Question

Unequal Lives

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 $9 million but realizes after-tax inflows of $3.5 million per year for 4 years. After 4 years, the machine must be replaced. Machine B costs $14 million and realizes after-tax inflows of $3 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 8%.

1. Using the replacement chain approach to project analysis, 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

Answer 1

Answer :

If the Company will select Machine B, it can save $218,919.41 per year.

The equivalent annual annuity of Machine A and B is $782,712.76, and $563,793.35. respectively.

The equivalent annual annuity is computed as:

Equivalent Annual Annuity (EAC) =r∗NPV1−(1+r)−n Equivalent Annual Annuity (EAC)=r∗NPV1−(1+r)−n

This is where:

• NPV is the net present value
• r is the interest rate
• n is the number of periods

But first we must compute the NPV of each machine. To get the present value of the annual after-tax inflows.

Present value of annuity (PVA) =P∗1−(1+r)−nr Present value of annuity (PVA) =P∗1−(1+r)−nr

This is where:

• P is the periodic payments
• r is the interest rate
• t is the number of periods

Machine A:

PVA=3,500,000∗1−(1+.08)−4.08=11,592,443.94PVA=3,500,000∗1−(1+.08)−4.08=11,592,443.94

Machine B:

PVA=3,000,000∗1−(1+.08)−8.08=17,239,916.83PVA=3,000,000∗1−(1+.08)−8.08=17,239,916.83

NPV:

Machine A = 11,592,443.94 - 9,000,000 = 2,592,443.94

Machine B = 17,239,916.83 - 14,000,000 = 3,239,916.83

And now we can compute for the equivalent annual annuity:

Equivalent Annual Annuity (A)=.08∗2,592,443.941−(1+.08)−4=782,712.76 Equivalent Annual Annuity (A)=.08∗2,592,443.941−(1+.08)−4=782,712.76

Equivalent Annual Annuity (B)=.08∗3,239,916.831−(1+.08)−8=563,793.35 Equivalent Annual Annuity (B)=.08∗3,239,916.831−(1+.08)−8=563,793.35

782,712.76 - 563,793.35 = 218,919.41

Therefore : 2.18 is right one.