# 3.John has just won the Flyball Lottery. He has two options for receiving his prize. The first option is to accept a \$135,000 cash payment today. The second option is to receive \$17,700 at the end of

3.John has just won the Flyball Lottery. He has two options for receiving his prize. The first option is to accept a \$135,000 cash payment today. The second option is to receive \$17,700 at the end of each of the next 19 years and a \$37,900 lump sum payment in the 20th year. John can invest money at a 10% rate.

(a) Calculate the present value of the two options. (For calculation purposes, use 4 decimal places as displayed in the factor table provided and round final answer to 0 decimal place, e.g. 58,971.)

(b) If John could invest money at 13%, calculate the present value of the two options. (For calculation purposes, use 4 decimal places as displayed in the factor table provided and round final answer to 0 decimal place, e.g. 58,971.)

4.Flounder’s Lawn Service needs to purchase a new lawnmower costing \$8,416 to replace an old lawnmower that cannot be repaired. The new lawnmower is expected to have a useful life of 6 years, with no salvage value at the end of that period.

(a)If Flounder’s required rate of return is 11%, what level of annual cash savings must the lawnmower generate to be considered an acceptable investment under the net present value method? (For calculation purposes, use 4 decimal places as displayed in the factor table provided and round final answer to 0 decimal place, e.g. 58,971.)

Annual cash savings should be?

(b)If Flounder’s required rate of return is 18%, what level of annual cash savings must the lawnmower generate to be considered an acceptable investment under the net present value method? (For calculation purposes, use 4 decimal places as displayed in the factor table provided and round final answer to 0 decimal place, e.g. 58,971.)

Annual cash savings should be?

5.The Bramble Company is planning to purchase \$487,000 of equipment with an estimated 7-year life and no estimated salvage value. The company has projected the following annual cash flows for the investment:

YearProjected       Cash Flows

1                               \$207,000

2                                 132,000

3                               109,000

4                              51,700

5                             61,200

6                             44,400

7                            46,300

Total                       \$651,600

Calculate the net present value of the proposed equipment purchase. Bramble uses a 6% discount rate. (For calculation purposes, use 4 decimal places as displayed in the factor table provided and round final answer to 0 decimal place, e.g. 58,971.)

Net present value?

11.William Brown is evaluating two new business opportunities. Each of the opportunities shown below has a 15-year life. William uses a 12% discount rate.

Option 1                 Option 2

Equipment purchase and installation   \$71,200                   \$82,800

Annual cash flow                                     \$29,000                    \$31,130

Equipment overhaul in year 6                 \$4,710                          –

Equipment overhaul in year 8                      –                              \$5,730

(a) Calculate the net present value of the two opportunities. (Round present value factor calculations to 4 decimal places, e.g. 1.2514 and the final answers to 0 decimal places, e.g. 59,991.)

Option 1                     Option 2

Net present value

(b) Calculate the profitability index of the two opportunities. (Round answers to 2 decimal places, e.g. 15.25.)

Option 1                Option 2

Profitability Index

12.Flint Pix currently uses a six-year-old molding machine to manufacture silver picture frames. The company paid \$95,000 for the machine, which was state of the art at the time of purchase. Although the machine will likely last another ten years, it will need a \$12,000 overhaul in four years. More important, it does not provide enough capacity to meet customer demand. The company currently produces and sells 9,000 frames per year, generating a total contribution margin of \$92,500.Martson Molders currently sells a molding machine that will allow Flint Pix to increase production and sales to 12,000 frames per year. The machine, which has a ten-year life, sells for \$138,000 and would cost \$14,000 per year to operate. Flint Pix’s current machine costs only \$8,000 per year to operate. If Flint Pix purchases the new machine, the old machine could be sold at its book value of \$5,000. The new machine is expected to have a salvage value of \$20,200 at the end of its ten-year life. Flint Pix uses straight-line depreciation.

