Question

# The United States purchased Alaska in 1867 for \$7,200,000. Assume that federal tax revenue from the...

The United States purchased Alaska in 1867 for \$7,200,000. Assume that federal tax revenue from the state of Alaska (net federal expenditures) is \$58,200,000 in 2014 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?

As we know, US purchased Alaska in 1867 for \$7,200,000

Therefore, Cash outflow (CO) = \$7,200,000

In order to compute NPV of tax revenue net of federal expenditure (CI) we have to compute present value (PV) of CI from 1868 till 2014.

Since we are given CI for 2014 as \$58,200,000 we have to compute the CI from 1867 to 2013 by doing at back calculation since the CI increases 3% every year. The calculations will be by theis formula

CI for 2013 = CI of 2014/1.03

CI of 2012 = CI of 2013/1,03 and so on and so forth till CI of 1867 is computed

The calculations will be as per below table

 Year Year No. Tax Revenue net of expenditure DF @ 6% PV @ DF 1868 1 7,77,478 0.943396 7,33,470 1869 2 8,00,802 0.889996 7,12,711 1870 3 8,24,827 0.839619 6,92,540 1871 4 8,49,571 0.792094 6,72,940 1872 5 8,75,058 0.747258 6,53,895 1873 6 9,01,310 0.704961 6,35,388 1874 7 9,28,350 0.665057 6,17,405 1875 8 9,56,200 0.627412 5,99,932 1876 9 9,84,886 0.591898 5,82,953 1877 10 10,14,433 0.558395 5,66,454 1878 11 10,44,866 0.526788 5,50,422 1879 12 10,76,212 0.496969 5,34,844 1880 13 11,08,498 0.468839 5,19,707 1881 14 11,41,753 0.442301 5,04,998 1882 15 11,76,005 0.417265 4,90,706 1883 16 12,11,286 0.393646 4,76,818 1884 17 12,47,624 0.371364 4,63,323 1885 18 12,85,053 0.350344 4,50,210 1886 19 13,23,604 0.330513 4,37,468 1887 20 13,63,313 0.311805 4,25,087 1888 21 14,04,212 0.294155 4,13,057 1889 22 14,46,338 0.277505 4,01,366 1890 23 14,89,728 0.261797 3,90,007 1891 24 15,34,420 0.246979 3,78,969 1892 25 15,80,453 0.232999 3,68,243 1893 26 16,27,867 0.21981 3,57,821 1894 27 16,76,703 0.207368 3,47,694 1895 28 17,27,004 0.19563 3,37,854 1896 29 17,78,814 0.184557 3,28,292 1897 30 18,32,178 0.17411 3,19,001 1898 31 18,87,143 0.164255 3,09,972 1899 32 19,43,758 0.154957 3,01,200 1900 33 20,02,071 0.146186 2,92,675 1901 34 20,62,133 0.137912 2,84,392 1902 35 21,23,997 0.130105 2,76,343 1903 36 21,87,717 0.122741 2,68,522 1904 37 22,53,348 0.115793 2,60,922 1905 38 23,20,948 0.109239 2,53,538 1906 39 23,90,577 0.103056 2,46,362 1907 40 24,62,294 0.097222 2,39,390 1908 41 25,36,163 0.091719 2,32,614 1909 42 26,12,248 0.086527 2,26,031 1910 43 26,90,615 0.08163 2,19,634 1911 44 27,71,334 0.077009 2,13,418 1912 45 28,54,474 0.07265 2,07,378 1913 46 29,40,108 0.068538 2,01,509 1914 47 30,28,311 0.064658 1,95,805 1915 48 31,19,161 0.060998 1,90,264 1916 49 32,12,735 0.057546 1,84,879 1917 50 33,09,117 0.054288 1,79,647 1918 51 34,08,391 0.051215 1,74,562 1919 52 35,10,643 0.048316 1,69,622 1920 53 36,15,962 0.045582 1,64,821 1921 54 37,24,441 0.043001 1,60,156 1922 55 38,36,174 0.040567 1,55,624 1923 56 39,51,259 0.038271 1,51,219 1924 57 40,69,797 0.036105 1,46,939 1925 58 41,91,891 0.034061 1,42,781 1926 59 43,17,648 0.032133 1,38,740 1927 60 44,47,177 0.030314 1,34,813 1928 61 45,80,593 0.028598 1,30,998 1929 62 47,18,010 0.02698 1,27,290 1930 63 48,59,551 