UNSW Business School
FINS1613: Business Finance Semester 1 Tutorial Quiz 2: Practice Questions -Decision Rules
Name: STUDENT NAME Student number: STUD STUDENT ENT ID Tutorial:
TUTORIAL
Instructions:
1. You must complete complete a Generalised Answer Sheet for this exam. (a) Complete the top portion of the sheet, providing your family name, initials, and student number. (b) If you are taking a quiz marked Extra , record the quiz number under taking a quiz quiz prepri preprint nted ed with your your stude student nt Other Other Data . If you are taking information, leave Other Data blank. (c) Answer Answer all questions using the generalised generalised answer answer sheet. Clearly Clearly fill in the response oval using a 2B pencil. 2. You must not retain any part of this examination document. All examination materials including this document must be submitted at the completion of the examination, otherwise your exam will not be marked. 3. All All exams exams are are un uniq ique ue and link linked to your your studen studentt number. umber. Sign Sign below below to confirm that your name and student number listed above are correct. Signature:
Information:
1. Time allowed: 40 minutes 2. Grading: (a) Total marks available: 100 marks (b) This examination paper consists of 10 (ten) multiple choice questions worth 10 (ten) marks each. (c) Incorrectly recording your student ID on the generalised answer sheet will result in a loss of 5 (f ive) marks. (d) All questions are graded on a correct/incorrect basis. There is no penalty for answering a question incorrectly. 3. Unless otherwise specified, each question is independent of the others and assumptions from one question do not carry over to the others. 4. Use of a UNSW approved calculator is allowed. 5. Some useful equations are printed below. (a) Standard annuity: Annuity V aluet = C t+1 ×
1 r
1−
1 (1 + r )n
(b) Growing annuity: Growing Annuity V aluet = C t+1 ×
GOOD LUCK!
1 r−g
n
1 + 1−
g 1 + r
Annuity Factors
1
n=1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
r=1%
2%
3%
4%
5%
6%
7%
8%
9%
10%
11%
12%
0.9901 1.9704 2.9410 3.9020 4.8534 5.7955 6.7282 7.6517 8.5660 9.4713 10.3676 11.2551 12.1337 13.0037 13.8651 14.7179 15.5623 16.3983 17.2260 18.0456 18.8570 19.6604 20.4558 21.2434 22.0232 22.7952 23.5596 24.3164
0.9804 1.9416 2.8839 3.8077 4.7135 5.6014 6.4720 7.3255 8.1622 8.9826 9.7868 10.5753 11.3484 12.1062 12.8493 13.5777 14.2919 14.9920 15.6785 16.3514 17.0112 17.6580 18.2922 18.9139 19.5235 20.1210 20.7069 21.2813
0.9709 1.9135 2.8286 3.7171 4.5797 5.4172 6.2303 7.0197 7.7861 8.5302 9.2526 9.9540 10.6350 11.2961 11.9379 12.5611 13.1661 13.7535 14.3238 14.8775 15.4150 15.9369 16.4436 16.9355 17.4131 17.8768 18.3270 18.7641
0.9615 1.8861 2.7751 3.6299 4.4518 5.2421 6.0021 6.7327 7.4353 8.1109 8.7605 9.3851 9.9856 10.5631 11.1184 11.6523 12.1657 12.6593 13.1339 13.5903 14.0292 14.4511 14.8568 15.2470 15.6221 15.9828 16.3296 16.6631
0.9524 1.8594 2.7232 3.5460 4.3295 5.0757 5.7864 6.4632 7.1078 7.7217 8.3064 8.8633 9.3936 9.8986 10.3797 10.8378 11.2741 11.6896 12.0853 12.4622 12.8212 13.1630 13.4886 13.7986 14.0939 14.3752 14.6430 14.8981
