The United States purchased Alaska in 1867 for $7.2M (where M stands for million
ID: 2641355 • Letter: T
Question
The United States purchased Alaska in 1867 for $7.2M (where M stands for million). Assume that federal tax revenue from the state of Alaska (net federal expenditures) is $55.1M in 2012 and that tax revenue started in 1868 and has steadily increased by 3% annually since then. Assume that the cost of capital (or interest rate) is 6%. What is the NPV of the Alaska purchase, assuming that you are in 1867 looking forward? (Enter just the number in dollars without the $ sign or a comma and round off decimals.) Hint: Simple payback calculation, but with discounting.
Explanation / Answer
Alternative 1 Alternative 2 50000000 70.56029 708613.9 708610 your answer Difference 31-12-1867 0 -7200000 1 -7200000 17641955 7200000 10441955 10515347 73391.87262 31-12-1868 1 708613.8669 0.934579 662256 31-12-1869 2 729872.2829 0.873439 637498.7 31-12-1870 3 751768.4514 0.816298 613667 Note: Part A is showing the calculation used in the first solution as posted by me 31-12-1871 4 774321.5049 0.762895 590726.2 Part B: showing the calulation for all the 144 years. 31-12-1872 5 797551.15 0.712986 568642.9 We are getting almost the same answer in both the cases. 31-12-1873 6 821477.6845 0.666342 547385.3 31-12-1874 7 846122.0151 0.62275 526922.3 31-12-1875 8 871505.6755 0.582009 507224.2 31-12-1876 9 897650.8458 0.543934 488262.6 31-12-1877 10 924580.3712 0.508349 470009.8 31-12-1878 11 952317.7823 0.475093 452439.3 31-12-1879 12 980887.3158 0.444012 435525.7 31-12-1880 13 1010313.935 0.414964 419244.4 31-12-1881 14 1040623.353 0.387817 403571.7 31-12-1882 15 1071842.054 0.362446 388484.9 31-12-1883 16 1103997.316 0.338735 373962.1 31-12-1884 17 1137117.235 0.316574 359982.2 31-12-1885 18 1171230.752 0.295864 346524.9 31-12-1886 19 1206367.675 0.276508 333570.7 31-12-1887 20 1242558.705 0.258419 321100.8 31-12-1888 21 1279835.466 0.241513 309097 31-12-1889 22 1318230.53 0.225713 297542 31-12-1890 23 1357777.446 0.210947 286418.9 31-12-1891 24 1398510.769 0.197147 275711.7 31-12-1892 25 1440466.092 0.184249 265404.7 31-12-1893 26 1483680.075 0.172195 255483 31-12-1894 27 1528190.477 0.16093 245932.3 31-12-1895 28 1574036.192 0.150402 236738.5 31-12-1896 29 1621257.277 0.140563 227888.5 31-12-1897 30 1669894.996 0.131367 219369.3 31-12-1898 31 1719991.846 0.122773 211168.6 31-12-1899 32 1771591.601 0.114741 203274.4 31-12-1900 33 1824739.349 0.107235 195675.4 31-12-1901 34 1879481.529 0.100219 188360.4 31-12-1902 35 1935865.975 0.093663 181318.9 31-12-1903 36 1993941.955 0.087535 174540.6 31-12-1904 37 2053760.213 0.081809 168015.7 31-12-1905 38 2115373.02 0.076457 161734.8 31-12-1906 39 2178834.21 0.071455 155688.6 31-12-1907 40 2244199.237 0.06678 149868.5 31-12-1908 41 2311525.214 0.062412 144265.9 31-12-1909 42 2380870.97 0.058329 138872.8 31-12-1910 43 2452297.099 0.054513 133681.3 31-12-1911 44 2525866.012 0.050946 128683.9 31-12-1912 45 2601641.993 0.047613 123873.3 31-12-1913 46 2679691.252 0.044499 119242.5 31-12-1914 47 2760081.99 0.041587 114784.8 31-12-1915 48 2842884.45 0.038867 110493.8 31-12-1916 49 2928170.983 0.036324 106363.2 31-12-1917 50 3016016.113 0.033948 102387 31-12-1918 51 3106496.596 0.031727 98559.44 31-12-1919 52 3199691.494 0.029651 94874.97 31-12-1920 53 3295682.239 0.027711 91328.25 31-12-1921 54 3394552.706 0.025899 87914.11 31-12-1922 55 3496389.287 0.024204 84627.6 31-12-1923 56 3601280.966 0.022621 81463.95 31-12-1924 57 3709319.394 0.021141 78418.57 31-12-1925 58 3820598.976 0.019758 75487.03 31-12-1926 59 3935216.946 0.018465 72665.09 31-12-1927 60 4053273.454 0.017257 69948.63 31-12-1928 61 4174871.658 0.016128 67333.73 31-12-1929 62 4300117.807 0.015073 