Question

“Austin Jack Inc.” is considering the following machines

Machine A

Cost $500,000

Expected Life 6 years

CF/Year $220,000

Machine B

Cost $260,000

Expected Life 3 years

CF/Year $200,000

Assume that the cost of capital is 12 percent.

15. What is the NPV for project A? *

A. $380,605

B. $404,510

C. $905,215

D. $510,000 E. None of the above

16. What is the NPV for project B? *

A. $220,366 B. $480,366

C. $740,366

D. $350,366

E. None of the above

17. What is the Equivalent Annual Annuity (EAA) for project A? *

A. $105,120

B. $98,387

C. $88,312

D. $77,200

E. None of the above

18. What is the Equivalent Annual Annuity (EAA) for project B? *

A. $91,749

B. $75,822

C. $108,200

D. $65,410

E. None of the above

Answer 1

The NPV is computed as shown below:

= Initial investment + Present value of future cash flows

Present value is computed as follows:

= Future value / (1 + r)ⁿ

So, the NPV of project A is computed as follows:

= - $ 500,000 + $ 220,000 / 1.12 + $ 220,000 / 1.12² + $ 220,000 / 1.12³ + $ 220,000 / 1.12⁴ + $ 220,000 / 1.12⁵ + $ 220,000 / 1.12⁶

= $ 404,510 Approximately

The NPV of project B is computed as follows:

= - $ 260,000 + $ 200,000 / 1.12 + $ 200,000 / 1.12² + $ 200,000 / 1.12³

= $ 220,366 Approximately

The EAA of Project A is computed as follows:

= NPV of Project A / Present value annuity factor of 12% for 6 years

Present value annuity factor of 12% for 6 years is computed as follows:

= [ (1 – 1 / (1 + r)ⁿ) / r ]

= (1 - 1 / (1 + 0.12)⁶ ) / 0.12 ]

= 4.111407324

So, the EAA will be computed as follows:

= $ 404,510 / 4.111407324

= $ 98,387 Approximately

The EAA of Project B is computed as follows:

= NPV of Project B / Present value annuity factor of 12% for 3 years

Present value annuity factor of 12% for 3 years is computed as follows:

= [ (1 – 1 / (1 + r)ⁿ) / r ]

= (1 - 1 / (1 + 0.12)³ ) / 0.12 ]

= 2.401831268

So, the EAA will be computed as follows:

= $ 220,366 / 2.401831268

= $ 91,749 Approximately

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