Spring Semester 2018 Problem #6 Assume you are considering buying a food truck t

Question

Spring Semester 2018 Problem #6 Assume you are considering buying a food truck to sell food at local events. The ready to use outfit costs $28,000.00, and has an expect an expected 10 year life. You think you can generate gross revenues of 1. ed salvage value of $10,000.00 at the end of for each of the first 5 years, and you think cash expenses will be $3,500.00 per year $10,000.00 per for the first 5 years. think gross revenue wi expenses expected to remain the same at $3,500.00 per year for the second five years of the truck's life as you learn more about how to operate it efficiently Payback Period, and the Simple Rate of Return for this proposed investment, AND After that you think you can find a few more customers, so you Il increase to $12,500.00 per year for the second 5 years, with cash . Calculate both the explain why the simple rate of return may provide a misleading answer in this instance After graduation you will be hounded by insurance agents interested in selling you "whole life" or "universal life" insurance. Assume (realistically) that there is a plan which you pay $450 per month for 20 years, and then you have your ($100,000 life insurance policy "paid up" for life (you never have to pay any more premiums, but you are guaranteed a $100,000 payout when you die). You make payments at the end of each month for a total of 240 payments. You want to compare the value of that plan to buying term insurance which costs you $95 per month for a S100,000 policy with the rate guaranteed for 20 years (in other words you would pay the $95 monthly premium for 20 years, then drop the policy and your coverage would end). The relevant comparison is to look at investing the difference (between the $450 and the $95) and see how long it would take you to accumulate the $100,000 in an account so you could "self-insure" Assume you can earn 9 (annual) on the invested difference. How long will it take you to accumulate $100,000? How much will you have accumulated at the end of 20 years? Solve the problem using the "Brute Force Method for finding monthly Future Values" in a spreadsheet 2. Should you buy the universal life, or buy the term insurance then self-insure?

Explanation / Answer

2)

Let us first calculate the time it will take to accumulate $100,000.

Amount invested per month = $500-$124 = $376

Now, the first investment is made immediately and from next month onwards, investment is made at the end of the month. So, if we leave the first investment, this becomes an annuity problem. The formula for calculating FV of annuity is given below:

FV = PMT (((1 + r)^n-1)/r)

Now, the future value required in this case, including the first investment, can be calculated as:

FV = PMT x (((1 + r)^n-1)/r) + PMT x (1 + r)^n

In our case, FV = $100,000, PMT = $376, r = 8%/12 (monthly interest rate) = 0.67%

Using the above formula we calculate n and it comes out to be 152.5. Hence, in 153 months (i.e. 12 years and 9 months) you will be able to accumulate little more than $100,000 ($100,519 to be precise).

Now if you keep investing for 20 years, an amount of $376 per month, you will have accumulated $223,324.2.

Below is the calculation done in excel.

The first payment will earn interest for 240 months. The second payment will earn interest for 239 months, third for 238 months and so on. The last installment will earn no interest. The formula used for the calculation of future value in last column is , FV = PMT * (1+r)^n. And finally add all the individual FVs to get the total.

Hence, you should not buy the Universal life insurance as you end up paying a lot more for a lot less in return. In 20 years, if one invests $500 monthly at 8% annual return, he/she will have $296,973.6 at the end of it which can be further invested to earn returns. But if you buy Universal life insurance, you all that money and get only $100,000 if at all. So, buy the term insurance and pay $29,760 in aggregate in 20 years time. Remaining money should be invested monthly in the asset giving 8% annual return.

NOTE: For making the two projects comparable, we are assuming that the money we save from investing in term life will be invested somewhere else. That is to say, what is the profitable way of spending the 500 dollars we have budgeted every month.

