SOLUTIONS TO BRIEF EXERCISES


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2 SOLUTIONS TO BRIEF EERCISES BRIEF EERCISE 121 $45, $5, 9 years BRIEF EERCISE 122 Net annual cash flows $4, 5.65 $226, 215, $ 11, The investment should be made because the net present value is positive. BRIEF EERCISE 123 value of net annual cash flows value of salvage value $25, 65, 1% Discount Factor $ 94,77 4,36 135,13 136, $ (87) Since the net present value is negative, the project is unacceptable. BRIEF EERCISE 124 value of net annual cash flows value of salvage value $34, 9% Discount Factor ($188,184) ( ) ( 188,184) ( 2,) ($ (11,816) The reduction in downtime would have to have a present value of at least $11,816 in order for the project to be acceptable.
3 BRIEF EERCISE 125 Project A 9% Discount Factor value of net annual cash flows value of salvage value $7, $449, ,236 4, $ 49,236 Profitability index $449,236/$4, 1.12 Project B 9% Discount Factor value of net annual cash flows value of salvage value $5, $32,883 32,883 28, $ 4,883 Profitability index $32,883/$28, 1.15 Project B has a lower net present value than Project A, but because of its lower capital investment, it has a higher profitability index. Based on its profitability index, Project B should be accepted. BRIEF EERCISE 126 Original estimate value of net annual cash flows value of salvage value $46, 1% Discount Factor $264, ,915 25, $ 14,915
4 BRIEF EERCISE 126 (Continued) Revised estimate value of net annual cash flows value of salvage value 1% Discount Factor $39, ($253,37) ( ) ( 253,37) ( 26,) ($ (6,693) The original net present value was projected to be a positive $14,915; however, the revised estimate is a negative $6,693. The project is not a success. BRIEF EERCISE 127 When net annual cash flows are expected to be equal, the internal rate of return can be approximated by dividing the capital investment by the net annual cash flows to determine the discount factor, and then locating this discount factor on the present value of an annuity table. $176,/$33, By tracing across on the 7year row we see that the discount factor for 8% is Thus, the internal rate of return on this project is approximately 8%. BRIEF EERCISE 128 When net annual cash flows are expected to be equal, the internal rate of return can be approximated by dividing the capital investment by the net annual cash flows to determine the discount factor, and then locating this discount factor on the present value of an annuity table. Since this exercise has a salvage value, not all cash flows are equal. In this case, the internal rate of return can be approximated by identifying the discount rate that will result in a net present value of zero. By experimenting with various rates, we determined that the net present value is approximately zero when a discount rate of approximately 9% is used.
5 BRIEF EERCISE 128 (Continued) Net annual cash flows $4, $15, $25, value of net annual cash flows value of salvage value $25, 716, 9% Discount Factor $1,79, ,567 2,44,75 2,45, $ (25) The 9% internal rate of return exceeds the company s 7% required rate of return; thus, the project should be accepted. BRIEF EERCISE 129 The annual rate of return is calculated by dividing expected annual income by the average investment. The company s expected annual income is: $13, $7, $6, Its average investment is: $47, + $1, 2 $24, Therefore, its annual rate of return is: $6,/$24, 25%
6 SOLUTIONS FOR DO IT! REVIEW EERCISES DO IT! 121 Estimated annual cash inflows... $8, Estimated annual cash outflows... 4, Net annual cash flow... $4, payback period $12,/$4, 3 years. DO IT! 122 Estimated annual cash inflows... $8, Estimated annual cash outflows... 4, Net annual cash flow... $4, Flow 12% Discount Factor value of net annual cash flows $4, a $121,494 12, $ 1,494 a Table 4, Appendix A. Since the net present value is positive, the project should be accepted DO IT! 123 Estimated annual cash inflows... $8, Estimated annual cash outflows... 4, Net annual cash flow... $4, $12,/$4, 3.. Using Table 4 of Appendix A and the factors that correspond with the fourperiod row, 3. is between the factors for 12% and 15%. Since the project has an internal rate that is more than 12%, the company s required rate of return, the project should be accepted.
