ABC Mining is evaluating the introduction of a new ore production process. Two alter¬natives 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 ABC Mining is to be indifferent between the two processes, what risk-adjusted discount rate must be used to evaluate B?

Question

ABC Mining is evaluating the introduction of a new ore production process. Two alter¬natives 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 ABC Mining is to be indifferent between the two processes, what risk-adjusted discount rate must be used to evaluate B?

Answer 1

To determine the risk-adjusted discount rate for Production Process B, we need to find the rate at which the present value of the net cash flows for both processes is equal. Here's how you can calculate it step by step:

1. Calculate the present value of the net cash flows for Production Process A:
- The net cash flow for each year is $13,000.
- The discount rate is 12%.
- The formula to calculate the present value of the cash flows is: PV = CF / (1 + r)^n, where PV is the present value, CF is the cash flow, r is the discount rate, and n is the number of years.
- Calculate the present value for each year and sum them up: PV_A = (13,000 / (1 + 0.12)^1) + (13,000 / (1 + 0.12)^2) + (13,000 / (1 + 0.12)^3) + (13,000 / (1 + 0.12)^4).

2. Calculate the present value of the net cash flows for Production Process B:
- The net cash flow for each year is $15,247.
- We need to find the discount rate that makes the present value of the cash flows equal to the present value of Process A.
- Let's call this unknown discount rate r_B.
- Calculate the present value for each year and sum them up: PV_B = (15,247 / (1 + r_B)^1) + (15,247 / (1 + r_B)^2) + (15,247 / (1 + r_B)^3) + (15,247 / (1 + r_B)^4).

3. Set the two present values equal to each other: PV_A = PV_B.
- Substitute the calculated present value of Process A and the unknown present value of Process B: (13,000 / (1 + 0.12)^1) + (13,000 / (1 + 0.12)^2) + (13,000 / (1 + 0.12)^3) + (13,000 / (1 + 0.12)^4) = (15,247 / (1 + r_B)^1) + (15,247 / (1 + r_B)^2) + (15,247 / (1 + r_B)^3) + (15,247 / (1 + r_B)^4).

4. Solve the equation to find the unknown discount rate r_B.
- You can use numerical methods such as trial and error or use Excel's Goal Seek function to find r_B. Start with a reasonable guess for r_B, substitute it into the equation, and iteratively refine your guess until the equation is satisfied.

5. Once you determine the value of r_B, you have found the risk-adjusted discount rate needed to evaluate Production Process B.

Note: The risk-adjusted discount rate takes into account the inherent riskiness of an investment and adjusts the discount rate accordingly. It may differ from the discount rate used for Process A, as determined by management.