Reading 27: Capital Budgeting-LOS a 习题精选

The operating cash flows equal the after-tax benefit plus the tax savings from depreciation. In the case of a replacement project, you must take the difference between the additional depreciation from the new asset minus the lost depreciation from the old asset. The firm gave up $10,000 per year for of depreciation on the old asset for years 1 and 2 of the new asset’s life.

CF1 = (revenue ? cost)1 × (1 ? tax rate) + net depreciation1 × (tax rate)
((40,000 ? 5,000) × 0.65) + [((0.33 × 100,000) ? 10,000) × (0.35)] = $30,800

(Study Session 8, LOS 28.a)

The total cash flow for the terminal year is equal to the operating cash flow plus the non-operating (or terminating) cash flow.
The operating cash flow equals:

CF3 = (revenue ? cost)3 × (1 ? tax rate) + net depreciation3 × (tax rate)
((40,000 – 5,000) × 0.65) + [((0.15 × 100,000) ? 0) × 0.35)] = $28,000

The year 3 non-operating cash flow equals:

Market or salvage value plus/minus tax consequences of selling it. The new machine will be sold for $20,000. The book value is:

$100,000 × 0.07 = $7,000
$20,000 – $7,000 = $13,000

The firm will pay taxes on the gain of:

13,000 × 0.35 = $4,550

Total terminal year cash flow = $28,000 + $20,000 – $4,550 = $43,450

Note: Once we have the project’s estimated cash flows, the next step in the process would be to calculate the net present value and internal rate of return for the project. (Study Session 8, LOS 28.a)

The initial outlay is the cost of the labeling machine, the shipping and installation costs, and the increase in net working capital (in this case the increase in spare parts inventory):

(?$50,000) + (?$7,500) + (?$2,000) = ?$59,500.

(Study Session 8, LOS 28.a)

The operating cash flows equal the after-tax benefit plus the tax savings from depreciation.

CF2 = Benefit2 × (1 ? tax rate) + depreciation2 ×  (tax rate)
($25,000 × 0.65) + ($57,500 × 0.32 × 0.35) = $22,690

Note that the shipping and installation costs are part of the depreciable basis for the machine. (Study Session 8, LOS 28.a)

The hotel and travel costs expended to research the projects would be expended whether Alias decided to take on the projects or not. The research costs are a sunk cost, which is a cash outflow that has previously been committed or has already occurred. Since these costs are not incremental, they should not be included as part of the analysis. Therefore Ralston’s statement is incorrect.

Atkinson’s statement is also incorrect. Although it is true that the expected inflation is built into the expected returns used to calculate the weighted average cost of capital, Atkinson and Ralston still need to adjust the project cash flows upward to account for inflation. If no adjustments are made to the project cash flows to account for inflation, the NPV will be biased downward. (Study Session 8, LOS 28.g)

The valuation method that shows the project’s impact on the value of the firm is net present value (NPV). To calculate NPV, we need to determine the initial investment outlay, the operating cash flows, and the terminal year cash flows. Then, we discount the cash flows at the WACC. The calculations are as follows:

Step 1: Initial Investment Outlay:

= cost of new machine + proceeds/loss from old machine + change in net working capital (NWC)

= -$90,000 + $30,000 - $6,800 + $5,000 = -$61,800 (cash outflow)

Details of calculation:

· Cost of new lathe = $90,000 outflow

· Sale of Old Machine:

o Sales price = $30,000 inflow

o Tax/tax credit: $6,800 outflow

§ = (Sales price – book value)*(tax rate) = (30,000 – 13,000)*0.4

· Change in NWC = $5,000 inflow

o DNWC = D current assets - D current liabilities = 20,000 – 25,000 = -5,000 (a decrease in working capital is a source of funds)

Step 2: Operating Cash Flows (years 1-4): Given as $16,800 inflow

Step 3: Terminal Value:

= year 5 cash flow + return/use of NWC + proceeds/loss from disposal of new machine + tax/tax credit