(a)Calculate the new machine’s net present value assuming a 14% discount rate. (For calculation purposes, use 4 decimal places as displayed in the factor table provided and round final answer to 0 decimal place, e.g. 58,971.)Net present value\$______?_______

(b)Use Excel or a similar spreadsheet application to calculate the new machine’s internal rate of return. (Round answer to 2 decimal places, e.g. 1.25%.)

Internal rate of return ______?___%

(c)Calculate the new machine’s payback period. (Round answer to 2 decimal places, e.g. 1.25.)

Payback period___?___years

3.John has just won the Flyball Lottery. He has two options for receiving his prize. The first option is to accept a \$135,000 cash payment today. The second option is to receive \$17,700 at the end of
Perifds 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 16% 18% 20% 10.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8621 0.8475 0.8333 20.9246 0.9070 0.8900 0.8734 0.8573 0.8417 0.8264 0.8116 0.7972 0.7831 0.7695 0.7432 0.7182 0.6944 30.8890 0.8638 0.8396 0.8163 0.7938 0.7722 0.7513 0.7312 0.7118 0.6931 0.6750 0.6407 0.6086 0.5787 40.8548 0.8227 0.7921 0.7629 0.7350 0.7084 0.6830 0.6587 0.6355 0.6133 0.5921 0.5523 0.5158 0.4823 50.8219 0.7835 0.7473 0.7130 0.6806 0.6499 0.6209 0.5935 0.5674 0.5428 0.5194 0.4761 0.4371 0.4019 60.7903 0.7462 0.7050 0.6663 0.6302 0.5963 0.5645 0.5346 0.5066 0.4803 0.4556 0.4104 0.3704 0.3349 70.7599 0.7107 0.6651 0.6227 0.5835 0.5470 0.5132 0.4817 0.4523 0.4251 0.3996 0.3538 0.3139 0.2791 80.7307 0.6768 0.6274 0.5820 0.5403 0.5019 0.4665 0.4339 0.4039 0.3762 0.3506 0.3050 0.2660 0.2326 90.7026 0.6446 0.5919 0.5439 0.5002 0.4604 0.4241 0.3909 0.3606 0.3329 0.3075 0.2630 0.2255 0.1938 10 0.6756 0.6139 0.5584 0.5083 0.4632 0.4224 0.3855 0.3522 0.3220 0.2946 0.2697 0.2267 0.1911 0.1615 11 0.6496 0.5847 0.5268 0.4751 0.4289 0.3875 0.3505 0.3173 0.2875 0.2607 0.2366 0.1954 0.1619 0.134612 0.6246 0.5568 0.4970 0.4440 0.3971 0.3555 0.3186 0.2858 0.2567 0.2307 0.2076 0.1685 0.1372 0.112213 0.6006 0.5303 0.4688 0.4150 0.3677 0.3262 0.2897 0.2575 0.2292 0.2042 0.1821 0.1452 0.1163 0.093514 0.5775 0.5051 0.4423 0.3878 0.3405 0.2992 0.2633 0.2320 0.2046 0.1807 0.1597 0.1252 0.0985 0.077915 0.5553 0.4810 0.4173 0.3624 0.3152 0.2745 0.2394 0.2090 0.1827 0.1599 0.1401 0.1079 0.0835 0.0649 16 0.5339 0.4581 0.3936 0.3387 0.2919 0.2519 0.2176 0.1883 0.1631 0.1415 0.1229 0.0930 0.0708 0.054117 0.5134 0.4363 0.3714 0.3166 0.2703 0.2311 0.1978 0.1696 0.1456 0.1252 0.1078 0.0802 0.0600 0.045118 0.4936 0.4155 0.3503 0.2959 0.2502 