Question

Revenues generated by a new fad product are forecast as follows

year Revenues

1 $50,000

2 40,000

3 20,000

4 10,000

Expenses are expected to be 50% of revenues, and working capital required in each year is expected to be 20% of revenues in the following year. The product requires an immediate investment of $40,000 in plant and equipment.

Required:

a. What is the initial investment in the product? Remember working capital.

b. If the plant and equipment are depreciated over 4 years to a salvage value of zero using straight-line depreciation, and the firm’s tax rate is 30%, what are the project cash flows in each year? Assume the plant and equipment are worthless at the end of 4 years.

c. If the opportunity cost of capital is 12%, what is the project's NPV?

d. What is project IRR?

Answer 1

Statement hsowing cash flow due to changes in WC

Particulars	0	1	2	3	4
Revenue		50000	40000	20000	10000
WC (20% of revenues in the following year)	10000	8000	4000	2000	0
Change in WC	10000	-2000	-4000	-2000	-2000
Change in cash	-10000	2000	4000	2000	2000

Statement showing NPV

Particulars	0	1	2	3	4	NPV = Sum of PV
Investment in plant and equipment.	-40000
Revenue		50000	40000	20000	10000
Expenses(50% of revenue)		-25000	-20000	-10000	-5000
Depreciation (40000/4)		-10000	-10000	-10000	-10000
PBT		15000	10000	0	-5000
Tax @ 30%		-4500	-3000	0	1500
PAT		10500	7000	0	-3500
Add: Depreciation		10000	10000	10000	10000
Annual cash flow		20500	17000	10000	6500
Cash flow due to WC	-10000	2000	4000	2000	2000
Total cash flow	-50000	22500	21000	12000	8500
PVIF @ 12%	1.0000	0.8929	0.7972	0.7118	0.6355
PV	-50000.00	20089.29	16741.07	8541.36	5401.90	773.62

Thus NPV = $ 773.62

IRR is rate at which NPV is 0

Assume r = 13%, then NPV =

Particulars	0	1	2	3	4	NPV = Sum of PV
Total cash flow	-50000	22500	21000	12000	8500
PVIF @ 13%	1.0000	0.8850	0.7831	0.6931	0.6133
PV	-50000.00	19911.50	16446.08	8316.60	5213.21	-112.60

Using Interpolation we can find IRR

R	NPV
12%	773.62
13%	-112.6
1%	886.22
?	773.62

= 773.62/886.22

= 0.87

Thus IRR = 12%+ 0.87% = 12.87%

Ans)

a) Initial investment in the product = $50,000

b) Cash flow from project

Particulars	0	1	2	3	4
Total cash flow	-50000	22500	21000	12000	8500

c) NPV = $773.62

d) IRR = 12.87%