,000 / (1 + 0.12)^4)

Simplifying this expression gives us the NPV_A for Process A.

Now, let's solve for the risk-adjusted discount rate for Process B that would make California Mining indifferent (same NPV) between Process A and Process B.

We want NPV_A = NPV_B, where NPV_B is the NPV for Process B. Using the same formula as above, NPV_B can be expressed as:

NPV_B = (-$25,000) + ($15,247 / (1 + Discount Rate_B)^1) + ($15,247 / (1 + Discount Rate_B)^2) + ($15,247 / (1 + Discount Rate_B)^3) + ($15,247 / (1 + Discount Rate_B)^4) + ($0 / (1 + Discount Rate_B)^4)

Now, we can set NPV_A equal to NPV_B and solve for the Discount Rate_B:

(-$25,000) + ($13,000 / (1 + 0.12)^1) + ($13,000 / (1 + 0.12)^2) + ($13,000 / (1 + 0.12)^3) + ($13,000 / (1 + 0.12)^4) + ($5,000 / (1 + 0.12)^4) = (-$25,000) + ($15,247 / (1 + Discount Rate_B)^1) + ($15,247 / (1 + Discount Rate_B)^2) + ($15,247 / (1 + Discount Rate_B)^3) + ($15,247 / (1 + Discount Rate_B)^4) + ($0 / (1 + Discount Rate_B)^4)

Simplifying this equation will give us the value of Discount Rate_B that makes the two NPVs equal.

You can substitute different values for Discount Rate_B and solve iteratively until you find the rate that makes the two NPVs equal. One way to do this is to use a spreadsheet tool like Microsoft Excel or Google Sheets and use the Goal Seek or Solver function to find the discount rate.