Cost of capital is the weighted minimum desired average rate that a company must pay for long-term capital while discounted rate of return is the maximum rate of interest that could be p
Trang 1CHAPTER 20 CAPITAL BUDGETING DECISIONS
I Questions
1 A capital investment involves a current commitment of funds with the expectation of generating a satisfactory return on these funds over a relatively extended period of time in the future
2 Cost of capital is the weighted minimum desired average rate that a company must pay for long-term capital while discounted rate of return
is the maximum rate of interest that could be paid for the capital employed over the life of an investment without loss on the project
3 The basic principles in capital budgeting are:
1 Capital investment models are focused on the future cash inflows and outflows - rather than on net income
2 Investment proposals should be evaluated according to their differential effects on the company’s cash flows as a whole
3 Financing costs associated with the project are excluded in the analysis of incremental cash flows in order to avoid the “double-counting” of the cost of money
4 The concept of the time value of money recognizes that a peso of present return is worth more than a peso of future return
5 Choose the investments that will maximize the total net present value of the projects subject to the capital availability constraint
4 The major classifications as to purpose are:
1 Replacement projects
- those involving replacements of worn-out assets to avoid disruption of normal operations, or to improve efficiency
2 Product or process improvement
- projects that aim to produce additional revenue or to realize cost savings
3 Expansion
- projects that enhance long-term returns due to increased profitable volume
5 Greater amounts of capital may be used in projects whose combined returns will exceed any alternate combination of total investment
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Trang 26 No This implies that any equity funds are cost free and this is a dangerous position because it ignores the opportunity cost or alternative earnings that could be had from the fund
7 Yes, if there are alternative earnings foregone by stockholders
8 Capital budgeting screening decisions concern whether a proposed investment project passes a preset hurdle, such as a 15% rate of return Capital budgeting preference decisions are concerned with choosing from among two or more alternative investment projects, each of which has passed the hurdle
9 The “time value of money” refers to the fact that a peso received today
is more valuable than a peso received in the future A peso received today can be invested to yield more than a peso in the future
10 Discounting is the process of computing the present value of a future cash flow Discounting gives recognition to the time value of money and makes it possible to meaningfully add together cash flows that occur at different times
11 Accounting net income is based on accruals rather than on cash flows Both the net present value and internal rate of return methods focus on cash flows
12 One simplifying assumption is that all cash flows occur at the end of a period Another is that all cash flows generated by an investment project are immediately reinvested at a rate of return equal to the discount rate
13 No The cost of capital is not simply the interest paid on long-term debt The cost of capital is a weighted average of the individual costs of all sources of financing, both debt and equity
14 The internal rate of return is the rate of return on an investment project over its life It is computed by finding that discount rate that results in a zero net present value for the project
15 The project profitability index is computed by dividing the net present value of the cash flows from an investment project by the investment required The index measures the profit (in terms of net present value) provided by each peso of investment in a project The higher the project profitability index, the more desirable is the investment project
16 Neither the payback method nor the simple rate of return method considers the time value of money Under both methods, a peso
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Trang 3received in the future is weighed the same as a peso received today Furthermore, the payback method ignores all cash flows that occur after the initial investment has been recovered
II Matching Type
III Exercises
Exercise 1 (Simple Rate of Return Method)
The annual incremental net operating income is determined by comparing the operating cost of the old machine to the operating cost of the new machine and the depreciation that would be taken on the new machine: Operating cost of old machine P33,000 Less operating cost of new machine 10,000 Less annual depreciation on the new machine (P80,000
÷ 10 years) 8,000 Annual incremental net operating income P15,000
Cost of the new machine P80,000 Less scrap value of old machine 5,000 Initial investment P75,000
Exercise 2 (Basic Present Value Concepts)
1 a P400,000 × 0.794 = P317,600
b P400,000 × 0.712 = P284,800
2 a P5,000 × 4.355 = P21,775
b P5,000 × 3.685 = P18,425
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Simple rate
of return = Annual incremental net operating income Initial investment
Trang 43 The factor for 10% for 20 years is 8.514 Thus, the present value of Tom’s winnings would be:
P50,000 × 8.514 = P425,700
Whether or not Tom really won a million pesos depends on your point
of view She will receive a million pesos over the next 20 years;
however, in terms of its value right now she won much less than a
million pesos as shown by the present value computation above
Exercise 3 (After-Tax Costs)
Multiply by 1 – 0.30 × 0.70
After-tax cost P 70,000
b Increased revenues P40,000
Multiply by 1 – 0.30 × 0.70
After-tax cash flow (benefit) P28,000
which has the effect of reducing taxes by 30% of that amount, or P9,000 per year
Exercise 4 (Basic Net Present Value Analysis)
Year(s) Cash Flows Amount of Factor 12% of Cash Flows Present Value
Sale of the stock 4 P22,500 0.636 14,310
*900 shares × P0.80 per share per year = P720 per year
No, Ms Cruz did not earn a 12% return on the share The negative net present value indicates that the rate of return on the investment is less than the discount rate of 12%
Exercise 5 (Internal Rate of Return and Net Present Value)
1
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Factor of the internal
rate of return = Required investmentAnnual cash inflow
Trang 5A factor of 5.468 represents an internal rate of return of 16%.
