Question

Instructions:

You are required to use a financial calculator or spreadsheet (Excel) to solve the following capital budgeting problem (sample questions and solutions are provided for guidance): Windrunner Corp. is considering a new machine that requires an initial investment of $800,000 installed, and has a useful life of 10 years. The expected annual after-tax cash flows for the machine are $120,000 during the first 5 years, $150,000 during years 6 through 8 and $180,000 during the last two years.

(i) Develop the timeline (linear representation of the timing of cash flows)

(ii) Calculate the Internal Rate of Return (IRR)

(iii) Calculate the Net Present Value (NPV) at the following required rates of return: (a) 9% (b) 10% (c) 11% (d) 12%

(iv) Using IRR and NPV criterion, comment if the project should be accepted or rejected at the following required rates of return: (a) 9% (b) 10% (c) 11% (d) 12%

(v) Plot the Net Present Value profile (NPV on Y axis and rates of return on X-axis).

Answer 1

(i) The timeline is provided in the image below. The cash flow in year 0 is a cash outflow and hence it is indicated with a downward arrow. Rest of the cash flows are inflows and hence an upward arrow is used.

(ii) IRR is the rate which makes the NPV as nil. I have computed it using the trial and error method.

Year	Cash flow	1+r	PVIF	PV = cash flow*PVIF
0	-800,000.00	1.108569	1.00	-800,000.00
1	120,000.000		0.90	108,247.64
2	120,000.000		0.81	97,646.26
3	120,000.000		0.73	88,083.14
4	120,000.000		0.66	79,456.60
5	120,000.000		0.60	71,674.91
6	150,000.00		0.54	80,819.16
7	150,000.00		0.49	72,904.03
8	150,000.00		0.44	65,764.07
9	180,000.00		0.40	71,188.05
10	180,000.00		0.36	64,216.15
			NPV	0.00

Thus IRR = 1.108569 - 1 = 0.108569 or 10.8569%. This can be rounded off to 10.86% (2 decimal place)

(iii) Using the above formulas only of PV = PVIF*Cash flow we get the following NPVs

Rate	NPV
9%	72,444.27
10%	32,250.69
11%	-5,198.83
12%	-40,132.33

The NPV table for 12% rate is shown below:

Year	Cash flow	1+r	PVIF	PV = cash flow*PVIF
0	-800,000.00	1.12	1.00	-800,000.00
1	120,000.000		0.89	107,142.86
2	120,000.000		0.80	95,663.27
3	120,000.000		0.71	85,413.63
4	120,000.000		0.64	76,262.17
5	120,000.000		0.57	68,091.22
6	150,000.00		0.51	75,994.67
7	150,000.00		0.45	67,852.38
8	150,000.00		0.40	60,582.48
9	180,000.00		0.36	64,909.80
10	180,000.00		0.32	57,955.18
			NPV	-40,132.33

(iv) (a) At 9% the project should be accepted as NPV>0 and IRR>required rate of return

(b) At 10%  the project should be accepted as NPV>0 and IRR>required rate of return

(c) At 11% the project should be rejected as NPV<0 and IRR<required rate of return

(d) At 12% the project should be rejected as NPV<0 and IRR<required rate of return

(v) The plot is shown in the attached image below: