Chapter 14 Homework Solutions - Wofford College

ACCOUNTING 342 Chapter 14 Homework Solutions Solutions to Questions 14-1 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. 14-4 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. 14-5 Discounted cash flow methods are superior to other methods of making capital budgeting decisions because they give specific recognition to the time value of money. 14-9 The internal rate of return is the rate of return of 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. 14-10 The cost of capital is a hurdle that must be cleared before an investment project will be accepted. In the case of the net present value method, the cost of capital is used as the discount rate. If the net present value of the project is positive, then the project is acceptable, since its rate of return will be greater than the cost of capital. In the case of the internal rate of return method, the cost of capital is compared to a project s internal rate of return. If the project s internal rate of return is greater than the cost of capital, then the project is acceptable. 14-14 No. If the project profitability index is negative, then the net present value of the project is negative, indicating that it does not provide the required minimum rate of return. 14-17 An outlay that is tax deductible results in some savings in taxes. The after-tax cost of an item is the amount of the outlay less the tax savings. In capital budgeting decisions, all tax-deductible cash expenses should be included on an after-tax cost basis, since the after-tax amount represents the actual net cash outflow.

© The McGraw-Hill Companies, Inc., 2006. All rights reserved. Solutions Manual, Chapter 14

Exercise 14- 1 1.

Cash Item Year(s) Flow Annual cost savings... 1-8 $7,000 Initial investment ...... Now $(40,000) Net present value......

12% Factor 4.968 1.000

Present Value of Cash Flows $ 34,776 (40,000) $ (5,224)

2. Cash Flow Item Years Annual cost savings... $7,000 8 Initial investment ...... $(40,000) 1 Net cash flow............

Total Cash Flows $ 56,000 (40,000) $ 16,000


Exercise 14- 3 1. Note: All present value factors in the computation below have been taken from Table 14C-3 in Appendix 14C, using a 12% discount rate. Amount of the investment............................ $104,950 Less present value of Year 1 and Year 2 cash inflows: Year 1: $30,000 × 0.893 ........................... $26,790 Year 2: $40,000 × 0.797 ........................... 31,880 58,670 Present value of Year 3 cash inflow............... $ 46,280 Therefore, the expected cash inflow for Year 3 would be: $46,280 ÷ 0.712 = $65,000. 2. The equipment s net present value without considering the intangible benefits would be: Item Year(s) Cost of the equipment .. Now Annual cost savings ...... 1-15 Net present value.........

Amount of 20% Present Value Cash Flows Factor of Cash Flows $(2,500,000) 1.000 $(2,500,000) $400,000 4.675 1,870,000 $ (630,000)

The annual value of the intangible benefits would have to be great enough to offset a $630,000 negative present value for the equipment. This annual value can be computed as follows:

Required increase in present value $630,000 = = $134,759 Factor for 15 years 4.675 3. Factor of the internal Investment in the project = rate of return Annual cash inflow

=

$106,700 = 5.335 $20,000

Looking in Table 14C-4, and scanning down the 10% column, we find that a factor of 5.335 equals 8 periods. Thus, the equipment will have to be used for 8 years in order to yield a return of 10%.


Exercise 14- 17 (1) Amount

(1) × (2) After-Tax (2) Tax Effect Cash Flows

Items and Computations Year(s) Project A: Investment in heavy trucks ........ Now $(130,000) Net annual cash inflows............. 1-9 $25,000 1 0.30 Depreciation deductions*........... 1-5 $26,000 0.30 Salvage value of the trucks ........ 9 $15,000 1 0.30 Net present value...................... Project B: Investment in working capital .... Net annual cash inflows............. Release of working capital ......... Net present value......................

Now 1-9 9

$(130,000) $25,000 1 $130,000

0.30

12% Factor

Present Value of Cash Flows

$(130,000) $17,500 $7,800 $10,500

1.000 5.328 3.605 0.361

$(130,000) 93,240 28,119 3,791 $ (4,850)

$(130,000) $17,500 $130,000

1.000 5.328 0.361

$(130,000) 93,240 46,930 $ 10,170

*$130,000 ÷ 5 years = $26,000 per year


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Exercise 14- 18 1.