2
Item Year(s) Cash Flows Amount of Factor 16% of Cash Flows Present Value
Initial investment Now P(136,700) 1.000 P(136,700) Net annual cash inflows 1-14 P25,000 5.468 136,700 Net present value P 0
The reason for the zero net present value is that 16% (the discount rate) represents the machine’s internal rate of return The internal rate of return
is the rate that causes the present value of a project’s cash inflows to just
3
The 6.835 factor is closest to 6.982, the factor for the 11% rate of return Thus, to the nearest whole percent, the internal rate of return is 11%
Exercise 6 (Basic Net Present Value and Internal Rate of Return Analysis)
1
Item Year(s) Cash Flows Amount of Factor 15% Present Value of Cash Flows
Yes, this is an acceptable investment Its net present value is positive, which indicates that its rate of return exceeds the minimum 15% rate of return required by the company
2
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Factor of the internal
rate of return = Required investmentAnnual cash inflow
Factor of the internal
rate of return = Net annual cash inflowInvestment required
Trang 6A factor of 5.575 represents an internal rate of return of 16%.
3
A factor of 5.650 represents an internal rate of return of 12% The company did not make a wise investment because the return promised
by the machine is less than the required rate of return
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Factor of the internal
rate of return = Net annual cash inflowInvestment required
Trang 7IV Problems
Problem 1 (Equipment Replacement Sensitivity Analysis)
Requirement 1
Total Present Value
A New Situation:
Recurring cash operating costs (P26,500 x
2.69)
P 71,285
Recurring cash operating costs (P45,000 x
2.69)
P121,050
Disposal value of old equipment four years
hence
(P2,600 x 0.516)
(1,342)
Requirement 2
Payback period for the new equipment =
Requirement 3
Let X = annual cash savings
Let O = net present value
X (2.69) + P5,000 - P44,000 - P1,342 = O
2.69X = P40,342
X = P14,997
If the annual cash savings decrease from P18,850 to P14,997 or by P3,503, the point of indifference will be reached
Another alternative way to get the same answer would be to divide the net present value of P9,423 by 2.690
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P44,000 – P5,000 P18,500
Trang 8Problem 2
Annual cash expenses of the manual bookkeeping
After Tax
P126,718
_
* The P15,600 tax benefit of the loss on the disposal of the computer at the end
of year 3 is computed as follows:
Estimated book value:
Accumulated depreciation 48,800 51,200
Tax effect of estimated loss P(15,600) Since the net present value is positive, the computer should be purchased replacing the manual bookkeeping system
Problem 3
Requirement 1
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Trang 9(a) Purchase price of new equipment P(300,000) Disposal of existing equipment:
Tax rate 0.4
(b) Increased cash flows resulting from
change in contribution margin:
Depreciation tax shield:
Depreciation on new equipment
Depreciation on existing equipment
Increased depreciation charge P48,000
_
* The new equipment is capable of producing 20,000 units, but ETC Products can sell only 18,000 units annually
The sales manager made several errors in his calculations of required investment and annual cash flows The errors are as follows:
Required investment:
- The cost of the market research study (P44,000) is a sunk cost because it was incurred last year and will not change regardless of whether the investment is made or not
- The loss on the disposal of the existing equipment does not result in an actual cash cost as shown by the sales manager The loss on disposal results in a reduction of taxes, which reduces the cost of the new equipment
Annual cash flows:
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Trang 10- The sales manager considered only the depreciation on the new equipment rather than just the additional depreciation which would result from the acquisition of the new equipment
- The sales manager also failed to consider that the depreciation is a noncash expenditure which provides a tax shield
- The sales manager’s use of the discount rate (i.e., cost of capital) was incorrect The discount rate should be used to reduce the value of future cash flows to their current equivalent at time period zero
Requirement 2
Problem 4
Requirement 1: P(507,000)
Requirement 2: P(466,200)
Requirement 3: P(23,400)
Problem 5
1 The net annual cost savings is computed as follows:
Reduction in labor costs P240,000 Reduction in material costs 96,000 Total cost reductions 336,000 Less increased maintenance costs (P4,250 × 12) 51,000 Net annual cost savings P285,000
