Question

FUN Corp. is planning to add a new doll “Lisa” to their production line. Instead of purchasing a third-party research report, the marketing department of FUN Corp. conducted their own analysis which saved at least $20,000 for the firm. The assumptions about the expected revenues, expenses and capital investments are presented as the followings. (All numbers are in thousands of US dollars).

Assumptions:

• Please assume that the analysis is taking place at the end of Year 0. FUN Corp can undertake this project for 4 years OR for 5 years.
• Expected revenues for the next 5 year are:

	Year 1	Year 2	Year 3	Year 4	Year 5 (if applicable)
Revenues	10,000	20,000	22,000	15,000	8,000

• Cost of goods sold is expected to be 20% of that year’s revenue.
• Capital investment of machinery is $40,000 and will be paid in 2 equal installments ($20,000 each) at the beginning of Year 1 and Year 2.
• The full amount of machinery will be depreciated to zero using a straight-line method over 5 years. FUN Corp. have the option to stop the project and sell the machinery for $10,000 at the end of Year 4. Otherwise, the machinery will be worth nothing ($0) on the market by the end of Year 5.
• Net working capital equal to 10% of the following year’s projected sales. NWC will be fully recovered by the end of the project (whenever it ends).
• If the firm undertakes the doll “Lisa”, the free cash flow from existing doll “Amy” is projected to increase by $1,000 in Year 1, $3,000 in Year 2, $3,500 in Year 3 due to better brand recognition.
• Corporate income tax rate is 30%. The cost of capital for this project is estimated to be 20%.

Please answer the following questions:

1. What is the NPV of the project if the firm undertakes it for 5 years? What if for 4 years?
2. What is the payback period of the project if the firm undertakes it for 5 years? What if for 4 years?
3. How long would you recommend the firm to undertake this project for? Why?

Answer 1

The working of worksheet shown below has following assumptions

All costs & values that impact cash flow negatively are shown in negative values

Cost of Goods sold are given.

Depreciation = (Equipment cost - Salvage Value) / Number of years of depreciation

Depreciation = (40000 -0) / 5 = 8,000

Tax is 30% on EBIT

Working Capital for year 0 = 0 . In subsequent years, it is the difference of previous and current year. If Working capital is increasing, it will bring down cash flow, thus shown as negative

So year, Working Capital for year 0 (Sales of next year X 10%) = 10% x Sales = 10000 x 10% =1000

The investment in WC in year 2 = (10% x 20000 -1000) = 1000. Because this will negatively impact cash flow, it is shown as negative. Like wise for subsequent years

In the terminal year, all investments in WC are returned back (for the 5 year project) = (1000+1000+200-700) = 1500

In the year 4, equipment would be sold at $10000

Net Cash flows from sale of equipment = Cash Flows from sale of equipment - Taxes

Tax on sale of equipment = (Sales Price - Book Value) x Taxes

Book Value = Purchase Price - Accumulated dividends

If the equipment is sold in 4th year,

Book Value = 40000 - 8000 x 4

= 40000 - 32000 =8000

Tax on sale of equipment = (10000 - 8000) x 30% = 600

Net Cash flows from sale of equipment = 10000 - 600 = 9400

Cash Flow = (Net Income + Depreciation + Net working capital investments + Return of Net working capital + Capital Expenditure + Cash flow from of equipment + Taxes) *

*Sign of cash flows are important here. One which increases CF is positive, other which decreases Cf is negative

PV of cash flows = CFt/ (1+k)^t

where CFt is cash flow in year t, k = Cost of capital (WACC) & t is the year of Cash flow

NPV = Sum of PV of all future cash flows - Sum of PV of all Investment

a. The NPV if the project is for 5 year = $6286

The NPV if the project is for 4 year = $8175.20

B. The pay back period if the project is for 5 years = 2.91 yrs

The pay back period if the project is for 4 years = 2.91 yrs

C. Firm should undertake the project for 4 years as it is generating a higher NPV than the 5 yr project, at 20% discount rate