7 DO IT! 124 Revenues... $8, Less: Expenses (excluding depreciation)... $4, Depreciation ($12,/4 years)... 3, 7, Annual net income... $ 1, Average investment ($12, + )/2 $6,. Annual rate of return $1,/$6, 16.7%. Since the annual rate of return, 16.7%, is greater than Wallowa s required rate of return, 12%, the proposed project is acceptable.
8 SOLUTIONS TO EERCISES EERCISE 121 (a) The cash payback period is: $56, $7,5 7.5 years The net present value is: value of net annual cash flows value of salvage value $ 7,5 27, 8% Discount Factor $43,1 14,587 57,687 56, $ 1,687 (b) In order to meet the cash payback criteria, the project would have to have a cash payback period of less than 4 years (8 2). It does not meet this criteria. The net present value is positive, however, suggesting the project should be accepted. The reason for the difference is that the project s high estimated salvage value increases the present value of the project. The net present value is a better indicator of the project s worth. EERCISE 122 (a) AA Year Net Annual Flow Cumulative Net Flow $ 7, 9, 12, $ 7, 16, 28, payback period 2.5 years $22, $16, $6, $6, $12,.5
9 EERCISE 122 (Continued) BB 22, 1, 2.2 years CC Year Net Annual Flow Cumulative Net Flow $13, 12, 11, $13, 25, 36, payback period 1.75 years $22, 13, $9, $9, $12,.75 The most desirable project is CC because it has the shortest payback period. The least desirable project is AA because it has the longest payback period. As indicated, only CC is acceptable because its cash payback is 1.75 years. (b) AA BB CC Discount Factor Flow Flow Flow Year Total present value Investment $ 7, 9, 12, $ 6,25 7,175 8,541 21,966 (22,) $ (34) $1, 1, 1, $ 8,929 7,972 7,118 24,19(1) (22,) $ 2,19 $13, 12, 11, $11,67 9,566 7,83 29,3 (22,) $ 7,3 (1) This total may also be obtained from Table 4: $1, $24,18. (The difference of $1 is due to rounding) Project CC is still the most desirable project. Also, on the basis of net present values, project BB is also acceptable. Project AA is not desirable.
10 EERCISE 123 Investment in new equipment... $2,45, Disposal of old equipment... (26,) Additional training required... 85, Net initial investment required... $2,275, Calculation of net present value: Year Discount Factor, 9% Amount flows $ 39, $ 357, , 336, , 317, , 31, , 282, , 259, , 238,55 Maintenance (1,) (64,993) Net cash flows from operations: 2,28,586 Terminal salvage , 191,461 value of cash inflows 2,22,47 Initial investment (2,275,) $ (54,953) Based on the net present calculation alone, the sewing machine should not be purchased. However, the internal rate of return would be only slightly lower than the 9% minimum required, so the company may want to look at some of the nonquantitative factors involved.
11 EERCISE 124 Machine A 9% Discount Factor value of net annual cash flows value of salvage value $15, $83,22 83,22 75,5 $ 7,522 Profitability index $83,22/$75,5 1.1 Machine B value of net annual cash flows value of salvage value $3, 9% Discount Factor ($166,45) ( ) ( 166,45) ( 18,) ($ (13,955) Profitability index $166,45/$18,.92 Machine B has a negative net present value, and also a lower profitability index. Machine B should be rejected and Machine A should be purchased. EERCISE 125 When net annual cash flows are expected to be equal, the internal rate of return can be approximated by dividing the capital investment by the net annual cash flows to determine the discount factor, and then locating this discount factor on the present value of an annuity table. $43,/$11, By tracing across on the 6year row, we see that the discount factor for 11% is Thus, the internal rate of return on this project is approximately 11%. Since this is above the company s required rate of return, the project should be accepted.
12 EERCISE 126 (a) Total net investment $29,3 + $1,5 $2, $28,8 Annual net cash flow $7, Payback period $28,8 $7, 4.1 years (b) approximates zero when discount rate is 12%. Item Amount Years PV Factor Net annual cash flows $7, $28,78 (28,8) $ (2) (c) Because the approximate internal rate of return of 12% exceeds the required rate of return of 1%, the investment should be accepted. EERCISE 127 (a) Project Capital Investment Net Annual * Internal Rate of Return Factor Closest Discount Factor Internal Rate of Return 22A 23A 24A $24, $27, $28, ($16,7 + $4,) ($2,6 + $3,) ($17,5 + $4,) % 12% 1% *(Annual income + Depreciation expense) (b) The acceptable projects are 22A and 23A because their rates of return are equal to or greater than the 11% required rate of return.