0.9434 1.8334 2.6730 3.4651 4.2124 4.9173 5.5824 6.2098 6.8017 7.3601 7.8869 8.3838 8.8527 9.2950 9.7122 10.1059 10.4773 10.8276 11.1581 11.4699 11.7641 12.0416 12.3034 12.5504 12.7834 13.0032 13.2105 13.4062
0.9346 1.8080 2.6243 3.3872 4.1002 4.7665 5.3893 5.9713 6.5152 7.0236 7.4987 7.9427 8.3577 8.7455 9.1079 9.4466 9.7632 10.0591 10.3356 10.5940 10.8355 11.0612 11.2722 11.4693 11.6536 11.8258 11.9867 12.1371
0.9259 1.7833 2.5771 3.3121 3.9927 4.6229 5.2064 5.7466 6.2469 6.7101 7.1390 7.5361 7.9038 8.2442 8.5595 8.8514 9.1216 9.3719 9.6036 9.8181 10.0168 10.2007 10.3711 10.5288 10.6748 10.8100 10.9352 11.0511
0.9174 1.7591 2.5313 3.2397 3.8897 4.4859 5.0330 5.5348 5.9952 6.4177 6.8052 7.1607 7.4869 7.7862 8.0607 8.3126 8.5436 8.7556 8.9501 9.1285 9.2922 9.4424 9.5802 9.7066 9.8226 9.9290 10.0266 10.1161
0.9091 1.7355 2.4869 3.1699 3.7908 4.3553 4.8684 5.3349 5.7590 6.1446 6.4951 6.8137 7.1034 7.3667 7.6061 7.8237 8.0216 8.2014 8.3649 8.5136 8.6487 8.7715 8.8832 8.9847 9.0770 9.1609 9.2372 9.3066
0.9009 1.7125 2.4437 3.1024 3.6959 4.2305 4.7122 5.1461 5.5370 5.8892 6.2065 6.4924 6.7499 6.9819 7.1909 7.3792 7.5488 7.7016 7.8393 7.9633 8.0751 8.1757 8.2664 8.3481 8.4217 8.4881 8.5478 8.6016
0.8929 1.6901 2.4018 3.0373 3.6048 4.1114 4.5638 4.9676 5.3282 5.6502 5.9377 6.1944 6.4235 6.6282 6.8109 6.9740 7.1196 7.2497 7.3658 7.4694 7.5620 7.6446 7.7184 7.7843 7.8431 7.8957 7.9426 7.9844
Annuity Factors
2
n= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
r= 13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23%
24%
0.8850 1.6681 2.3612 2.9745 3.5172 3.9975 4.4226 4.7988 5.1317 5.4262 5.6869 5.9176 6.1218 6.3025 6.4624 6.6039 6.7291 6.8399 6.9380 7.0248 7.1016 7.1695 7.2297 7.2829 7.3300 7.3717 7.4086 7.4412
0.8772 1.6467 2.3216 2.9137 3.4331 3.8887 4.2883 4.6389 4.9464 5.2161 5.4527 5.6603 5.8424 6.0021 6.1422 6.2651 6.3729 6.4674 6.5504 6.6231 6.6870 6.7429 6.7921 6.8351 6.8729 6.9061 6.9352 6.9607
0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.3125 6.3587 6.3988 6.4338 6.4641 6.4906 6.5135 6.5335
0.8621 1.6052 2.2459 2.7982 3.2743 3.6847 4.0386 4.3436 4.6065 4.8332 5.0286 5.1971 5.3423 5.4675 5.5755 5.6685 5.7487 5.8178 5.8775 5.9288 5.9731 6.0113 6.0442 6.0726 6.0971 6.1182 6.1364 6.1520
0.8547 1.5852 2.2096 2.7432 3.1993 3.5892 3.9224 4.2072 4.4506 4.6586 4.8364 4.9884 5.1183 5.2293 5.3242 5.4053 5.4746 5.5339 5.5845 5.6278 5.6648 5.6964 5.7234 5.7465 5.7662 5.7831 5.7975 5.8099
0.8475 1.5656 2.1743 2.6901 3.1272 3.4976 3.8115 4.0776 4.3030 4.4941 4.6560 4.7932 4.9095 5.0081 5.0916 5.1624 5.2223 5.2732 5.3162 5.3527 5.3837 5.4099 5.4321 5.4509 5.4669 5.4804 5.4919 5.5016
0.8403 1.5465 2.1399 2.6386 3.0576 3.4098 3.7057 3.9544 4.1633 4.3389 4.4865 4.6105 4.7147 4.8023 4.8759 4.9377 4.9897 5.0333 5.0700 5.1009 5.1268 5.1486 5.1668 5.1822 5.1951 5.2060 5.2151 5.2228
0.8333 1.5278 2.1065 2.5887 2.9906 3.3255 3.6046 3.8372 4.0310 4.1925 4.3271 4.4392 4.5327 4.6106 4.6755 4.7296 4.7746 4.8122 4.8435 4.8696 4.8913 4.9094 4.9245 4.9371 4.9476 4.9563 4.9636 4.9697
