Question

You are manager of a manufacturing business. Business is going very well and one production line is at full capacity. You want to double the size of the production line. Engineering has estimated the cost and time required. It can be accomplished without effecting the existing production. The timing of the cash flows for the facility is as follows.

Month	Cash Flow
1	$       (20,000.00)
2	$       (45,000.00)
3	$       (55,000.00)
4	$       (70,000.00)
5	$       (75,000.00)
6	$       (80,000.00)
7	$       (90,000.00)
8	$       (90,000.00)
9	$     (120,000.00)
10	$     (140,000.00)
11	$     (180,000.00)
12	$     (200,000.00)
13	$     (225,000.00)
14	$     (175,000.00)
15	$     (200,000.00)
16	$       (50,000.00)
Total	$ (1,815,000.00)

The current cost of capital is 9% APR. What is the total cost of the project?

You pay interest on the project every year (i.e., you do not pay off the capital, only the interest.) Calculate the total project cost including interest. Use annual numbers to calculate the internal rate of return.

Sales start after the project is completed. You estimate that sales for the first year will be at 30% of capacity and increase to 60% in year 2. Sales after year 2 are estimated at 85% of capacity. The current production line generates $1,100,000 in net profit. The profit at 30% is 0. The profit above 30% will be proportional to the percent capacity utilized. The company demands a minimum 20% internal rate of return for capital projects. Does the 10-year rate of return meet the company requirements? Assume that the company pays interest on the capital for the entire ten years. (Show correct total project cost including Interest, 10 year cash flow, and IRR for project)

Please identify formulas and explain why. Thank you!

Answer 1

Month = n	Cash Flow	Int.=Cash flow*9%*(16-n)/12
1	20,000	2250
2	45,000	4725
3	55,000	5363
4	70,000	6300
5	75,000	6188
6	80,000	6000
7	90,000	6075
8	90,000	5400
9	120,000	6300
10	140,000	6300
11	180,000	6750
12	200,000	6000
13	225,000	5063
14	175,000	2625
15	200,000	1500
16	50,000	0
Total	1,815,000	76,838	1,891,838
Total capital incl.int. at timt =mth 16 end=1815000+76838=1891838
Future value at time mth 16 end=1891838
So, value(PV) of the total capital at t=0 (beginning of the yr.)=
PV=1891838/(1.0075)^4=
1836131

Explanation for-- Int.=Cash flow*9%*(16-n)/12 (Column 3)

Given that "total project cost to be calculated including interest"

Formula used for purpose of calculation in EXCEL.

Interest for the amount borrowed (assuming end of month borrowing)at the rate of 9% p.a for ,so many months,

ie.amt. was borrowed over a period of 16 months.

20000*9%*15/12=2250

45000*9%*14/12=4725

55000*9%*13/12=5363

& so on till 16 the mth(which carries no interest as 16-16-0)

At the end of 16 months, total interest comes to $ 76838

which when added to the principal ,puts the cost of the total investment(Principal+interest) at time t=16 mths.= 1891838.

Then this 1891838 was brought down(discounted) to its Present Value at end of t=12 mths or beginning of the next time= 0 as 1836131 using monthly interest of 9% /12 =0.0075

Year		Capacity utilised
Yr. 0 Project cost	-1836131
1	0	30%		Profit at 30%	0
2	660000	60%		100% capacity	1100000
3	935000	85%		60%	1100000/100*60=	660000
4	935000	85%		85%	1100000/100*85=	935000
5	935000	85%
6	935000	85%
7	935000	85%
8	935000	85%
9	935000	85%
10	935000	85%
IRR	32.60%
Cash flows after annual interest at 9%*1836131=165252
Year		Capacity utilised
Yr. 0 Project cost	-1836131
1	-165252	30%
2	494748	60%
3	769748	85%
4	769748	85%
5	769748	85%
6	769748	85%
7	769748	85%
8	769748	85%
9	769748	85%
10	769748	85%
IRR	24.84%
Given,
The company demands a minimum 20% internal rate of return for capital projects
As the IRR in both the above cases >20%, the project is recommended.