Question

A and B COMPANY puchase a machine .the cost of capital is 12% .the cost ofd the machine is $35,000 and is expected to provide additional net cash flows of $5000 per year .the machine will last for 15 years .calculate the NPV and IRR. (B) The machine are willing to offer a permanent service contract for an annual fee of $500 .this will keep the machine new always for ever.the net cash flows will be reduced to $4500 per year .calculate npv and irr for the purchase accompained by service contract.

Answer 1

A) Computation of NPV and IRR at No Service Contract

NPV

(In $)

Year	Cash Flow	Discounting Factor (DF) @12%	Present Value (PV)
0	(35,000)	1	(35,000)
1-15	5,000	6.811	34,055
15	0 (Salvage Value)	0.181	0
	NPV		(945)

NPV = $(945)

IRR Computation

Since at 12% the NPV is negative the IRR must be less than 12% because at IRR present Value of Cash Outflows (PVCO) must be equal to Present Value of Cash Inflows (PVCI).

i.e. PVCI must be $ 35,000 at IRR.

We will use trial and error method for computing IRR as follows :-

Year	Cash Flow	DF @ 10%	PV	DF @ 11%	PV
1-15	5000	7.606	38,030	7.191	35,955

Assume Rate 1 = 10% (Since less than 12%).

Assume Rate 2 = 12% (Since at 10% the PVCI is more than $35000, hence we need to increase rate from 10% but must be below 12%).

At discount rate of 12% (For NPV) the PVCI is 34,055. If we decrease the rate by 1% i.e. 11% than the PVCI = 35,955.

We need to Increase PVCI only by $945 (35000-34055), however a one percent decrease in rate result into increase in PVCI by $1900 (35,955-34,055).

Thereby for Increase of $ 945 the decrease in rate must be = (945*1)/1900 = 0.497%.

Therefore the IRR = 12-0.497 =11.503%.

There may be minor difference from exact IRR due to the rounding off differences.

B) Computation of NPV and IRR at No Service Contract

It is prominent to note that with Service contract the Machine will always be new, that means at the end of machine life we will get full Salvage Value of $ 35,000.

NPV Computation

(In $)

Year	Cash Flow	Discounting Factor (DF) @12%	Present Value (PV)
0	(35,000)	1	(35,000)
1-15	4,500	6.811	30,649.50
15	35,000	0.181	6,335
	NPV		1,984.50

NPV = $1984.50.

Computation of IRR

At IRR PVCI = PVCO

?At 12% the NPV is positive that means the IRR must be more than 12%.

Using Trail and Error Method as follows :-

Year	Cash Flow	DF @ 14%	PV	DF @ 13%	PV
1-15	4,500	6.142	27,639	6.462	29,079
15	35,000	0.14	4,900	0.16	5,600
	PVCI		32,539		34,679

Assumption Rate 1 = 14% (Since more than 12%).

Assumption Rate 2 = 13%(Since at 14% PVCI is less than $35,000. IRR must be between 12% and 14%. hence 13% assumed).

At the rate of 14% the PVCI is $32,539. So we have to increase the PVCI by $2,461 (35,000-32,539).

A decrease in rate by 1% increase PVCI by $ 2,140 (34,679-32,539).

Hence we need a further incraese in PVCI by $321(2,461-2,140) by decreasing in rate.

So the decrease in rate would be = (321*1)/2140 =0.15%.

Hence the IRR =13-0.15 =12.85%.

There may be minor difference from exact IRR due to the Rounding off Errors.

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