Answer to Question #121760 in Financial Math for Francisca

Question

Suppose that ABC Ltd is considering purchasing one of three new processing machines. Either machine would make it possible for the company to produce its products more efficiently.
Estimates regarding each machine are provided below:

Machine A Machine B Machine C
Original cost $79,000 $110,000 $244,000
Estimated life 7 years 8 years 10 years
Salvage value Nil Nil $30,000
Estimated annual cash inflows $30,000 $ 60,000 $58,500
Estimated annual cash outflows $ 7,000 $ 35,000 $18,500



A. If the projects cannot be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital? (9 marks)

B. If the projects can be repeated, which machine should ABC Ltd choose based on the NPV criteria at an 8% cost of capital? (6 marks)

C. Calculate the internal rate of return for Machine A? [Hint: internal rate of return is the rate which results in a zero NPV using linear interpolation], and discuss 1 drawback of the IRR against the NPV (5 marks)

Answer 1

A. Machine to consider

Net Present Value (NPV)

Machine A

NPV = - I.O / (1+r)ⁿ + NCF /(1+r)ⁿ

NPV = - 79,000 / (1+0.08)⁰ + Net Cashflow (NCF) /(1+0.08)⁷

NPV = - 79,000 / (1.08)⁰ + NCF/ (1.08)⁷

Machine B

NPV = - I.O / (1+r)ⁿ + NCF /(1+r)ⁿ

NPV = - 110,000 / (1+0.08)⁰ + Net Cashflow (NCF) /(1+0.08)⁸

NPV = - 110,000 / (1.08)⁰ + NCF/ (1.08)⁸

Machine C

NPV = - I.O / (1+r)ⁿ + NCF /(1+r)ⁿ

NPV = - 110,000 / (1+0.08)⁰ + Net Cashflow (NCF) /(1+0.08)ⁿ + Net Cashflow (NCF)+Terminal Value /(1+0.08)¹⁰

Decision Criteria

From the analysis, machines A should be selected since it has the highest NPV of 40,746.51. 

B). If machines can be repeated

Machine B should be considered since it has a higher payback on NPV based on the NPV and initial cost/outlay.

C). IRR & NPV

IRR_A = 18%

NPV_A = $ 40,746.51

Decision criteria

Based on the NPV, machine A should be accepted.

Based on the IRR, machine A should be accepted since it is greater than the cost of capital (8%).

Disadvantage of IRR over NPV

The disadvantage of internal rate of return (IRR) is that it does not account for the project size, ignores futures costs and does not account for reinvestment rates. Ideally, it is weak for use especially when considering more than 1 project.