= $16,800 - $5,000 + $15,000 + $1,920 = $28,720 inflow

Details of calculation:

· Year 5 cash flow (given) = $16,800 inflow

· Working capital (reverse 5,000 initial inflow) = $5,000 outflow

· Sale of New Lathe:

o Sales price = $15,000 inflow

o Tax/tax credit: $1,920 inflow

§ = (Sales price – book value)*(tax rate)

§ Here, the Book value = Purchase price – depreciated amount. Using MACRS we have depreciated 78% of the value, or have 22% remaining. 0.22 * 90,000 = 19,800

§ Tax effect = (15,000 – 19,800)*(0.4) = -1,920, or a tax credit

Step 4: Calculate NPV:

NPV = -$61,800 + ($16,800 / 1.13¹) + ($16,800 / 1.13²) +($16,800 / 1.13³) +($16,800 / 1.13⁴) +($28,720 / 1.13⁵) = $3,759.

Since the NPV is positive, Patch Grove should replace the old lathe with the new one, because the new lathe will increase the firm’s value by the amount of the NPV, or $3,759.

You may also solve this problem quickly by using the cash flow (CF) key on your calculator.

Calculating NPVA with the HP12C?
Key Strokes	Explanation	Display
[f]→[FIN]→[f]→[REG]	Clear Memory Registers	0.00000
[f]→[5]	Display 5 decimals – you only need to do this once.	0.00000
61,800→[CHS]→[g]→[CF0]	Initial Cash Outlay	-61,800.00000
16,800→[g]→[CFj]	Period 1 Cash flow	16,800.00000
4→[g]→[Nj]	Cash Flow Occurs for 4 periods	4.00000
28,720→[g]→[CFj]	Period 5 Cash flow	28,720.00000
13→	WACC	13.00000
[f]→[NPV]	Calculate NPV	3,759.18363

Calculating NPVA with the TI Business Analyst II Plus→
Key Strokes	Explanation	Display
[2nd]→[Format]→[5]→[ENTER]	Display 5 decimals – you only need to do this once.	DEC= 5.00000
[CF]→[2nd]→[CLR WORK]	Clear Memory Registers	CF0 = 0.00000
61,800?[+/-]→[ENTER]	Initial Cash Outlay	CF0 = -61,800.00000
[↓]→16,800→[ENTER]	Period 1 Cash Flow	C01 = 16,800.00000
[↓] 4 [ENTER]	Frequency of Cash Flow 1	F01 = 4.00000
[↓]→28,720→[ENTER]	Period 2 Cash Flow	C02 = 28,720.00000
[↓]	Frequency of Cash Flow 2	F02 = 1.00000
[NPV]→13→[ENTER]	WACC	I = 13.00000
[↓]→[CPT]	Calculate NPV	NPV = 3,759.18363

The first year MACRS depreciation equals 60,000 × 20%, or 60,000 × 0.2 = 12,000.

Initial cash outlay = up-front costs (including cost) and changes in working capital. Here, the price of the machine is 60,000 and the working capital initally decreases 15,000 (which is a source of funds). Thus, the initial cash outlay = 60,000 cost ? 15,000 working capital = 45,000.

The first year's cash flow equals the after-tax impact of the 5,000 operating savings and the depreciation tax shield, or (5,000)(0.6) + (60,000)(0.2)(0.4) = 3,000 + 4,800 = 7,800.

The terminal cash flow = [Sales (salvage) price ? book value] × (1 ? tax rate) ± change in working capital. Here, = (10,000 ? 0) × (1 ? 0.40) ? 15,000 (increased working capital is a use of funds) = 6,000 ? 15,000 = ?9,000.

Firms that tend to have high operating leverage are those that invest up front to produce a product, but have low variable costs when it comes to distributing the product. A software development firm will have to spend a great deal of money up front to create the software, but the costs of distributing the software will be relatively low. Retailers and restaurants are more likely to have a variable cost structure, which would imply low operating leverage.