Question

A new computer system will require an initial outlay of $17,500, but it will increase the firm’s cash flows by $3,500 a year for each of the next 8 years. a. Calculate the NPV and decide if the system is worth installing if the required rate of return is 9%. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.) b. Calculate the NPV and decide if the system is worth installing if the required rate of return is 14%. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.) c. How high can the discount rate be before you would reject the project? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

Answer 1

a)

Computation of NPV for required rate of return 9 %

Year	Cash Flow (C)	PV factor computation	PV factor @ 9 % (F)	PV (= C x F)
0	($17,500)	1/(1+0.09)^0	1	($17,500.00000)
1	$3,500	1/(1+0.09)^1	0.917431192661	$3,211.009174
2	$3,500	1/(1+0.09)^2	0.841679993267	$2,945.879976
3	$3,500	1/(1+0.09)^3	0.772183480061	$2,702.642180
4	$3,500	1/(1+0.09)^4	0.708425211065	$2,479.488239
5	$3,500	1/(1+0.09)^5	0.649931386298	$2,274.759852
6	$3,500	1/(1+0.09)^6	0.596267326879	$2,086.935644
7	$3,500	1/(1+0.09)^7	0.547034244843	$1,914.619857
8	$3,500	1/(1+0.09)^8	0.501866279673	$1,756.531979
			NPV	$1,871.866902

NPV is $1,871.866902 or $1,871.87

As NPV is positive system is worth installing.

b)

Computation of NPV for required rate of return 14 %

Year	Cash Flow (C)	PV factor computation	PV factor @ 14 % (F)	PV (= C x F)
0	($17,500)	1/(1+0.14)^0	1	($17,500.00000)
1	$3,500	1/(1+0.14)^1	0.877192982456	$3,070.175439
2	$3,500	1/(1+0.14)^2	0.769467528470	$2,693.136350
3	$3,500	1/(1+0.14)^3	0.674971516202	$2,362.400307
4	$3,500	1/(1+0.14)^4	0.592080277370	$2,072.280971
5	$3,500	1/(1+0.14)^5	0.519368664360	$1,817.790325
6	$3,500	1/(1+0.14)^6	0.455586547684	$1,594.552917
7	$3,500	1/(1+0.14)^7	0.399637322530	$1,398.730629
8	$3,500	1/(1+0.14)^8	0.350559054851	$1,226.956692
			NPV	($1,263.976371)

NPV is ($1,263.976371) or ($1,263.98)

As NPV is negative, system is not worth installing.

c)

Let’s compute IRR of the system using excel:

	A	B
1	Year	Cash Flow
2	0	($17,500)
3	1	$3,500
4	2	$3,500
5	3	$3,500
6	4	$3,500
7	5	$3,500
8	6	$3,500
9	7	$3,500
10	8	$3,500
11	IRR	11.81%

If excel sheet looks like above table, insert formula “=IRR(B2:B10)” in cell B11 to get as 11.81%

Project is not acceptable, If rate of return is higher than IRR of the system which will result in negative NPV.

Hence project should be rejected, if discount rate is more than 11.81 %.