Question

Caspian Sea Drinks is considering the production of a diet drink. The expansion of the plant and the purchase of the equipment necessary to produce the diet drink will cost $25.00 million. The plant and equipment will be depreciated over 10 years to a book value of $1.00 million, and sold for that amount in year 10. Net working capital will increase by $1.21 million at the beginning of the project and will be recovered at the end. The new diet drink will produce revenues of $9.23 million per year and cost $2.24 million per year over the 10-year life of the project. Marketing estimates 10.00% of the buyers of the diet drink will be people who will switch from the regular drink. The marginal tax rate is 27.00%. The WACC is 12.00%. Find the IRR (internal rate of return).

Answer 1

Answer:

First of all we will calculate cash flow for each year,

	Year	Net Revenue per year = ($ 9.23 million -$ 2.24 million cost) =	Depreciation = (purchase value-salvage value at the end of life)/number of years) = ($25 million-$1million)/10 years	Profit before tax = Net revenue-Depreciation	tax @ 27% on profit before tax	Net cash flow = (profit before tax -tax + depreciation)
Equipment purchased	1					$          25.00
Working capital invested	1					$           -1.21
	1	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	2	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	3	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	4	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	5	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	6	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	7	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	8	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	9	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
	10	$                            6.99	$                                             2.40	$             4.59	$       1.24	$             5.75
Working capital	10					$             1.21

Now to find out IRR we will calculate NPV with two differenct discount rates,

	Year	Cash inflow =(A)	PV factor @ 12% =(B)	Present value of cash flow =('C) =(A*B)
	1	$       5.75	0.8929	$       5.13
	2	$       5.75	0.7972	$       4.58
	3	$       5.75	0.7118	$       4.09
	4	$       5.75	0.6355	$       3.65
	5	$       5.75	0.5674	$       3.26
	6	$       5.75	0.5066	$       2.91
	7	$       5.75	0.4523	$       2.60
	8	$       5.75	0.4039	$       2.32
	9	$       5.75	0.3606	$       2.07
	10	$       5.75	0.3220	$       1.85
	10	$       1.21	0.3220	$       0.39
(A)	Total present value of cash inflow =			$    32.88
(B)	Total value of initial investment			$   -23.79
(A)-(B)	NPV of project			$       9.09

at 12% discount rate NPV is positive. Hence, IRR must be higher than 12%. Now we will calculate NPV with 21% discount rate

	Year	Cash inflow =(A)	PV factor @ 21% =(B)	Present value of cash flow =('C) =(A*B)
	1	$       5.75	0.8264	$       4.75
	2	$       5.75	0.6830	$       3.93
	3	$       5.75	0.5645	$       3.25
	4	$       5.75	0.4665	$       2.68
	5	$       5.75	0.3855	$       2.22
	6	$       5.75	0.3186	$       1.83
	7	$       5.75	0.2633	$       1.51
	8	$       5.75	0.2176	$       1.25
	9	$       5.75	0.1799	$       1.03
	10	$       5.75	0.1486	$       0.85
	10	$       1.21	0.1486	$       0.18
(A)	Total present value of cash inflow =			$    23.49
(B)	Total value of initial investment			$   -23.79
(A)-(B)	NPV of project			$     -0.30

With 21% discount rate NPV is negative. Hence, IRR is less than 21%

Now we will calculate IRR with the help of above noted answers,

IRR =12% +  (Total value of cash inflow at 12% discount rate - total value of initial investment)

(Total value of cash inflow at 12% discount rate - total value of cash flow at 21% discount rate) x   

(differenceindiscountrate)

IRR =12% +  ($ 32.88 - $23.79)

($32.88 - $23.49 ) x   

(21-12)

IRR =12% +  ($ 9.09)

($9.39 ) x   $\left (9 \right )$%

IRR = 12% + (0.968051) x9%

IRR = 12% +8.71% = 20.71%(approx)