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?

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Risk-adjusted discount rate Answer: e Diff: M





A: Inputs: CF0 = -25000; CF1 = 13000; Nj = 3; CF2 = 18000; I = 12.
Output: NPVA = 17,663.13.

B: Inputs: CF0 = -42663.13 (-25000 + -17663.13); CF1 = 15247; Nj = 4.
Output: IRR = 16.0% = k.

Risk-adjusted discount rate Answer: e Diff: M

can any one further explain calculation on project B

16%

15%

Apart from using scientific calculator is there any method to use in finding of that 16%

To compare the two production processes A and B, we need to calculate the present value (PV) of the net cash flows for each process, using the given risk-adjusted discount rates.

Let's start by calculating the present value of net cash flows for Process A:

Step 1: Calculate the net cash flow per year:
Net cash flow per year for Process A = $13,000

Step 2: Calculate the present value of net cash flows for each year using the risk-adjusted discount rate of 12 percent:
PV of net cash flow Year 1 = $13,000 / (1 + 0.12)^1
PV of net cash flow Year 2 = $13,000 / (1 + 0.12)^2
PV of net cash flow Year 3 = $13,000 / (1 + 0.12)^3
PV of net cash flow Year 4 = $13,000 / (1 + 0.12)^4

Step 3: Calculate the total present value of net cash flows for Process A:
Total PV of net cash flows for Process A = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4

Now let's calculate the present value of net cash flows for Process B:

Step 1: Calculate the net cash flow per year:
Net cash flow per year for Process B = $15,247

Step 2: Calculate the present value of net cash flows for each year using the unknown risk-adjusted discount rate, let's call it r:
PV of net cash flow Year 1 = $15,247 / (1 + r)^1
PV of net cash flow Year 2 = $15,247 / (1 + r)^2
PV of net cash flow Year 3 = $15,247 / (1 + r)^3
PV of net cash flow Year 4 = $15,247 / (1 + r)^4

Step 3: Calculate the total present value of net cash flows for Process B:
Total PV of net cash flows for Process B = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4

Now, according to the problem, ABC Mining is indifferent between the two processes. This means that the total present value of net cash flows for both processes should be equal.

Therefore, we can set up the equation:
Total PV of net cash flows for Process A = Total PV of net cash flows for Process B

Plugging in the values we know:
(PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4) for Process A = (PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4) for Process B

Since the initial investment and the net salvage value are the same for both processes, only the net cash flow per year differs, and it is given as $13,000 for Process A and $15,247 for Process B. Therefore, we can simplify the equation:

PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 for Process A = PV Year 1 + PV Year 2 + PV Year 3 + PV Year 4 for Process B

Now solve for the unknown risk-adjusted discount rate (r) for Process B.