13 EERCISE 128 The annual rate of return is calculated by dividing expected annual income by the average investment. The company s expected annual income is: $7, $41,5 $28,5 Its average investment is: $3, + $8, 2 $19, Therefore, its annual rate of return is: $28,5 $19, 15% EERCISE 129 (a) Cost of hoist: $35, + $3,3 + $7 $39,. Net annual cash flows: Number of extra mufflers 5 52 weeks (a) 26 Contribution margin per muffler ($72 $36 $12) (b) $24 Total net annual cash flows (a) (b) $6,24 payback period $39, $6, years. (b) Average investment: ($39, + $3,) 2 $21,. Annual depreciation: ($39, $3,) 8 $4,5. Annual net income: $6,24 $4,5 $1,74. Annual rate of return $1,74 $21, 8.3% (rounded).
14 EERCISE 121 (a) 1. payback period: $19, $5, 3.8 years. 2. Annual rate of return: $12, [($19, + $) 2] 12.63%. (b) Item Amount Years PV Factor Net annual cash flows $ 5, $18,239)) (19,) $ (9,761))) EERCISE (a) Year Net Annual Flow Cumulative Net Flow $45, 4, 35, $ 45, 85, 12, payback period 2.57 years (2 + [($15, $85,) $35,]) (b) Average annual net income ($1, + $12, + $14, + $16, + $18,) 5 $14, Average investment ($15, + $) 2 $52,5 Annual rate of return $14, $52, % (c) Discount Year Factor, 12% Amount Net cash flows $45, $ 4, , 31, , 24, , 19, , 14,186 value of cash in flows 13,231 Initial investment (15,) $ 25,231
15 SOLUTIONS TO PROBLEMS PROBLEM 121A (a) Project Kilo $15, ($14, + $3,) 3.41 years Project Lima Year Flow Cumulative Flow $51, ($18, + $33,) $5, ($17, + $33,) $49, ($16, + $33,) $45, ($12, + $33,) $42, ($ 9, + $33,) $ 51, $11, $15, $195, $237, payback period 3.33 years $165, $15, $15, $15, $45,.33 Project Oscar Year Flow Cumulative Flow $67, ($27, + $4,) $63, ($23, + $4,) $61, ($21, + $4,) $53, ($13, + $4,) $52, ($12, + $4,) $ 67, $13, $191, $244, $296, payback period 3.17 years $2, $191, $9, $9, $53,.17
16 PROBLEM 121A (Continued) (b) Project Kilo Item Amount Years PV Factor Net annual cash flows Negative net present value $44, $147,495 (15,) $ (2,55) Discount Year Factor Total Positive (negative) net present value Project Lima Flow PV $ 51, $ 44,348 5, 37,87 49, 32,218 45, 25,729 42, 2,882 $237, 16,984 (165,) $ (4,16) Project Oscar Flow PV $ 67, $ 58,261 63, 47,637 61, 4,19 53, 3,33 52, 25,853 $296, 22,163 (2,) $ 2,163 (c) Project Kilo $14, [($15, + $) 2] 18.67%. Project Lima $14,4 [($165, + $) 2] 17.5%. Project Oscar $19,2 [($2, + $) 2] 19.2%. (d) Project Kilo Lima Oscar Payback Net Annual Rate of Return The best project is Oscar.
17 PROBLEM 122A (a) (1) Annual Net Income Sales Expenses Drivers salaries Outofpocket expenses Depreciation Total expenses Net income inflow *$18,* * 48,* * 3,* * 25,* * 13,* *$ 5,* (2) Annual Inflow $18, 48, 3, 78, $ 3, *5 vans 1 trips 6 students 3 weeks $12. $18,. (b) 1. payback period $75, $3,* 2.5 years. *$5, + $25, 2. Annual rate of return $5, ($75, + ) %. (c) value of annual cash inflows ($3, *) $68,497 (75,) $ (6,53) *3 years at 15%, PV of annuity of 1. (d) The computations show that the commuter service is not a wise investment for these reasons: (1) annual net income will only be $5,, (2) the annual rate of return (13.33%) is less than the cost of capital (15%), (3) the cash payback period is 83% (2.5 3) of the useful life of the vans, and (4) net present value is negative.
