Solution manual cost accounting 14e by carter ch23

The payback method, which ignores the time value of money and all cash flows beyond the payback period for the project, is the measure of the time it will take to recover the initial cap

CHAPTER 23

DISCUSSION QUESTIONS

23-1

Q23-1 The weighted average cost of capital is

com-puted by the following steps:

(a) Calculate each component of capital as a

percentage of total capital.

(b) Calculate the after-tax cost of each

indi-vidual capital component.

(c) For each capital component, multiply (a)

by (b) and sum the results.

Q23-2 Using the cost of a specific source of funds

may lead to faulty decisions For example,

when debt is used, low-return projects would

be acceptable while better investments would

have to be ruled out in a following period, when

common stock shares are sold to obtain funds.

Q23-3 There are two problem areas associated with

estimating the firm’s weighted average cost of

capital—the proportions of each source of

funds and the cost of each source of funds.

The proportions that are expected over the

investment horizon should be used Since

these amounts are typically unknown, the

proportions desired by management in the

long run are usually used With respect to

costs, the market prices of each source of

funds should be used Since the market price

varies over time as creditor and investor

expectations change, current market prices

adjusted for changes expected by

manage-ment are commonly used.

CGA-Canada (adapted) Reprint with

permis-sion.

Q23-4 The payback (or payout) period method

mea-sures the length of time required by a project

to recover the initial investment outlay.

Q23-5 In computing the accounting rate of return on

original investment, the denominator is the

original investment, whereas in computing

the accounting rate of return on average

investment, the denominator is the average

investment.

Q23-6 The present value concept states that a dollar

received today is worth more than a dollar to

be received at a future date because of the

earnings the “today” dollar can generate in the

interim It is important in capital budgeting

because of the relatively long periods between the investment of funds and the return of those funds as earnings (i.e., dollars returned a long time in the future are worth considerably less than those invested today) Q23-7 The basic difference between the payback

method and the net present value method cerns the recognition of the time value of money The payback method, which ignores the time value of money and all cash flows beyond the payback period for the project, is the measure of the time it will take to recover the initial capital investment in net cash inflows The net present value method does con- sider the time value of money This method involves comparing the present value of all future cash inflows and outflows of a given project, using some minimum desired rate of return A positive result implies that the pro- ject’s rate of return exceeds this minimum rate, whereas a negative result indicates that the project’s rate of return is less than this mini- mum rate.

con-Q23-8 In the net present value method, the discount

rate is known; whereas, in the internal rate of return method, the discount rate is not known.

In the internal rate of return method, the count rate is the one that will result in a net present value of zero.

dis-Q23-9 The net present value method assumes that

earnings are reinvested at a rate of return equal to the firm’s cost of capital, whereas the internal rate of return method assumes that earnings are reinvested at the rate of return of the particular project being considered The firm’s cost of capital rate is more realistic If an investment proposal is predicted to be extremely profitable (e.g., having an internal rate of return of 50%), it is unlikely that similar proposals are available However, a firm should ordinarily have several investment opportuni- ties at or near the rate of its cost of capital CGA-Canada (adapted) Reprint with permis- sion.

Q23-10 Setting the discount rate at something in

excess of the cost of capital in order to

com-pensate for risk and uncertainty associated

with a capital expenditure proposal is

concep-tually unsound, because the reinvestment

potential of cash flows is overstated Cash

received in early periods has more value than

cash received in later periods, because only

the cash received in the early periods can be

reinvested As a consequence, the use of a

rate in excess of the reinvestment rate in the

net present value method will result in an

overstatement of the value of cash received early in the life of the capital expenditure proj- ect A better approach would be to compute the terminal value of the cash flows using the reinvestment rate (i.e., compute the value of all cash flows at the end of the life of the proj- ect), and then discount the total to present value at a risk-adjusted discount rate An even better approach is to explicitly consider uncer- tainty by using probability analysis, as dis- cussed in Chapter 24.

EXERCISES E23-1

Proportion After-Tax Weighted

Bonds (10% × (1 – 45% tax rate)) 30% 5.5% 1.65%

Preferred stock 10% 12.5% * 1.25%

Common stock and retained earnings 60% 15.0% ** 9.00%

*(12% × $100 par value for preferred stock) ÷ $96 market value

**($75,000 ÷ 50,000 shares of common stock) ÷ $10 market price per share

(1) Annual cash inflow before income tax $15,000 $15,000

Less depreciation (the same for financial accounting

and income tax purposes ($40,000 cost ÷

8 years)) 5,000

Annual taxable income $10,000

Annual income tax ($10,000 taxable income × 40%) 4,000 4,000 Annual income after taxes $ 6,000

