Answer to Question #122654 in Financial Math for nehal

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

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

Machines A should be selected since it has the highest NPV of $40,746.51. 

B. NPV If projects can be repeated

If the projects can be repeated, ABC ltd should invest in all of these projects because they all have positive NPVs.

C. Internal rate of return for Machine A

The net cashflow = Cash Inflow – Cash Outflow

r= cost of capital = 8%

Period (n) = period of cashflow

Present value interest factor (PVIF) = 1/(1+r)ⁿ

PV of cashflows = Net cashflows / PVIF

Internal Rate of Return (IRR) is the rate at which the NPV = 0

0 = - 79,000 / (r)⁰ + NCF/ (r)¹+ NCF/ (r)²+ NCF/ (r)³+ NCF/ (r)⁴+ NCF/ (r)⁵+ NCF/ (r)⁶+ NCF/ (r)⁷

0 = - 79,000 *(r)⁰ + 23,000* (r)^-1++ 23,000* (r)^-2+ 23,000* (r)^-3+ 23,000* (r)^-4+ 23,000* (r)^-5+ 23,000* (r)^-6+ 23,000* (r)^-7

Solving for r;

IRR_A = 0.13~13%

Decision criteria

Since the IRR > Cost of capital, machine A should be accepted.

Disadvantage of IRR over NPV

The internal rate of return (IRR) does not take consider the size of the project and does not produce accurate results when ranking projects given their size.