Annual cost of operating the present equipment ....... Annual cost of the new dishwashing machine: Cost for wages of operators .................................. Cost for maintenance ........................................... Net annual cost savings (cash inflow) ......................

$85,000 $48,000 2,000

50,000 $35,000

2. The net present value analysis would be as follows: (1) × (2) After-Tax (1) (2) Cash Items and Computations Year(s) Amount Tax Effect Flows Cost of the new dishwashing machine . Now $(140,000) $(140,000) Net annual cost savings (above) ......... 1-12 $35,000 1 0.30 $24,500 Depreciation deductions* ................... 1-7 $20,000 0.30 $6,000 Cost of the new water jets ................. 6 $(15,000) 1 0.30 $(10,500) Salvage value of the new machine ...... 12 $9,000 1 0.30 $6,300 Net present value ..............................

14% Factor 1.000 5.660 4.288 0.456 0.208

Present Value of Cash Flows $(140,000) 138,670 25,728 (4,788) 1,310 $ 20,920

*$140,000 ÷ 7 years = $20,000 per year Yes, the new dishwashing machine should be purchased.


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Problem 14- 19 Amount of 20% Item Year(s) Cash Flows Factor Cost of new equipment ............ Now R(275,000) 1.000 Working capital required .......... Now R(100,000) 1.000 Net annual cash receipts .......... 1-4 R120,000 2.589 Cost to construct new roads ..... 3 R(40,000) 0.579 Salvage value of equipment...... 4 R65,000 0.482 Working capital released .......... 4 R100,000 0.482 Net present value ....................

Present Value of Cash Flows R(275,000) (100,000) 310,680 (23,160) 31,330 48,200 R (7,950)

No, the project should not be accepted; it has a negative net present value at a 20% discount rate. This means that the rate of return on the investment is less than the company s required rate of return of 20%.

© The McGraw-Hill Companies, Inc., 2006 Solutions Manual, Chapter 14

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Problem 14-20 1. The net annual cost savings would be: Reduction in labor costs ........................................... $108,000 Reduction in material waste ..................................... 6,500 Total....................................................................... 114,500 Less increased maintenance costs ($3,000 × 12) ....... 36,000 Net annual cost savings ........................................... $ 78,500 2. Using this cost savings figure, and other data from the text, the net present value analysis would be: Amount of Item Year(s) Cash Flows Cost of the machine.............. Now $(500,000) Software and installation....... Now $(80,000) Salvage of the old equipment......................... Now $12,000 Annual cost savings (above) .. 1-12 $78,500 Replacement of parts............ 7 $(45,000) Salvage of the new machine.. 12 $20,000 Net present value .................

Present 16% Value of Factor Cash Flows 1.000 $(500,000) 1.000 (80,000) 1.000 5.197 0.354 0.168

12,000 407,965 (15,930) 3,360 $(172,605)

No, the automated welding machine should not be purchased. It has a negative net present value at a 16% discount rate. 3. The dollar value per year that would be required for the intangible benefits would be:

Negative net present value to be offset $172,605 = = $33,212 Present value factor 5.197 Thus, the automated welding machine should be purchased if management believes that the intangible benefits are worth at least $33,212 per year.


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Problem 14-22 1. The income statement would be: Sales revenue ........................................... Less variable expenses: Cost of ingredients (20% × $300,000)...... $60,000 Commissions (12.5% × $300,000) ........... 37,500 Contribution margin................................... Less operating expenses: Salaries .................................................. $70,000 Rent ($3,500 × 12) ................................. 42,000 Depreciation* ......................................... 16,800 Insurance............................................... 3,500 Utilities .................................................. 27,000 Net operating income ................................

$300,000

97,500 202,500

159,300 $ 43,200

* $270,000 $18,000 = $252,000 $252,000 ÷ 15 years = $16,800 per year. 2. The formula for the simple rate of return is:

Simple rate of return = =

Annual incremental net operating income Initial investment $43,200 = 16.0% $270,000

Yes, the franchise would be acquired since it promises a rate of return in excess of 12%.


