Question

3. A frozen food company plans to buy a freeze ray from Cisco Frost. The freeze ray has the following Costs and incomes: Initial cost of $5,000 in year 0 Maintenance costs of $2,000 per year from years 1 to 10. Income of $6,000 per year from years 5 to 10. Salvage income of $1,000 in Year 10. Background information: Before-tax MARR is 8%, and after-tax MARR is 6% The tax rate, t, is 25% Refrigeration equipment such as a freeze ray has a CCA rate of d 20% per year. Tax deductions can NOT be carried forward to future years. There is no recapture or terminal loss (the firm has other refrigeration equipment) a. (12 marks) What is the present worth of this investment? Show your work. Present Worth: b. (3 marks) Suppose that in Year 5, the company receives a one-time tax deduction of $500, AND a one- time refundable tax credit of $250. What is the present (Year 0) value of the benefits (tax savings) from these incentives? Show your work. Present value of benefits:

Answer 1

a]

The cash flows and NPV are calculated as below :

Depreciation in each year = (purchase price - accumulated depreciation) * 20%

In the years 1 to 4, there is no tax as there are losses, and they cannot be carried forward.

net cash from sale of equipment in year 10 = sale price - (sale price - book value) * (tax rate) = $1000 - ($1000 - ($5000 - $4463)) * (25%)

net cash flow in each year = income after taxes + depreciation

Present value of each year's cash flow is calculated using 6% discount rate. We use the after-tax MARR since we are calculating the after-tax cash flows. The sum of these present values is the NPV

NPV = $503

- K10/1.06^A10 L10 B A D E G H J K Net Cash from Sale PV of Net Income Income maintenance Accumulated before after Net Cash Cash Flow ($5,000) $5,000) ($2,000) $1,887) ($2,000) of Depreciation depreciation taxes Investment Revenue taxes equipment Flow Cost Taxes 1 Year ($5,000) 7 0 ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($2,000) ($1,000) ($800) ($640) ($512) ($410) ($328) ($262) ($210) ($168) ($134) ($1,000) ($3,000) ($1,800) ($2,440) $2,640) ($2,952) ($2,512) ($3,362) ($3,689) ($3,951) ($4,161) ($4,329) ($4,463) $0 ($3,000) ($2,800) $0 1 ($2,800) $0 ($1,780) ($2,000) ($1,679) ($2,000) $1,584) $3,102 2 ($2,640) $0 3 4 ($2,512) $2,693 6 $6,000 $3,590 ($898) ($918) ($934) ($948) ($958) ($966) $2,318 5 $6,000 $3,672 $2,754 $3,082 $2,173 6 $6,000 $3,738 $2,803 $3,066 $2,039 9 7 $6,000 $3,790 $2,843 $3,052 $1,915 $1,801 10 8 $6,000 $3,832 $2,874 $3,042 11 9 $2,188 $6,000 $3,866 $2,899 $884 $3,918 10 12 NPV $503 13

b]

cash inflow from tax deduction = deduction amount * tax rate = $500 * 25% = $125

cash inflow from tax credit = $250

total cash inflow in year 5 = $375

present value = $375 / (1 + 6%)⁵ = $280