0.8264 1.5095 2.0739 2.5404 2.9260 3.2446 3.5079 3.7256 3.9054 4.0541 4.1769 4.2784 4.3624 4.4317 4.4890 4.5364 4.5755 4.6079 4.6346 4.6567 4.6750 4.6900 4.7025 4.7128 4.7213 4.7284 4.7342 4.7390
0.8197 1.4915 2.0422 2.4936 2.8636 3.1669 3.4155 3.6193 3.7863 3.9232 4.0354 4.1274 4.2028 4.2646 4.3152 4.3567 4.3908 4.4187 4.4415 4.4603 4.4756 4.4882 4.4985 4.5070 4.5139 4.5196 4.5243 4.5281
0.8130 1.4740 2.0114 2.4483 2.8035 3.0923 3.3270 3.5179 3.6731 3.7993 3.9018 3.9852 4.0530 4.1082 4.1530 4.1894 4.2190 4.2431 4.2627 4.2786 4.2916 4.3021 4.3106 4.3176 4.3232 4.3278 4.3316 4.3346
0.8065 1.4568 1.9813 2.4043 2.7454 3.0205 3.2423 3.4212 3.5655 3.6819 3.7757 3.8514 3.9124 3.9616 4.0013 4.0333 4.0591 4.0799 4.0967 4.1103 4.1212 4.1300 4.1371 4.1428 4.1474 4.1511 4.1542 4.1566
Annuity Factors
2
n= 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
r= 13%
14%
15%
16%
17%
18%
19%
20%
21%
22%
23%
24%
0.8850 1.6681 2.3612 2.9745 3.5172 3.9975 4.4226 4.7988 5.1317 5.4262 5.6869 5.9176 6.1218 6.3025 6.4624 6.6039 6.7291 6.8399 6.9380 7.0248 7.1016 7.1695 7.2297 7.2829 7.3300 7.3717 7.4086 7.4412
0.8772 1.6467 2.3216 2.9137 3.4331 3.8887 4.2883 4.6389 4.9464 5.2161 5.4527 5.6603 5.8424 6.0021 6.1422 6.2651 6.3729 6.4674 6.5504 6.6231 6.6870 6.7429 6.7921 6.8351 6.8729 6.9061 6.9352 6.9607
0.8696 1.6257 2.2832 2.8550 3.3522 3.7845 4.1604 4.4873 4.7716 5.0188 5.2337 5.4206 5.5831 5.7245 5.8474 5.9542 6.0472 6.1280 6.1982 6.2593 6.3125 6.3587 6.3988 6.4338 6.4641 6.4906 6.5135 6.5335
0.8621 1.6052 2.2459 2.7982 3.2743 3.6847 4.0386 4.3436 4.6065 4.8332 5.0286 5.1971 5.3423 5.4675 5.5755 5.6685 5.7487 5.8178 5.8775 5.9288 5.9731 6.0113 6.0442 6.0726 6.0971 6.1182 6.1364 6.1520
0.8547 1.5852 2.2096 2.7432 3.1993 3.5892 3.9224 4.2072 4.4506 4.6586 4.8364 4.9884 5.1183 5.2293 5.3242 5.4053 5.4746 5.5339 5.5845 5.6278 5.6648 5.6964 5.7234 5.7465 5.7662 5.7831 5.7975 5.8099
0.8475 1.5656 2.1743 2.6901 3.1272 3.4976 3.8115 4.0776 4.3030 4.4941 4.6560 4.7932 4.9095 5.0081 5.0916 5.1624 5.2223 5.2732 5.3162 5.3527 5.3837 5.4099 5.4321 5.4509 5.4669 5.4804 5.4919 5.5016
0.8403 1.5465 2.1399 2.6386 3.0576 3.4098 3.7057 3.9544 4.1633 4.3389 4.4865 4.6105 4.7147 4.8023 4.8759 4.9377 4.9897 5.0333 5.0700 5.1009 5.1268 5.1486 5.1668 5.1822 5.1951 5.2060 5.2151 5.2228
0.8333 1.5278 2.1065 2.5887 2.9906 3.3255 3.6046 3.8372 4.0310 4.1925 4.3271 4.4392 4.5327 4.6106 4.6755 4.7296 4.7746 4.8122 4.8435 4.8696 4.8913 4.9094 4.9245 4.9371 4.9476 4.9563 4.9636 4.9697
0.8264 1.5095 2.0739 2.5404 2.9260 3.2446 3.5079 3.7256 3.9054 4.0541 4.1769 4.2784 4.3624 4.4317 4.4890 4.5364 4.5755 4.6079 4.6346 4.6567 4.6750 4.6900 4.7025 4.7128 4.7213 4.7284 4.7342 4.7390
0.8197 1.4915 2.0422 2.4936 2.8636 3.1669 3.4155 3.6193 3.7863 3.9232 4.0354 4.1274 4.2028 4.2646 4.3152 4.3567 4.3908 4.4187 4.4415 4.4603 4.4756 4.4882 4.4985 4.5070 4.5139 4.5196 4.5243 4.5281
0.8130 1.4740 2.0114 2.4483 2.8035 3.0923 3.3270 3.5179 3.6731 3.7993 3.9018 3.9852 4.0530 4.1082 4.1530 4.1894 4.2190 4.2431 4.2627 4.2786 4.2916 4.3021 4.3106 4.3176 4.3232 4.3278 4.3316 4.3346