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Problem 14-22 (continued) 3. The formula for the payback period is:

Payback period =

Investment required Net annual cash inflow

=

$270,000 = 4.5 years $60,000*

*$43,200 Net operating income + $16,800 Depreciation = $60,000 Net annual cash inflow According to the payback computation, the franchise would not be acquired. The 4.5 years payback is greater than the maximum 4 years allowed. Payback and simple rate of return can give conflicting signals as in this example.


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Problem 14- 23

(1) Items and Computations Year(s) Amount Investment in the new trucks ........... Now $(350,000) Salvage from sale of the old trucks ... Now $16,000 Net annual cash receipts .................. 1-7 $105,000 Depreciation deductions* ................. 1-5 $70,000 Replacement of motors .................... 4 $(45,000) Salvage from the new trucks ............ 7 $18,000 Net present value ............................

(2) Tax Effect 1 1

0.30 0.30 0.30 1 0.30 1 0.30

(1) × (2) Present After-Tax Value of Cash 16% Cash Factor Flows Flows $(350,000) 1.000 $(350,000) $11,200 1.000 11,200 $73,500 4.039 296,867 $21,000 3.274 68,754 $(31,500) 0.552 (17,388) $12,600 0.354 4,460 $ 13,893

*$350,000 ÷ 5 years = $70,000 per year Since the project has a positive net present value, the contract should be accepted


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Problem 14-24 1. The net annual cash inflows would be: Reduction in annual operating costs: Operating costs, present hand method ................. $30,000 Operating costs, new machine ............................. 7,000 Annual savings in operating costs......................... 23,000 Increased annual contribution margin: 6,000 boxes × $1.50 per box ............................... 9,000 Total net annual cash inflows.................................. $32,000 2.

Present Amount of 20% Value of Item Year(s) Cash Flows Factor Cash Flows Cost of the machine ........... Now $(120,000) 1.000 $(120,000) Replacement of parts.......... 6 $(9,000) 0.335 (3,015) Annual cash inflows (above)........................... 1-12 $32,000 4.439 142,048 Salvage value of the machine.......................... 12 $7,500 0.112 840 Net present value ............... $ 19,873


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Problem 14-26 1. Factor of the internal Investment required = rate of return Net annual cash inflow

=

$330,000 = 4.125 $80,000

From Table 14C-4, reading along the 9-period line, a factor of 4.125 is closest to 19%. 2. Factor of the internal Investment required = rate of return Net annual cash inflow We know the investment is $330,000, and we can determine the factor for an internal rate of return of 14% by looking in Table 14C-4 along the 9-period line. This factor is 4.946. Using these figures in the formula, we get:

$330,000 = 4.946 Net annual cash inflow Therefore, the annual cash inflow would be: $330,000 ÷ 4.946 = $66,721. 3. a. 6-year useful life: The factor for the internal rate of return would still be 4.125 [as computed in (1) above]. From Table 14C-4, reading along the 6period line, a factor of 4.125 falls closest to 12%. b. 12-year useful life: The factor of the internal rate of return would again be 4.125. From Table 14C-4, reading along the 12-period line, a factor of 4.125 falls closest to 22%.


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Problem 14-26 (continued) The 12% return in part (a) is less than the 14% minimum return that Ms. Winder wants to earn on the project. Of equal or even greater importance, the following diagram should be pointed out to Ms. Winder:

6 Years 12%

3 years shorter

A decrease of 7%

9 Years 19%

3 years longer

12 Years 22%

An increase of 3%

As 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, Ms. Winder 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.


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Problem 14- 26 (continued) 4. a. The expected annual cash inflow would be: $80,000 × 80% = $64,000.

$330,000 = 5.156 (rounded) $64,000 From Table 14C-4, reading along the 9-period line, a factor of 5.156 is closest to 13%. b. The expected annual cash inflow would be: $80,000 × 120% = $96,000.