18 PROBLEM 123A (a) (1) Option A 8% Discount Factor value of net annual cash flows value of cost to rebuild value of salvage value a $4, a ( (5,) ( ) ($28,255) ( (36,752) ( ) ($171,53) ( (16,) ($ 11,53) a Net annual cash flows $7, $3, $4, (2) Profitability index $171,53/$16, 1.7 (3) The internal rate of return can be approximated by finding the discount rate that results in a net present value of approximately zero. This is accomplished with a 1% discount rate. 1% Discount Factor value of net annual cash flows value of cost to rebuild value of salvage value a $4, a ( (5,) ( ) ($194,737) ( (34,151) ( ) ($16,586) (16,) ($ 586 a Net annual cash flows $7, $3, $4, (1) Option B 8% Discount Factor value of net annual cash flows value of cost to rebuild value of salvage value b $54, b 8, $281,144 4,668 $285,812 (227,) $ 58,812 b Net annual cash flows $8, $26, $54, (2) Profitability index $285,812/$227, 1.26
19 PROBLEM 123A (Continued) (3) Internal rate of return on Option B is 15%, as calculated below: 15% Discount Factor value of net annual cash flows value of cost to rebuild value of salvage value b $54, b 8, $224,663 3,8 $227,671 (227,) $ 671 b Net annual cash flows $8, $26, $54, (b) Option A has a lower net present value than Option B, and also a lower profitability index and internal rate of return. Therefore, Option B is the preferred project.
20 PROBLEM 124A (a) The net present value based on the original estimates is as follows: value of net annual cash flows value of cost of overhaul value of salvage value $ 8, ( (6,) ( 12,) 9% Discount Factor ($ 44,279 ( (4,251) ( 6,22 ($ 46,5 (6,) ($(13,95) Based on its negative net present value, the tow truck should not be purchased. (b) The net present value based on the revised estimates is as follows: value of net annual cash flows value of cost of overhaul value of salvage value $13,5* ( (6,)* ( 12, * 9% Discount Factor ($74,72) ( (4,251) ( 6,22) ($76,491) (6,) ($16,491) *$8, + ($3, + $75 + $1, + $75) Based on the revised figures, the tow truck has a positive net present value and therefore should be purchased. (c) The present value of the intangible benefits was $3,441 (the increase in the net present value from a negative $13,95 to a positive $16,491). Rick s estimates of the value of these intangible benefits may be overly optimistic. In order for the project to be acceptable, the present value of the intangible benefits would only have to be $13,95. That is the amount by which the original estimate fell short of having a positive net present value.
21 PROBLEM 125A (a) Using the original estimates, the net present value is calculated as follows: value of net annual cash flows value of salvage value ($3, + $6,) a $ 1, a 1,5, 8% Discount Factor $ 981, ,825 1,33,64 (9,) $ 43,64 a Net annual cash flows $94, $84, The positive net present value of the project suggests that it should be accepted. (b) Using the revised estimates, the net present value is calculated as follows: value of net annual cash flows value of salvage value b $ 5, b 1,5, 8% Discount Factor $(49,98) (321,825) $(812,733) (9,) $ (87,267) b Net annual cash flows $8, $75, Under these revised estimates, the project should be rejected. It appears that many of the camp s costs are fixed; thus, when the number of players declines, cash inflows decline, but cash outflows don t decline proportionately.
22 PROBLEM 125A (Continued) (c) Using the original estimates, but an 11% discount rate, the net present value is calculated as follows: value of net annual cash flows value of salvage value c $ 1, c 1,5, 11% Discount Factor $ 796, ,45 $ 982,378 (9,) $ 82,378 c Net annual cash flows $94, $84, The positive net present value of the project suggests that it should be accepted; however, it is not nearly as profitable using an 11% discount rate. (d) The internal rate of return can be determined by calculating the discount rate that results in a net present value of approximately zero. In this case the internal rate of return was approximately 12%. 12% Discount Factor value of net annual cash flows value of salvage value $ 4, 1,332, $144, ,817 $9,8 (9,) $ 8 The project had a high internal rate of return, even though the business itself was not generating much cash flows, because the property increased significantly in value during the 5year period.
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