0.8065 1.4568 1.9813 2.4043 2.7454 3.0205 3.2423 3.4212 3.5655 3.6819 3.7757 3.8514 3.9124 3.9616 4.0013 4.0333 4.0591 4.0799 4.0967 4.1103 4.1212 4.1300 4.1371 4.1428 4.1474 4.1511 4.1542 4.1566
Investment Decision Rules
1. Texas LLP chooses projects using a two-step investment decision rule. First, all projects are screened by payback period. All projects that payback in more than 30 years are rejected. Second, projects that pay back in 30 years or less are evaluated for Net Present Value. The firm invests in any positive NPV project from the second step. Which of the following is true about this investment decision rule? (a) Since the payback period is very long, the time value of money does not factor into the investment decision. (b) With a long payback period, the firm will end up investing only in risky projects. (c) By combining the two rules, project risk is overemphasised in the decision relative to the time value of money. (d) By combining the two rules, the time value of money is overemphasised in decision relative to project risk. (e) The firm may fail to maximise firm value. Answer: e
Investment Decision Rules
1. Texas LLP chooses projects using a two-step investment decision rule. First, all projects are screened by payback period. All projects that payback in more than 30 years are rejected. Second, projects that pay back in 30 years or less are evaluated for Net Present Value. The firm invests in any positive NPV project from the second step. Which of the following is true about this investment decision rule? (a) Since the payback period is very long, the time value of money does not factor into the investment decision. (b) With a long payback period, the firm will end up investing only in risky projects. (c) By combining the two rules, project risk is overemphasised in the decision relative to the time value of money. (d) By combining the two rules, the time value of money is overemphasised in decision relative to project risk. (e) The firm may fail to maximise firm value. Answer: e The firm may reject positive NPV projects that take a long amount of time to payback through the initial screening process. In so doing, the firm does not maximise value. 2.
A project requires an initial capital expenditure at time t=0 of 3,017. It then generates constant annual cash flows for the next 23 years of 350 with the first payment due at t=1. After this period, payments grow at a rate of 3% annually and are paid in perpetuity. The net present value of this project is 2,829 dollars at an annual discount rate of 7.0%. Given this, the IRR of the project is . (a) equal to 7.0% (b) greater than 7.0% (c) less than 7.0% (d) not enough information (e) there are multiple IRRs Answer: b The first part of the question establishes that the cash flows are conventional. This means that as the discount rate increases, the NPV of the project decreases (the NPV profile slopes down and to the right). If the NPV is positive at 7%, then the IRR (the discount rate where the NPV is zero) must be greater than 7%. 5
3.