Annual after-tax cash inflow $11,000

$40,000 initial cash outflow = 3.636 years to payback

$11,000 annual cash inflow

(2) $6,000 average annual income = 15 or 15% rate of return

$40,000 original investment on original investment

E23-4

(1) $33,000 initial cash outflow = 3.3 years to payback

$10,000 annual cash inflow

(2) Present value of annual cash inflows for six years

($10,000 annual cash inflow × 3.784) $37,840 Less initial cash outflow to acquire investment 33,000 Net present value of investment 4,840

(3) Cash desired at end of six years $33,000

Present value of $1 compounded annually at 15% × 432 Investment required $14,256 E23-5

(1) Present value of annual cash inflows for 10 years

($20,000 annual cash inflow × 5.216) $104,320 Present value of salvage value at end of 10-year life

($10,000 cash inflow from salvage × 270) 2,700 Present value of all cash inflows $107,020 Less initial cash outflow to purchase press (99,000) Net present value of investment $ 8,020 (2) Present $8,020 net present value

value index = $99,000 initial investment = 08101 or 8.1%

Present

Tax

Year Inflows Deduction (1) – (2) Rate (3) × (4) (1) – (5) @ 15% (6) × (7)

Present value of periodic after-tax cash inflows $516,911

Plus present value of after-tax salvage ($100,000 × (1 – 40%) × 247) 14,820

Present value of cash inflows over useful life of new airplane $531,731

Less initial cash outflow (cost of new airplane) 500,000

Net present value of investment $ 31,731

Cost of new machine $38,000

Trade-in allowance for old machine 18,000

Net cash outflow at beginning of project $20,000

Tax basis of old machine traded in 16,000

Tax basis of new machine $36,000

Annual cost of operating old machine $40,000

Annual cost of operating new machine 34,000

Annual cost savings with new machine $6,000

*Note that year 1 is actually the second year the old property is depreciated Therefore,

the recovery rate for the second year is used to compute the amount of depreciation

on the old property in the first year of the capital expenditure proposal.

E23-9 (Concluded)

Additional

New Old Machine New Income Tax Tax Inflow

Year Machine Machine (1) – (2) Machine (4) – (3) Rate (5) × (6) (4) – (7)

Total increase in periodic cash inflow $29,600

Less initial cash outlay for new machine 20,000

Increase in cash inflows over initial cash outlay for new machine $ 9,600

Present Present Net Value Value

Internal rate of return

Recommendation: The investment may be acceptable because the internal rate of

return exceeds the company’s cost of capital; however, the internal rate of return on

this project should be compared with the internal rate of return for other projects to

determine if this is the best use of available funds.

Cash Inflow PV of $1 PV of PV of $1 Cash

Cash Inflow PV of $1 PV of PV of $1 Cash

(3) Using the internal rate of return method, Project A is superior to Project B Using

the net present value method, Project B is more attractive than A The decision hinges on assumptions made about reinvestment of cash inflow Theory sug- gests resorting to the net present value method because the cost of capital rein- vestment assumption implicit in this method is considered more realistic than the internal rate of return method, where a reinvestment at the project’s internal rate is assumed.

PROBLEMS P23-1

Plan Financing After-Tax Cost Total Required Cost (a) Debt 12% × (1 – 40% tax rate) $10,000,000 7.20%

$10,000,000 (b) Debt 12% × (1 – 40% tax rate) $5,000,000 3.60%

$10,000,000

stock (1 – 4% issue cost) $10,000,000

8.29%

(c) Common $2.10 earnings per share $10,000,000 11.05%

stock ($20 × (1 – 5% issue cost)) $10,000,000

$90,000,000

$90,000,000 Common stock $2.10 earnings per share $60,000,000* 7.00%

$20 market price per share $90,000,000

9.33%

*3,000,000 shares outstanding × $20 market price per share

P23-1 (Concluded)

Plan Financing After-Tax Cost Total Required Cost

Water from City

of Grant Well

The City of Grant must also consider the offsetting increase in property and sales taxes

arising from the ongoing economic health of this part of the total business activity that

occurs within the city This consideration may cause the negotiated land price to be

reduced Of course, the uncertainty of the various estimates must be recognized.