The below sheets shows the workings for all 3

If the project continues for 5 years

Revenue forecast	0	1	2	3	4	5
Revenues (A)		10,000	20,000	22,000	15,000	8,000
COGS (B)		(2,000)	(4,000)	(4,400)	(3,000)	(1,600)
Depreciation (C = G/20)		(8,000)	(8,000)	(8,000)	(8,000)	(8,000)
EBT (D = A + B + C )		-	8,000	9,600	4,000	(1,600)
Taxes @ 30% (E = D x 30%)		-	(2,400)	(2,880)	(1,200)	480
Net Income (F = D + E)		-	5,600	6,720	2,800	(1,120)
Depreciation (D)		8,000	8,000	8,000	8,000	8,000
Net Working Capital Investments (G = Current WC - Previous WC)		(1,000)	(1,000)	(200)	700
Return of Net Working Capital (H)						1,500
Capital Expenditure on Building (I)		(20,000)	(20,000)
Cash Flow from Sale of Equipment (J)
Tax paid on sale of Equipment (K)
Free Cash Flow (O =F + D + G+ H + I+ J+ K)	-	(13,000)	(7,400)	14,520	11,500	8,380
Additional FCF of Amy (P)		1,000	3,000	3,500
Total Free Cash Flows for the firm (O+P)		(12,000)	(4,400)	18,020	11,500	8,380
Discount Rate	20%
PV of cash Flows		(10,000)	(3,056)	10,428	5,546	3,368
NPV	6,286
Working Capital P (10% of nest yr sale	1,000	2,000	2,200	1,500	800	-

NPV = (-10000 - 3056 + 10428 + 5546 + 3368) = $6286

If the project continues for only 4 years

Revenue forecast	0	1	2	3	4
Revenues (A)		10,000	20,000	22,000	15,000
COGS (B)		(2,000)	(4,000)	(4,400)	(3,000)
Depreciation (C = G/20)		(8,000)	(8,000)	(8,000)	(8,000)
EBT (D = A + B + C )		-	8,000	9,600	4,000
Taxes @ 30% (E = D x 30%)		-	(2,400)	(2,880)	(1,200)
Net Income (F = D + E)		-	5,600	6,720	2,800
Depreciation (D)		8,000	8,000	8,000	8,000
Net Working Capital Investments (G = Current WC - Previous WC)		(1,000)	(1,000)	(200)
Return of Net Working Capital (H)					2,200
Capital Expenditure on Building (I)		(20,000)	(20,000)
Cash Flow from Sale of Equipment (J)					10,000
Tax paid on sale of Equipment (K)					(600)
Free Cash Flow (O =F + D + G+ H + I+ J+ K)	-	(13,000)	(7,400)	14,520	22,400
Additional FCF of Amy (P)		1,000	3,000	3,500
Total Free Cash Flows for the firm (O+P)		(12,000)	(4,400)	18,020	18,000
Discount Rate	20%
PV of cash Flows		(10,000)	(3,056)	10,428	10,802.20
NPV	8175.20
Working Capital P (10% of next yr sale	1,000	2,000	2,200	1,500	-

NPV = (-10000 - 3056 + 10428 + 10802.20) = $8175.20

Pay Back Period

Year	Total FCF from 5 yr project	Cumulative CF from 5 yr Project	Total FCF from 4 yr project	Cumulative CF from 4 yr Project
0	0	0	0	0
1	-12000	-12000	-12000	-12000
2	-4400	-16400	-4400	-16400
3	18020	1620	18020	1620
4	11500	13120	22400	24020
5	8380	21500
Pay Back Period		2.91		2.91

Pay Back Period = The last year in which cumulative cash flows are negative + Cumulative cash flows in this year / Cash flows in next year

= 2 + (16400/ 18020) = 2 + 0.91 years = 2.91 years