Question

The Lesseig Company has an opportunity to invest in one of two mutually exclusive machines that will produce a product the company will need for the next 8 years. Machine A costs $8.9 million but will provide after-tax inflows of $4.5 million per year for 4 years. If Machine A were replaced, its cost would be $9.8 million due to inflation and its cash inflows would increase to $4.7 million due to production efficiencies. Machine B costs $13.9 million and will provide after-tax inflows of $4.3 million per year for 8 years. A. If the WACC is 9%, which machine should be acquired?B. By how much would the value of the company increase if it accepted the better machine?
C. What is the equivalent annual annuity for each machine?

Answer 1

Answer:

A. If the WACC is 9%, which machine should be acquired?

• Since machine B's NPV is higher, it should be acquired. Even though machine A's IRR is higher, the NPV is always the first and most important parameter to consider.

B. By how much would the value of the company increase if it accepted the better machine?

• if machine B is acquired, then company's value will be $743,518 (= $11,879,562 - $11,136,044) higher than if machine A was acquired.

C. What is the equivalent annual annuity for each machine?

• EAA machine A = $2,011,998
• EAA machine B = $2,146,333

Explanation:

we need to determine the NPV of each investment project:

Machine A:

initial investment -$8,900,000

NCF 1 $4,500,000

NCF 2 $4,500,000

NCF 3 $4,500,000

NCF 4 $4,500,000 - $9,800,000 = -$5,300,000

NCF 5 $4,700,000

NCF 6 $4,700,000

NCF 7 $4,700,000

NCF 8 $4,700,000

WACC = 9%

using an excel spreadsheet to calculate the NPV = $11,136,044 , IRR = 35.74%

equivalent annual annuity (EAA) = (r x NPV) / [1 - (1 + r)⁻ⁿ]

• r = 9%
• NPV = $11,136,044
• n = 8

EAA = (0.09 x $11,136,044) / [1 - (1 + 0.09)⁻⁸] = $1,002,244 / 0.4981 = $2,011,998

Machine B:

initial investment -$13,900,000

NCF 1 $4,300,000

NCF 2 $4,300,000

NCF 3 $4,300,000

NCF 4 $4,300,000

NCF 5 $4,300,000

NCF 6 $4,300,000

NCF 7 $4,300,000

NCF 8 $4,300,000

WACC = 9%

using an excel spreadsheet to calculate the NPV = $11,879,562 , its IRR = 27.42%

equivalent annual annuity (EAA) = (r x NPV) / [1 - (1 + r)⁻ⁿ]

• r = 9%
• NPV = $11,879,562
• n = 8

EAA = (0.09 x $11,879,562) / [1 - (1 + 0.09)⁻⁸] = $1,069,161 / 0.4981 = $2,146,333