0.2120 0.1799 0.1528 0.1300 0.1108 0.0946 0.0691 0.0508 0.037619 0.4746 0.3957 0.3305 0.2765 0.2317 0.1945 0.1635 0.1377 0.1161 0.0981 0.0829 0.0596 0.0431 0.031320 0.4564 0.3769 0.3118 0.2584 0.2145 0.1784 0.1486 0.1240 0.1037 0.0868 0.0728 0.0514 0.0365 0.0261 PV n, b = \$1 _ (1 + i) n APPENDIX 9.1 Present value of \$1 received in n periods. APPENDIX 9.2 Present value of an annuity of \$1 per period. Perifds 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 16% 18% 20% 1 0.9615 0.9524 0.9434 0.9346 0.9259 0.9174 0.9091 0.9009 0.8929 0.8850 0.8772 0.8621 0.8475 0.8333 2 1.8861 1.8594 1.8334 1.8080 1.7833 1.7591 1.7355 1.7125 1.6901 1.6681 1.6467 1.6052 1.5656 1.5278 3 2.7751 2.7232 2.6730 2.6243 2.5771 2.5313 2.4868 2.4437 2.4018 2.3612 2.3216 2.2459 2.1743 2.1065 4 3.6299 3.5460 3.4651 3.3872 3.3121 3.2397 3.1698 3.1024 3.0373 2.9745 2.9137 2.7982 2.6901 2.5887 5 4.4518 4.3295 4.2124 4.1002 3.9927 3.8897 3.7907 3.6959 3.6048 3.5172 3.4331 3.2743 3.1272 2.9906 6 5.2421 5.0757 4.9173 4.7665 4.6229 4.4859 4.3553 4.2305 4.1114 3.9975 3.8887 3.6847 3.4976 3.3255 7 6.0021 5.7864 5.5824 5.3893 5.2064 5.0330 4.8684 4.7122 4.5638 4.4226 4.2883 4.0386 3.8115 3.6046 8 6.7327 6.4632 6.2098 5.9713 5.7466 5.5348 5.3349 5.1461 4.9676 4.7988 4.6389 4.3436 4.0776 3.8372 9 7.4353 7.1078 6.8017 6.5152 6.2469 5.9952 5.7590 5.5370 5.3282 5.1317 4.9464 4.6065 4.3030 4.0310 10 8.1109 7.7217 7.3601 7.0236 6.7101 6.4177 6.1446 5.8892 5.6502 5.4262 5.2161 4.8332 4.4941 4.1925 11 8.7605 8.3064 7.8869 7.4987 7.1390 6.8052 6.4951 6.2065 5.9377 5.6869 5.4527 5.0286 4.6560 4.3271 12 9.3851 8.8633 8.3838 7.9427 7.5361 7.1607 6.8137 6.4924 6.1944 5.9176 5.6603 5.1971 4.7932 4.4392 13 9.9856 9.3936 8.8527 8.3577 7.9038 7.4869 7.1034 6.7499 6.4235 6.1218 5.8424 5.3423 4.9095 4.5327 14 10.5631 9.8986 9.2950 8.7455 8.2442 7.7862 7.3667 6.9819 6.6282 6.3025 6.0021 5.4675 5.0081 4.6106 15 11.1184 10.3797 9.7122 9.1079 8.5595 8.0607 7.6061 7.1909 6.8109 6.4624 6.1422 5.5755 5.0916 4.6755 16 11.6523 10.8378 10.1059 9.4466 8.8514 8.3126 7.8237 7.3792 6.9740 6.6039 6.2651 5.6685 5.1624 4.7296 17 12.1657 11.2741 10.4773 9.7632 9.1216 8.5436 8.0216 7.5488 7.1196 6.7291 6.3729 5.7487 5.2223 4.7746 18 12.6593 11.6896 10.8276 10.0591 9.3719 8.7556 8.2014 7.7016 7.2497 6.8399 6.4674 5.8178 5.2732 4.8122 19 13.1339 12.0853 11.1581 10.3356 9.6036 8.9501 8.3649 7.8393 7.3658 6.9380 6.5504 5.8775 5.3162 4.8435 20 13.5903 12.4622 11.4699 10.5940 9.8181 9.1285 8.5136 7.9633 7.4694 7.0248 6.6231 5.9288 5.3527 4.8696 P VA n,b = \$1 − 1 _______ (1 + b) n ___________ b