0.025453 1,23,688 1931 64 50,05,337 0.024012 1,20,187 1932 65 51,55,497 0.022653 1,16,786 1933 66 53,10,162 0.02137 1,13,480 1934 67 54,69,467 0.020161 1,10,269 1935 68 56,33,551 0.01902 1,07,148 1936 69 58,02,558 0.017943 1,04,115 1937 70 59,76,634 0.016927 1,01,169 1938 71 61,55,933 0.015969 98,305 1939 72 63,40,611 0.015065 95,523 1940 73 65,30,830 0.014213 92,820 1941 74 67,26,755 0.013408 90,193 1942 75 69,28,557 0.012649 87,640 1943 76 71,36,414 0.011933 85,160 1944 77 73,50,506 0.011258 82,750 1945 78 75,71,022 0.01062 80,408 1946 79 77,98,152 0.010019 78,132 1947 80 80,32,097 0.009452 75,921 1948 81 82,73,060 0.008917 73,772 1949 82 85,21,251 0.008412 71,684 1950 83 87,76,889 0.007936 69,655 1951 84 90,40,196 0.007487 67,684 1952 85 93,11,401 0.007063 65,768 1953 86 95,90,744 0.006663 63,907 1954 87 98,78,466 0.006286 62,098 1955 88 1,01,74,820 0.00593 60,341 1956 89 1,04,80,064 0.005595 58,633 1957 90 1,07,94,466 0.005278 56,974 1958 91 1,11,18,300 0.004979 55,361 1959 92 1,14,51,849 0.004697 53,794 1960 93 1,17,95,405 0.004432 52,272 1961 94 1,21,49,267 0.004181 50,792 1962 95 1,25,13,745 0.003944 49,355 1963 96 1,28,89,157 0.003721 47,958 1964 97 1,32,75,832 0.00351 46,601 1965 98 1,36,74,107 0.003312 45,282 1966 99 1,40,84,330 0.003124 44,000 1967 100 1,45,06,860 0.002947 42,755 1968 101 1,49,42,066 0.00278 41,545 1969 102 1,53,90,328 0.002623 40,369 1970 103 1,58,52,038 0.002475 39,227 1971 104 1,63,27,599 0.002334 38,116 1972 105 1,68,17,427 0.002202 37,038 1973 106 1,73,21,950 0.002078 35,989 1974 107 1,78,41,608 0.00196 34,971 1975 108 1,83,76,856 0.001849 33,981 1976 109 1,89,28,162 0.001744 33,019 1977 110 1,94,96,007 0.001646 32,085 1978 111 2,00,80,887 0.001553 31,177 1979 112 2,06,83,314 0.001465 30,294 1980 113 2,13,03,813 0.001382 29,437 1981 114 2,19,42,928 0.001304 28,604 1982 115 2,26,01,215 0.00123 27,794 1983 116 2,32,79,252 0.00116 27,008 1984 117 2,39,77,629 0.001094 26,243 1985 118 2,46,96,958 0.001033 25,501 1986 119 2,54,37,867 0.000974 24,779 1987 120 2,62,01,003 0.000919 24,078 1988 121 2,69,87,033 0.000867 23,396 1989 122 2,77,96,644 0.000818 22,734 1990 123 2,86,30,543 0.000772 22,091 1991 124 2,94,89,460 0.000728 21,465 1992 125 3,03,74,144 0.000687 20,858 1993 126 3,12,85,368 0.000648 20,268 1994 127 3,22,23,929 0.000611 19,694 1995 128 3,31,90,647 0.000577 19,137 1996 129 3,41,86,366 0.000544 18,595 1997 130 3,52,11,957 0.000513 18,069 1998 131 3,62,68,316 0.000484 17,557 1999 132 3,73,56,365 0.000457 17,060 2000 133 3,84,77,056 0.000431 16,578 2001 134 3,96,31,368 0.000406 16,108 2002 135 4,08,20,309 0.000383 15,653 2003 136 4,20,44,918 0.000362 15,210 2004 137 4,33,06,266 0.000341 14,779 2005 138 4,46,05,454 0.000322 14,361 2006 139 4,59,43,617 0.000304 13,954 2007 140 4,73,21,926 0.000287 13,559 2008 141 4,87,41,584 0.00027 13,176 2009 142 5,02,03,831 0.000255 12,803 2010 143 5,17,09,946 0.000241 12,440 2011 144 5,32,61,245 0.000227 12,088 2012 145 5,48,59,082 0.000214 11,746 2013 146 5,65,04,854 0.000202 11,414 2014 147 5,82,00,000 0.000191 11,091 Total 2,55,35,155

Therefore, PV of all CIs will be \$25,535,155

Therefore NPV = \$25,535,155-\$7,200,000 = \$18,335,155

#### Earn Coins

Coins can be redeemed for fabulous gifts.