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?

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

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

Step 1: Computation of Initial Investment
Particulars	A	B	C
Initial Cost	$    79,000.00	$ 1,10,000.00	$ 2,44,000.00
Step 2: Computation of Net Inflow per annum
Particulars
Annual cash inflow	$    30,000.00	$    60,000.00	$    58,500.00
Annual cash outflow	$       7,000.00	$    35,000.00	$    18,500.00
Net Cash Inflow	$    23,000.00	$    25,000.00	$    40,000.00
Step 3: Computation of Net Present Value
Net Cash Inflow	$    23,000.00	$    25,000.00	$    40,000.00
Discount Rate	8%	8%	8%
Estimated Useful life	7	8	10
PVF	5.2064	5.7466	6.7101
Present value of Net Cash Inflow (Net Cash Inflow* PVF)	$ 1,19,746.51	$ 1,43,665.97	$ 2,68,403.26
Salvage value	$                   -	$                   -	$    30,000.00
Present value of Salvage Value	$                   -	$                   -	$    13,895.80
(30000/(1+0.08)^10)
Present value of all cash inflows	$ 1,19,746.51	$ 1,43,665.97	$ 2,82,299.06
Net Present Value	$    40,746.51	$    33,665.97	$    38,299.06
Ranking	1	3	2
(Present Value of all inflows - Initial Investment)

a. If the project has a shorter duration and cannot be repeated then Machine A should be purchased because Machine A gives highest NPV within a shorter period which is 7 years, which means Machine A can payback the money faster.

b. If the project can be repeated, then also Machine A should be preferred since it has the highest NPV and the cash outflow is minimum and cash inflow proportion is higher compared to the cost of other machines

c.

At Internal Rate of Return, Net Present Value = 0

Net Present Value = Present Value of all Cash Inflows - Present Value of all Cash Outflows

When Net Present Value = 0,

Present Value of all Cash Inflows = Present Value of all Cash Outflows

For computation of IRR, we have to compute the Present Value of Cash Inflows at two different levels, one at a level which gives Present Value at an amount lower than the Initial Investment and one at a level which gives Present Value at an amount higher than the Initial Investment.

We will first Compute Present Value of Cash Flow of all years at PVF @ 23%.

PV = Cash Flow*PVF

Cash Flow= 23000

PVF at 23% = 3.3270

Present Value of Cash Flow = 23000*3.3270

76521

Since at PVF 23% the amount is lower than the Initial Investment, now we have to compute the Present Value of all Cash Inflows at a rate which gives an amount higher than the initial investment. So now we will compute Present Value of Cash Flow of all years at PVF @ 20% (Lower the rate, higher the Present Value will be).

PV = Cash Flow*PVF

Cash Flow= 23000

PVF at 20% = 3.6046

Present Value of Cash Flow = 23000*3.6046

82905.8

We have computed PV at both 23% and 20% to get the Present Value at a level above the Initial Investment and at a level lower than Initial Investment.

Now we can compute the IRR using the following equation,

IRR = Lower Rate + [(Higher Rate - Lower Rate)/ (PV at Lower Rate - PV at Higher Rate)] * (PV at Lower Rate - Initial Investment)

/= 20 + [(23 - 20) / (82905.8 - 76521.83)] * (82905.8 -  79000)

21.8354

IRR = 21.84%

Note: The rate 23% and 20% is taken as an assumption to for lower rate and higher rate. The objective is to find a rate above and below the IRR rate. Student may take any rate above 22 for Higher Rate and any rate below 21 as lower rate, the answer would remain same.

Drawback of IRR

If later cash inflows are not sufficient to cover the initial investment IRR cannot be calculated.

I hope this solution helps you. If you require any further clarification, kindly let me know.

Thank you,