$330,000 = 3.438 (rounded) $96,000 From Table 14C-4, reading along the 9-period line, a factor of 3.438 is closest to 25%. Unlike changes in time, increases and decreases in cash flows at a given point in time have basically the same impact on the rate of return, as shown below:

20% decrease $64,000 Cash Inflow 13%

A decrease of 6%

$80,000 Cash Inflow 19%

20% increase

$96,000 Cash Inflow 25%

An increase of 6%


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Problem 14- 26 (continued) 5. Since the cash flows are not even over the 8-year period (there is an extra $135,440 cash inflow from sale of the equipment at the end of the eighth year), some other method has to be used to compute the internal rate of return. Using trial-and-error or more sophisticated methods, it turns out that the internal rate of return is 10%. This can be verified by computing the net present value of the project, which is zero at the discount rate of 10%, as shown below:

Amount of 10% Item Year(s) Cash Flows Factor Investment in the equipment . Now $(330,000) 1.000 Annual cash inflow ................ 1-8 $50,000 5.335 Sale of the equipment ........... 8 $135,440 0.467 Net present value................................

Present Value of Cash Flows $(330,000) 266,750 63,250 $ 0


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Problem 14- 29 1. The annual incremental net operating income can be determined as follows: Ticket revenue (50,000 × $3.60) .... Less operating expenses: Salaries ...................................... Insurance................................... Utilities ...................................... Depreciation* ............................. Maintenance............................... Total operating expenses ............... Net operating income ....................

$180,000 $85,000 4,200 13,000 27,500 9,800 139,500 $ 40,500

*$330,000 ÷ 12 years = $27,500 per year. 2. The simple rate of return would be:

Annual incremental net operating income Simple rate = of return Initial investment (net of salvage from old equipment) =

$40,500 $40,500 = = 15% $330,000 - $60,000 $270,000

Yes, the water slide would be constructed. Its return is greater than the specified hurdle rate of 14%. 3. The payback period would be:

Payback = Investment required (net of salvage from old equipment) period Net annual cash inflow =

$330,000 - $60,000 $270,000 = = 3.97 years (rounded) $68,000* $68,000*

*Net operating income + depreciation = $40,500 + $27,500 = $68,000. Yes, the water slide would be constructed. The payback period is within the maximum 5 years required by Mr. Sharkey.


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Problem 14- 33

(1) Amount

(2) Tax Effect

Items and Computations Year(s) Alternative 1: Investment in the bonds................ Now $(225,000) Interest on the bonds (10% × $225,000) ..................... 1-12 $22,500 1 Maturity of the bonds .................... 12 $225,000 Net present value..........................

(1) × (2) After-Tax Cash 8% Factor Flows


$(225,000) 1.000 $(225,000) 0.40

$13,500 $225,000

7.536 0.397

101,736 89,325 $ (33,939)


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Problem 14- 33 (continued)

(1) Amount

(2) Tax Effect

(1) × (2) After-Tax Cash 8% Factor Flows


Items and Computations Year(s) Alternative 2: Investment in the business ..................... Now $(225,000) $(225,000) 1.000 $(225,000) Net annual cash receipts ($850,000 $780,000 = $70,000)........... 1-12 $70,000 1 0.40 $42,000 7.536 316,512 Depreciation deductions: Year 1: 14.3% of $80,000 .................... 1 $11,440 0.40 $4,576 0.926 4,237 Year 2: 24.5% of $80,000 .................... 2 $19,600 0.40 $7,840 0.857 6,719 Year 3: 17.5% of $80,000 .................... 3 $14,000 0.40 $5,600 0.794 4,446 Year 4: 12.5% of $80,000 .................... 4 $10,000 0.40 $4,000 0.735 2,940 Year 5: 8.9% of $80,000 .................... 5 $7,120 0.40 $2,848 0.681 1,939 Year 6: 8.9% of $80,000 .................... 6 $7,120 0.40 $2,848 0.630 1,794 Year 7: 8.9% of $80,000 .................... 7 $7,120 0.40 $2,848 0.583 1,660 Year 8: 4.5% of $80,000 .................... 8 $3,600 0.40 $1,440 0.540 778 Payment to break the lease ....................... 12 $(2,000) 1 0.40 $(1,200) 0.397 (476) Recovery of working capital ($225,000 $80,000 = $145,000)............ 12 $145,000 $145,000 0.397 57,565 Net present value ....................................... $173,114 Net present value in favor of alternative 2 .. $207.053


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Chapter 14 Homework Solutions - Wofford College

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