P23-3 (Continued)

After-Tax PV of $1 PV of PV of $1 PV of Year Cash Flows @14% Cash Flows @ 16% Cash Flows

Project 1 internal rate of return

Project 2 After-Tax PV of $1 PV of PV of $1 PV of Year Cash Flows @ 16% Cash Flows @ 18% Cash Flows

Net present value $2,290 $(2,385)

Project 2 internal rate of return = + ×

P23-3 (Concluded)

(3) The net present value of Project 1 is greater than the net present value of Project

2 ($15,420 compared to $12,675); however, the internal rate of return for Project

1 is less than the internal rate of return for Project 2 (15.67% compared to 16.98%) As a result, it is not altogether clear which project is the more profitable The difference in rankings occurs because of the difference in the pattern of cash flows; i.e., the cash inflows for Project 1 are smaller in early years and larger in later years than those of Project 2 The internal rate of return for Project

2 is substantially larger than the company’s weighted average cost of capital It may not be possible for the cash flows received in early years to be reinvested

at a rate of return equal to the internal rate of return of Project 2; consequently, cash flows received from Project 2 may not be as valuable to the firm as indi- cated by the internal rate of return On the other hand, the weighted average cost

of capital is a realistic earnings rate expected by the company over the ment horizon Assuming that there is no difference in the riskiness of the expected cash flows for the two projects, it may be safer to rely on the net pres- ent value ranking than the internal rate of return This would mean that Project 1 should be selected.

invest-P23-4

Initial Outlay

Total payback in years 5.36

(2) Net after-tax cash inflows $5,250,000

Less depreciation 2,200,000

Net income over economic life of asset $3,050,000

Accounting rate of return

on original investment

= Net income Economic life Original investment

Net income over economic life of Machine 1 $500,000

Accounting rate of return

on original investment

Machine 2

Net after-tax cash inflows $1,400,000

Less depreciation 600,000

Net income over economic life of Machine 2 $800,000

Accounting rate of return

$ ,

500 000

125 000 4

Net present value of Machine 1 $60,875

*Present value of $1 received annually for 8 years from Table 23-2 of the text.

Net present value of Machine 2 $42,050

Net present value index for Machine 1 = Net present value

Initial cash outlay

= ye

P23-5 (Concluded)

(5) Machine 1

PV of Cash Inflow PV of $1 PV of PV of $1 Cash

Cash

Year Maintenance Capacity (2) + (3) ciation* (4) – (5) (6) × 40% (4) – (7)

($6,000 salvage × (1 – 40 tax rate)) 3,600

Total after-tax cash inflows $104,100

*The tax depreciation is determined by multiplying the depreciable basis of $54,000 (i.e., the

cash purchase price plus the tax basis of zero) by the MACRS percentages provided in Exhibit

22-4 of the text for the five-year property class.

(1)

Recovery of Initial Outlay

Less financial accounting depreciation

($54,000 cash + $4,000 book value – $6,000 salvage) 52,000

$ 48,500 Less tax on salvage ($6,000 salvage × 40 tax rate) 2,400

Net income over the life of the property $ 46,100

Net present value $ 11,269

*$13,500 cash inflow in year 7 plus $3,600 after-tax salvage.

Net present value index = $11,269

= 209

$54,000 (4)

*$13,500 cash inflow in year 7 plus $3,600 after-tax salvage.

Internal rate of return = + ×

= yea

= ye

Adjusted Estimate of

P23-7 (Continued)

Federal Income Net

Net Cash Deprec- (Loss) Income (Reduction) Inflows Year Inflows iation (1) – (2) Tax Rate (3) × (4) (1) – (5)

Total payback period in years 3.9

(2) Accounting rate of return on original investment:

Total inflation-adjusted after-tax cash inflow $240,985

Less financial accounting depreciation 100,000

Net income over economic life of project $140,985

Average = Net income = $140,985 = $14,099

annual return Economic life 10 years

Accounting rate

of return on original = Average annual return = $14,099 = 1410 or 14.10%

investment Original investment $100,000

P23-7 (Continued)

(3) Accounting rate of return on average investment:

Accounting rate of

return on average = Average annual return = $14,099 = 2820 or 28.20%

investment Original investment ÷ 2 $50,000

(4) Net present value and net present value index:

Net present value $ 24,883

Net present = Net present value $24,883 = 249

value index Required investment = $100,000

(5) Present value payback in years:

Recovery of Present Initial Cash Outlay Years

P23-7 (Concluded)

(6) Internal rate of return:

After-Tax Present Cash Flow Present Cash Flow Cash Value Discounted Value Discounted

Reduced Reduced Inventory Contribution Savings from Maintenance with CIM

Year Cost Setup Time Cost Avoided (1) + (2) + (3) + (4) CIM System (5) – (6)

P23-8 (Continued)

Year with CIM zation* (7) – (8) Rate (9) × (10) (7) – (11) Inflation (12) × (13)

Total Tax

Amorti-Recovery MACRS Depreci- Straight-Line Amorti- zation and Property 5-year ation Software Amortization zation Depreciation Year Tax Basis Property (1) × (2) Tax Basis Rate (4) × (5) (3) + (6)