The following table presents sales forecasts for Golden Gelt Giftware. The unit
ID: 2673721 • Letter: T
Question
The following table presents sales forecasts for Golden Gelt Giftware. The unit price is $40. The unit cost of the giftware is $20.
Year Unit Sales
1 40,000
2 45,000
3 17,000
4 10,000
Thereafter 0
It is expected that net working capital will amount to 20% of sales in the following year. For example, the store will need an initial (year-0) investment in working capital of .20 × 40,000 × $40 = $320,000. Plant and equipment necessary to establish the Giftware business will require an additional investment of $218,000. This investment will be depreciated using MACRS and a 3-year life. After 4 years, the equipment will have an economic and book value of zero. The firm’s tax rate is 35%. What is the net present value of the project? The discount rate is 20%.
Explanation / Answer
a. The initial investment in this project are the $45,000 of plant and equipment plus the working capital of Year 1's sales, which amount to 0.2*40000=$8,000. Therefore, the initial investment is $53,000 b. The working capital required each year becomes smaller each year until it reaches 0 in Year 4. Since this question doesn't specify that the working capital depreciates over time, I'll assume it does not depreciate. Furthermore, I'll assume that this firm uses exactly the required working capital each year. This means that, each time a year passes, the firm will be left with excess working capital. I'll assume that the firm can sell this excess. For example, the required working capital in Year 0 is $8,000. The required working capital in Year 1 is 0.2*30000=$6,000. I'll assume then that the firm has an extra $2,000 in its cash flow this year, as a result of the sale of excess working capital. I'll also assume that no taxes are levied on this sale. Regarding depreciation, since we're using straight-line depreciation over 4 years to a salvage value of $0, and the initial value is $45,000, then depreciation each year is 45000/4 = $11,250. Since the tax rate is 40%, then the firm only gets to keep 60% of its income. The taxable income is Revenues - Expenses - Depreciation. Finally, depreciation should be added back to the cash flow. So these are the project cash flows: Year 0 -45,000 - 8,000 = -53,000 Year 1 0.6*[40,000 - 0.4*40,000 - 11,250] + 11,250 + 2,000 = $20,900 Year 2 0.6*[30,000 - 0.4*30,000 - 11,250] + 11,250 + 2,000 = $17,300 Year 3 0.6*[20,000 - 0.4*20,000 - 11,250] + 11,250 + 2,000 = $13,700 Year 4 10,000 - 0.4*10,000 + $2,000 = $8,000 Thereafter 0 Since in year 4 income net of depreciation is negative (10,000 - 0.4*10,000 - 11,250 = -$5,250), I assumed that no tax is levied; hence the different calculations. As you can see, I've made several assumptions throughout this question, which may be not what you had in mind. Please check that these assumptions are correct or if you're curently working with different ones. In any case, I think the reasoning is clear enough in order to re-calculate the results under different assumptions. Please request clarification otherwise. c. The project NPV is: NPV = -53,000 + 20,900/1.12 + 17,300/1.12^2 + 13,700/1.12^3 + 8,000/1.12^4 = -5712 At this discount rate, the project should not be undertaken. d. Plugging the cash flow values in Excel, we get that the IRR is 5.96%
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