Annual return 8% Monthly return 0.67% =8/12% Monthly payment for Universal Life plan 500 USD Term life 124 USD Total term 240 months Amount (USD) 0 240 1852.5 1 239 1840.2 2 238 1828.0 3 237 1815.9 4 236 1803.9 5 235 1791.9 6 234 1780.1 7 233 1768.3 8 232 1756.6 9 231 1744.9 10 230 1733.4 11 229 1721.9 12 228 1710.5 13 227 1699.2 14 226 1687.9 15 225 1676.7 16 224 1665.6 17 223 1654.6 18 222 1643.7 19 221 1632.8 20 220 1622.0 21 219 1611.2 22 218 1600.5 23 217 1589.9 24 216 1579.4 25 215 1569.0 26 214 1558.6 27 213 1548.2 28 212 1538.0 29 211 1527.8 30 210 1517.7 31 209 1507.6 32 208 1497.7 33 207 1487.7 34 206 1477.9 35 205 1468.1 36 204 1458.4 37 203 1448.7 38 202 1439.1 39 201 1429.6 40 200 1420.1 41 199 1410.7 42 198 1401.4 43 197 1392.1 44 196 1382.9 45 195 1373.7 46 194 1364.6 47 193 1355.6 48 192 1346.6 49 191 1337.7 50 190 1328.8 51 189 1320.0 52 188 1311.3 53 187 1302.6 54 186 1294.0 55 185 1285.4 56 184 1276.9 57 183 1268.4 58 182 1260.0 59 181 1251.7 60 180 1243.4 61 179 1235.2 62 178 1227.0 63 177 1218.9 64 176 1210.8 65 175 1202.8 66 174 1194.8 67 173 1186.9 68 172 1179.0 69 171 1171.2 70 170 1163.5 71 169 1155.8 72 168 1148.1 73 167 1140.5 74 166 1133.0 75 165 1125.5 76 164 1118.0 77 163 1110.6 78 162 1103.2 79 161 1095.9 80 160 1088.7 81 159 1081.5 82 158 1074.3 83 157 1067.2 84 156 1060.1 85 155 1053.1 86 154 1046.1 87 153 1039.2 88 152 1032.3 89 151 1025.5 90 150 1018.7 91 149 1011.9 92 148 1005.2 93 147 998.6 94 146 992.0 95 145 985.4 96 144 978.9 97 143 972.4 98 142 966.0 99 141 959.6 100 140 953.2 101 139 946.9 102 138 940.6 103 137 934.4 104 136 928.2 105 135 922.1 106 134 915.9 107 133 909.9 108 132 903.9 109 131 897.9 110 130 891.9 111 129 886.0 112 128 880.1 113 127 874.3 114 126 868.5 115 125 862.8 116 124 857.1 117 123 851.4 118 122 845.7 119 121 840.1 120 120 834.6 121 119 829.1 122 118 823.6 123 117 818.1 124 116 812.7 125 115 807.3 126 114 802.0 127 113 796.7 128 112 791.4 129 111 786.1 130 110 780.9 131 109 775.8 132 108 770.6 133 107 765.5 134 106 760.5 135 105 755.4 136 104 750.4 137 103 745.4 138 102 740.5 139 101 735.6 140 100 730.7 141 99 725.9 142 98 721.1 143 97 716.3 144 96 711.6 145 95 706.9 146 94 702.2 147 93 697.5 148 92 692.9 149 91 688.3 150 90 683.8 151 89 679.2 152 88 674.7 153 87 670.3 154 86 665.8 155 85 661.4 156 84 657.0 157 83 652.7 158 82 648.4 159 81 644.1 160 80 639.8 161 79 635.6 162 78 631.4 163 77 627.2 164 76 623.0 165 75 618.9 166 74 614.8 167 73 610.7 168 72 606.7 169 71 602.7 170 70 598.7 171 69 594.7 172 68 590.8 173 67 586.9 174 66 583.0 175 65 579.1 176 64 575.3 177 63 571.5 178 62 567.7 179 61 563.9 180 60 560.2 181 59 556.5 182 58 552.8 183 57 549.1 184 56 545.5 185 55 541.9 186 54 538.3 187 53 534.7 188 52 531.2 189 51 527.7 190 50 524.2 191 49 520.7 192 48 517.3 193 47 513.8 194 46 510.4 195 45 507.0 196 44 503.7 197 43 500.3 198 42 497.0 199 41 493.7 200 40 490.5 201 39 487.2 202 38 484.0 203 37 480.8 204 36 477.6 205 35 474.4 206 34 471.3 207 33 468.2 208 32 465.1 209 31 462.0 210 30 458.9 211 29 455.9 212 28 452.9 213 27 449.9 214 26 446.9 215 25 443.9 216 24 441.0 217 23 438.1 218 22 435.2 219 21 432.3 220 20 429.4 221 19 426.6 222 18 423.8 223 17 421.0 224 16 418.2 225 15 415.4 226 14 412.7 227 13 409.9 228 12 407.2 229 11 404.5 230 10 401.8 231 9 399.2 232 8 396.5 233 7 393.9 234 6 391.3 235 5 388.7 236 4 386.1 237 3 383.6 238 2 381.0 239 1 378.5 240 0 376.0 Total 223,324.2

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