64816.58 31-12-1930 63 4429121.342 0.014087 62393.53 31-12-1931 64 4561994.982 0.013166 60061.07 31-12-1932 65 4698854.831 0.012304 57815.79 31-12-1933 66 4839820.476 0.011499 55654.45 31-12-1934 67 4985015.09 0.010747 53573.91 31-12-1935 68 5134565.543 0.010044 51571.15 31-12-1936 69 5288602.509 0.009387 49643.26 31-12-1937 70 5447260.585 0.008773 47787.43 31-12-1938 71 5610678.402 0.008199 46000.99 31-12-1939 72 5778998.754 0.007662 44281.33 31-12-1940 73 5952368.717 0.007161 42625.95 31-12-1941 74 6130939.779 0.006693 41032.45 31-12-1942 75 6314867.972 0.006255 39498.53 31-12-1943 76 6504314.011 0.005846 38021.95 31-12-1944 77 6699443.431 0.005463 36600.57 31-12-1945 78 6900426.734 0.005106 35232.32 31-12-1946 79 7107439.536 0.004772 33915.23 31-12-1947 80 7320662.722 0.00446 32647.37 31-12-1948 81 7540282.604 0.004168 31426.91 31-12-1949 82 7766491.082 0.003895 30252.07 31-12-1950 83 7999485.815 0.00364 29121.15 31-12-1951 84 8239470.389 0.003402 28032.51 31-12-1952 85 8486654.501 0.00318 26984.56 31-12-1953 86 8741254.136 0.002972 25975.8 31-12-1954 87 9003491.76 0.002777 25004.74 31-12-1955 88 9273596.513 0.002596 24069.98 31-12-1956 89 9551804.408 0.002426 23170.17 31-12-1957 90 9838358.54 0.002267 22303.99 31-12-1958 91 10133509.3 0.002119 21470.2 31-12-1959 92 10437514.58 0.00198 20667.58 31-12-1960 93 10750640.01 0.001851 19894.96 31-12-1961 94 11073159.21 0.00173 19151.22 31-12-1962 95 11405353.99 0.001616 18435.29 31-12-1963 96 11747514.61 0.001511 17746.12 31-12-1964 97 12099940.05 0.001412 17082.71 31-12-1965 98 12462938.25 0.001319 16444.1 31-12-1966 99 12836826.4 0.001233 15829.37 31-12-1967 100 13221931.19 0.001152 15237.62 31-12-1968 101 13618589.12 0.001077 14667.99 31-12-1969 102 14027146.8 0.001007 14119.65 31-12-1970 103 14447961.2 0.000941 13591.82 31-12-1971 104 14881400.04 0.000879 13083.71 31-12-1972 105 15327842.04 0.000822 12594.6 31-12-1973 106 15787677.3 0.000768 12123.77 31-12-1974 107 16261307.62 0.000718 11670.55 31-12-1975 108 16749146.85 0.000671 11234.27 31-12-1976 109 17251621.25 0.000627 10814.29 31-12-1977 110 17769169.89 0.000586 10410.02 31-12-1978 111 18302244.99 0.000548 10020.86 31-12-1979 112 18851312.34 0.000512 9646.249 31-12-1980 113 19416851.71 0.000478 9285.642 31-12-1981 114 19999357.26 0.000447 8938.515 31-12-1982 115 20599337.98 0.000418 8604.365 31-12-1983 116 21217318.12 0.00039 8282.707 31-12-1984 117 21853837.66 0.000365 7973.073 31-12-1985 118 22509452.79 0.000341 7675.014 31-12-1986 119 23184736.37 0.000319 7388.097 31-12-1987 120 23880278.46 0.000298 7111.907 31-12-1988 121 24596686.82 0.000278 6846.041 31-12-1989 122 25334587.42 0.00026 6590.114 31-12-1990 123 26094625.04 0.000243 6343.755 31-12-1991 124 26877463.8 0.000227 6106.605 31-12-1992 125 27683787.71 0.000212 5878.321 31-12-1993 126 28514301.34 0.000198 5658.571 31-12-1994 127 29369730.38 0.000185 5447.035 31-12-1995 128 30250822.29 0.000173 5243.408 31-12-1996 129 31158346.96 0.000162 5047.393 31-12-1997 130 32093097.37 0.000151 4858.705 31-12-1998 131 33055890.29 0.000141 4677.071 31-12-1999 132 34047567 0.000132 4502.227 31-12-2000 133 35068994.01 0.000124 4333.92 31-12-2001 134 36121063.83 0.000115 4171.904 31-12-2002 135 37204695.74 0.000108 4015.945 31-12-2003 136 38320836.62 0.000101 3865.816 31-12-2004 137 39470461.72 9.43E-05 3721.3 31-12-2005 138 40654575.57 8.81E-05 3582.186 31-12-2006 139 41874212.83 8.23E-05 3448.272 31-12-2007 140 43130439.22 7.7E-05 3319.365 31-12-2008 141 44424352.4 7.19E-05 3195.277 31-12-2009 142 45757082.97 6.72E-05 3075.827 31-12-2010 143 47129795.46 6.28E-05 2960.843 31-12-2011 144 48543689.32 5.87E-05 2850.157 31-12-2012 145 50000000 5.49E-05 2743.609 NPV 10444699
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