Question

A company is considering purchasing a new production machine and have identified two potential options. Option A has a first cost of $1450 but will produce annual revenues of $650 while incurring $245 worth of maintenance. Option B has a purchase price of $1130 with annual revenues of $445 and maintenance costs of $147. One of your colleagues has done an internal rate of return analysis on Option A and determined it had an IRR=12.28%

a. Your boss has asked you to determine the IRR for option B, assuming that both options have same service life
b. Assuming the two production machines are independent and the company has a MARR of 11%, what should the company do?

Answer 1

To calculate the IRR for option B, we need to find the discount rate that makes the NPV of the cash flows equal to zero. To determine the best option, compare the IRR of each option to the MARR. Choose the option with the highest IRR if it is greater than the MARR.

Step-by-step explanation:

To calculate the internal rate of return (IRR) for option B, we need to find the discount rate that makes the net present value (NPV) of the cash flows equal to zero. In this case, the cash flows for option B would be the annual revenues of $445 and maintenance costs of $147. Using the IRR formula, we can calculate the IRR for option B.

To determine the best option for the company, we need to compare the internal rate of return (IRR) of each option to the company's minimum acceptable rate of return (MARR). If the IRR is greater than the MARR, it means that the project is expected to generate a return higher than the company's desired rate of return. In this case, if the IRR of both options is greater than 11%, the company should choose the option with the highest IRR, as it would provide the highest return on investment.

Answer 2

a. The IRR for the option B will be 9.988%.

b. The company would accept option A and reject the option B

Step-by-step explanation:

a. To calculate the IRR for option B we first need to determine the service life of the option A.

If R = 12.28%

Net annual benefits = 650-245=$405

Then, 1450= 405*(1-1/1.1228^n)/.1228

1/1.1228^n =1 - 1450*.1228/405 = .5603

1.1228^n = 1.7846

n = log(1.7846)/log(1.1228) = 5 years

Therefore, For option B

Let, IRR = R

Net annual benefit = 445-147 = $298

1130 = 298*(1-1/(1+R)^5)/R

At R = 9%

PV of cash inflows = $1159.12

At R = 10%

PV of cash inflows = $1129.65

As per the method of interpolation,

R = 9% + ((1159.12 - 1130)/( 1159.12-1129.65))*(10%-9%)

R = 9.988%

Thus, IRR for the option B will be 9.988%.

b. According to the given data to selection the any option, the value of IRR must be greater than or equal to the MARR. in this case, option A has the IRR of 12.28% that is greater than the MARR of 11%. But, it is not the case with option B whose IRR is only 9.988% and it is less than the MARR of 11%.

Thus, option A will be accepted and option B will be rejected.