Answer to Question #122416 in Financial Math for Ishal

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

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

Answer 1

Machine A

Computing the PV of cashflows

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

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

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

Solving for r;

IRR_A = 0.13~13%

Decision criteria

Since the IRR of machine A is higher than the cost of capital (8%), machine A should be accepted.

Disadvantage of IRR over NPV

The internal rate of return (IRR) ignores futures costs and reinvestment rates and as such, it is not a good method of evaluation to use when considering a huge portfolio of projects.