Paranoia Inc. is evaluating a number of exterminators to control a chupacabra infestation. Jackalope Pest Control offers a 5 year contract requiring an upfront payment (t=0 ) of 190,000 and quarterly payments of 2,300 with the first payment due in three months. What is the annual cost of the service as an equivalent annual annuity at a discount rate of 24.0% EAR (effective annual rate)? (a) 47,200 (b) 86,167 (c) 74,675 (d) 70,407 (e) 79,198 Answer: e First, compute the present value of the contract’s cash flows. It consists of an initial payment and a 5-year quarterly annuity. The discount rate of 24% EAR must be converted to a periodic rate to value the annuity: quarterly rate = (1.24) − 1 = 0.05525. Then, the annuity, which makes 20 quarterly payments of 2,300 has a value of: 1 4
$2300 ×
1 1 20 1− 0.05525 1.05525
= $27429
Adding the initial payment of 190,000 gives the total contract cost in present value terms of 217,429. Second, convert the present value of the contract into an equivalent annual annuity. Divide the present value cost by the annuity factor for a 5 year contract and a 24% discount rate. Since this is an annual cost, the annuity factor is for 5 periods at the annual rate, 24%. In the annuity table, the annuity factor is 2.7454. Therefore, the equivalent annual annuity cost is 217429/2.7454 = $79, 198.
6
4.
CGA Technologies Inc. is offering your firm a 18-year contract to create and host a sixteen-color website on its collection of Pentium computers. The contract terms specify annual payments of 15,000 for 9 years followed by annual payments of 25,950 for another 9 years (In other words, payments of 15,000 from t=1 to t=9 and payments of 25,950 from t=10 to t=18 ). The annual discount rate is 4.0%. What is the equivalent annual annuity cost of the web hosting service? (a) 19,519 (b) 40,950 (c) 16,083 (d) 17,594 (e) 22,531 Answer: a To compute the equivalent annual annuity, first compute the NPV of the cash flows. The cash flows consist of a 9-year annuity of cash flows of 15000 followed by another 9-year annuity with cash flows of 25950. The annuity factor for a 9-year annuity at a discount rate of 4% is 7.4353. Applying this to the 15000 gives a present value of 7.4353*15000 = 111529.5. The second part is a 9-year annuity starting at t=10. Applying the annuity factor to the cash flow of 25950 gives a t=9 value. So, discount this nine periods to get the present value.
Total present value = 7.4353 × 15000 +
7.4353 × 25950 = 247090.82 1.049
The equivalent annual annuity cost is the 18-year annuity that has the same present value. The annuity factor for an 18-year annuity at a discount rate of 4% is 12.6593. Therefore, Equivalent annual annuity =
7
247090.82 = 19518.52 ≈ 19519 12.6593
5.
A firm recently evaluated a project requiring an initial capital expenditure at time t=0 of 34,900. Annual cash flows from the project were expected to begin in 1 year at t=1 with 6,000 and grow at a rate g in perpetuity. Although the firm did not know what precise discount rate to use for project valuation, it was certain that correct annual discount rate was between 19% and 21%. It was able to approve the project for all discount rates in that range. Given this, what must be true about the growth rate of the cash flows? (a) g is greater than 1.8% (b) g is less than 3.8% (c) g is greater than 3.8% (d) g is less than 1.8% (e) g is greater than 0.8% Answer: c This project has conventional cash flows, so the internal rate of return decision rule can be used. If the firm approved the project, then it must be that the IRR was greater than all potential discount rates used in valuation. Worst case would be that the IRR was 21%. If that was the case, then NPV at 21% was 0. Using the NPV expression for an initial cash flow and a growing perpetuity means that at a 21% discount rate 34900 +
−
6000 6000 = 0 → .21 − g = .21 − g 34900
→
g = 3.8%
If the growth rate was less than 3.8%, then the firm may have wanted to reject the project for some discount rates. Therefore, it must be that g is greater than 3.8%.
8
6.
A firm is trying to decide which combination of projects make the best use of its limited resources. The firm has decided to prioritize projects by net present value. It will invest in the highest NPV project first. Should resources remain after investing in the highest NPV project, the firm will invest in the next highest NPV project. It will follow this sequential procedure until all resources are consumed. Should two projects have identical NPVs, the firm will pick the project with the highest internal rate of return. Which of the following is true about this investment decision rule? (a) The firm will efficiently allocate resources. (b) The firm should not choose between projects with equivalent NPVs based on their IRRs. Instead, it should pick the project with the lower discount rate. (c) The firm will maximize value by prioritizing projects by NPV. (d) Using IRR to choose between projects with identical IRR helps protect the firm should the project cash flows be lower than expected. (e) None of the above When resources are limited, decisions should be made on the profitability index, not based on net present value. By choosing projects based on net present value, the firm may not efficiently allocate resources. All the other options are not correct. Therefore, the answer is None of the above.
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