Question

The machine is estimated to cost $100,000 which can last for 7 years before it becomes too costly to maintain and can be sold for scrap at $15,000. The project is estimated to bring in additional $30,000 cash inflow and incur $10,000 in additional expenses related to the running the machine in the first year. The company expects there will be an annual sales growth of 5% from year 2 onward. Expenses are also expected to grow by 2% annually from the second year of the operation.  

The company plans to fund the purchase of the new machine using a bank loan with an interest rate of 10%.

1. How long is the payback period for this project?  years. Case sensitive. Type in 7.00 (two decimal places) for 7 years.
2. What is the NPV for this project? $.  Case sensitive. Type in 120,000.00 (two decimal places) for $120,000.00, or -120,000.00 for negative $120,000.00.
3. What is the IRR for this project?  %.  Case sensitive. Type in 20.00 (two decimal places) for 20%.
4. p.s no other information given

Answer 1

The given is the below information:

Outlfow: 100,000

Cost of capital: 10%

Revenue : 30,000. Increase of 5% year on year

Cost: 10,000. Increase of 2% year on year

Scrap value end of 7 year is 15,000.

The cash flow is projected as given below

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7
Outflow	(100,000)
Sales- 5 % increase from year 2		30,000	31,500	33,075	34,729	36,465	38,288	40,203
Expenses- 2 % increase from year 2		(10,000)	(10,200)	(10,404)	(10,612)	(10,824)	(11,041)	(11,262)
Scrap Value								15,000
Cash flow	(100,000)	20,000	21,300	22,671	24,117	25,641	27,248	43,941

Payback period

Payback period is calculated as given below

Capital Investment	100,000
Cumulative Cash flow till year 4	88,088
Remaining Cost to be recovered (a)	11,912
Net Cash flow year 2 (b)]	25,641
Payback Period, year 4 (a) / (b)	0.46
Total Cash Payback period in years	4.46

NPV of the project

The cash flows are discounted using the cost of capital. Discounting factor is caculated basis the below formula

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7
Discounting Factor	1	=1/(1.1)^1	=1/(1.1)^2	=1/(1.1)^3	=1/(1.1)^4	=1/(1.1)^5	=1/(1.1)^6	=1/(1.1)^7
Discounting Factor	1.00	0.91	0.83	0.75	0.68	0.62	0.56	0.51

The NPV is calculated as given below

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7
Outflow	(100,000.00)
Sales- 5 % increase from year 2		30,000.00	31,500.00	33,075.00	34,728.75	36,465.19	38,288.45	40,202.87
Expenses- 2 % increase from year 2		(10,000.00)	(10,200.00)	(10,404.00)	(10,612.08)	(10,824.32)	(11,040.81)	(11,261.62)
Scrap Value								15,000.00
Cash flow	(100,000.00)	20,000.00	21,300.00	22,671.00	24,116.67	25,640.87	27,247.64	43,941.25
Discounting Factor	1.00	0.91	0.83	0.75	0.68	0.62	0.56	0.51
Discounted Cash flow = cash flow x disc factor	(100,000.00)	18,181.82	17,603.31	17,033.06	16,472.01	15,920.96	15,380.58	22,548.81
Total Discounted Cash flow	23,140.54

The NPV is 23,140.54

IRR of the proejct

IRR is when NPV is 0. This is calculated using trial and error method. Basis that, the IRR shall be as given below

Particulars	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6	Year 7
Outflow	(100,000.00)
Sales- 5 % increase from year 2		30,000.00	31,500.00	33,075.00	34,728.75	36,465.19	38,288.45	40,202.87
Expenses- 2 % increase from year 2		(10,000.00)	(10,200.00)	(10,404.00)	(10,612.08)	(10,824.32)	(11,040.81)	(11,261.62)
Scrap Value								15,000.00
Cash flow	(100,000.00)	20,000.00	21,300.00	22,671.00	24,116.67	25,640.87	27,247.64	43,941.25
Discounting Factor	1.00	0.86	0.74	0.64	0.55	0.48	0.41	0.35
Discounted Cash flow	(100,000.00)	17,247.96	15,841.46	14,540.99	13,339.78	12,231.27	11,209.23	15,589.31
Total Discounted Cash flow	0.00

The IRR is 0 when cost of capital is 15.96% and discounting is done at the same rate.