Question

The Perez Company has the opportunity to invest in one of two mutually exclusive machines that will produce a product it will need for the foreseeable future. Machine A costs $8 million but realizes after tax inflows of $4.5 million per year for 4 years. After 4 years, the machine must be replaced. Machine B costs $17 million and realizes after-tax inflows of $4 million per year for 8 years, after which it must be replaced. Assume that machine prices are not expected to rise because inflation will be offset by cheaper components used in the machines. The cost of capital is 13%. Using the replacement chain approach to project analysis, by how much would the value of the company increase if it accepted the better machine? Do not round intermediate calculations. Enter your answer in millions. For example, an answer of $1.23 million should be entered as 1.23, not 1,230,000. Round your answer to two decimal places. $ million What is the equivalent anrual annuity for each machine? Do not round intermediate calculations. Enter your answers in millions. For example, an answer of $1,23 million should be entered as 1.23, not 1,230,000. Round your answers to two decimal places.

Answer 1

The Perez Company would increase its value by $18.20 million by accepting the better machine (Machine B).

Step-by-step explanation:

Replacement Chain Approach:

Calculate Equivalent Annual Annuity (EAA):

Machine A:

Present Value (PV) of 4 years of $4.5 million inflows at 13% cost of capital: PV = $4.5m * (1 - 1/1.13^4) / 13% = $12.02 million

Annuity factor for 4 years at 13%: (1 - 1/1.13^4) = 0.7606

EAA = PV / annuity factor = $12.02 million / 0.7606 = $15.81 million

Machine B:

Present Value (PV) of 8 years of $4 million inflows at 13% cost of capital: PV = $4m * (1 - 1/1.13^8) / 13% = $21.11 million

Annuity factor for 8 years at 13%: (1 - 1/1.13^8) = 0.4911

EAA = PV / annuity factor = $21.11 million / 0.4911 = $43.00 million

Calculate Net Present Value (NPV) of Replacement Chains:

Machine A: NPV = EAA - Initial Cost = $15.81 million - $8 million = $7.81 million

Machine B: NPV = EAA - Initial Cost = $43.00 million - $17 million = $26.00 million

Identify the Better Machine:

Machine B has a higher NPV ($26.00 million) compared to Machine A ($7.81 million).

Calculate Value Increase:

The increase in company value is the difference between the NPVs of the two machines: $26.00 million - $7.81 million = $18.19 million

Therefore, the Perez Company would increase its value by $18.19 million by choosing Machine B. Rounding to two decimal places gives the final answer: $18.20 million.