The Perez Company has the opportunity to invest in one of two mutually exclusive

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 $10 million but realizes after-tax inflows of $4 million per year for 4 years. After 4 years, the machine must be replaced. Machine B costs $15 million and realizes after-tax inflows of $3.5 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 10%.

By how much would the value of the company increase if it accepted the better machine? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answer to two decimal places.
$   million

What is the equivalent annual annuity for each machine? Enter your answer in millions. For example, an answer of $1.2 million should be entered as 1.2, not 1,200,000. Round your answers to two decimal places.

Machine A $   million Machine B $   million

Explanation / Answer

Machine A’s simple NPV is calculated as follows: Enter CF 0 = -10 and CF 1-4 = 4. Then enter I/YR = 10, and press the NPV key to get NPV A = $2.679 million

However, this does not consider the fact that the project can be repeated again. Enter these values into the cash flow register: CF 0 = -10; CF 1-3 = 4; CF 4 = -6; CF 5-8 = 4. Then enter I/YR = 10, and press the NPV key to get extended NPV A = $ 4.5096 $4.51 million..

For Machine B’s NPV, enter these cash flows into the cash flow register, along with the interest rate, and press the NPV key to get NPV B = $3.672 $3.67 million

Compute EAA of the two projects

The EAA of Machine A is found by first finding the PV: N = 4, I/YR = 10, PMT = 4, FV = 0; solve for PV = $12.679. The NPV is $12.679 $10 = $2.679 million .

We convert this to an equivalent annual annuity by inputting: N = 4, I/YR = 10, PV = 2.679, FV = 0, and solve for PMT (EAA): EAA A = 0.845 $0.85 million

For Machine B, we already found the NPV of $3.672 million .

We convert this to an equivalent annual annuity by inputting: N = 8, I/YR = 10, PV = 3.672, FV = 0, and solve for PMT (EAA)

: EAA B = 0.688 $0.69 million .

Again, the EAA method demonstrates that Machine A is the better project since EAA A > EAA B

0 1 2 3 4 5 6 7 8 A -10 4 4 4 4 4 4 4 4 -10 -6

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