2.Using this cost savings figure, and other data provided in the text, the net present value analysis is:
Year(s) Cash Flows Amount of Factor 18%
Present Value of Cash Flows
Cost of the machine Now P(900,000) 1.000 P (900,000)
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Trang 11Installation and software Now P(650,000) 1.000 (650,000) Salvage of the old machine Now P70,000 1.000 70,000 Annual cost savings 1-10 P285,000 4.494 1,280,790 Overhaul required 6 P(90,000) 0.370 (33,300) Salvage of the new machine 10 P210,000 0.191 40,110 Net present value P (192,400)
No, the etching machine should not be purchased It has a negative net present value at an 18% discount rate
3 The intangible benefits would have to be worth at least P42,813 per year as shown below:
Thus, the new etching machine should be purchased if management believes that the intangible benefits are worth at least P42,813 per year
to the company
Problem 6
Items and Computations Year(s)
(1) Amount
(2) Tax Effect
(1) × (2) After-Tax Cash Flows
12%
Factor
Present Value of Cash Flows
Investment in new trucks Now P(450,000) P(450,000) 1.000 P(450,000) Salvage from sale of the old trucks Now P30,000 1 – 0.30 P21,000 1.000 21,000 Net annual cash receipts 1-8 P108,000 1 – 0.30 P75,600 4.968 375,581 Depreciation deductions* 1-8 P56,250 0.30 P16,875 4.968 83,835 Overhaul of motors 5 P(45,000) 1 – 0.30 P(31,500) 0.567 (17,861) Salvage from the new trucks 8 P20,000 1 – 0.30 P14,000 0.404 5,656 Net present value P 18,211
* P450,000 ÷ 8 years = P56,250 per year
Since the project has a positive net present value, the contract should be accepted
Problem 7
1
A factor of 3.812 equals an 18% rate of return
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Required increase in net present value
P192,400 4.494 = P42,813
Factor of the internal
rate of return = Required investmentAnnual cash inflow
Trang 12Verification of the 18% rate of return:
Amount of Cash Flows
18%
Factor
Present Value
of Cash Flows
Investment in equipment Now P(142,950) 1.000 P(142,950) Annual cash inflows 1-7 P37,500 3.812 142,950 Net present value P 0
2
We know that the investment is P142,950, and we can determine the factor for an internal rate of return of 14% by looking at the PV table along the 7-period line This factor is 4.288 Using these figures in the formula, we get:
Therefore, the annual cash inflow would have to be:
P142,950 ÷ 4.288 = P33,337
3 a 5-year life for the equipment:
The factor for the internal rate of return would still be 3.812 [as computed in (1) above] Reading along the 5-period line of the PV table,
a factor of 3.812 is closest to 3.791, the factor for 10% Thus, to the nearest whole percent, the internal rate of return is 10%
b 9-year life for the equipment:
The factor of the internal rate of return would again be 3.812 From the
PV table, reading along the 9-period line, a factor of 3.812 is closest to 3.786, the factor for 22% Thus, to the nearest whole percent, the internal rate of return is 22%
The 10% return in part (a) is less than the 14% minimum return that Dr Blue wants to earn on the project Of equal or even greater importance, the following diagram should be pointed out to Dr Blue:
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Factor of the internal
rate of return = Required investmentAnnual cash inflow
P142,950
Trang 13As this illustration shows, a decrease in years has a much greater impact on the rate of return than an increase in years This is because of
the time value of money; added cash inflows far into the future do little
to enhance the rate of return, but loss of cash inflows in the near term
can do much to reduce it Therefore, Dr Blue should be very concerned
about any potential decrease in the life of the equipment, while at the same time realizing that any increase in the life of the equipment will
do little to enhance her rate of return
4 a The expected annual cash inflow would be:
P37,500 x 120% = P45,000
Reading along the 7-period line of the PV table, a factor of 3.177 is closest to 3.161, the factor for 25%, and is between that factor and the factor for 24% Thus, to the nearest whole percent, the internal rate of return is 25%
b The expected annual cash inflow would be:
P37,500 x 80% = P30,000
Reading along the 7-period line of the PV table, a factor of 4.765 is closest to 4.712, the factor for 11% Thus, to the nearest whole percent, the internal rate of return is 11%
Unlike changes in time, increases and decreases in cash flows at a
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P142,950
P142,950