Solutions To Chapter 5 Problems

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					                             Solutions to Homework #3

6-7    PWA(20%) = -$28,000 + ($23,000 - $15,000)(P/A,20%,10) + $6,000(P/F,20%,10)
                  = $6,509

       PWB(20%) = -$55,000 + ($28,000 - $13,000)(P/A,20%,10) + $8,000(P/F,20%,10)
                 = $9,180

       PWC(20%) = -$40,000 + ($32,000 - $22,000)(P/A,20%,10) + $10,000(P/F,20%,10)
                 = $3,540

       Select Alternative B to maximize present worth.

       Note: If you were to pick the alternative with the highest total IRR, you would have
             incorrectly selected Alternative A.


6-27    (a) Repeatability assumption
           AWE1(15%) = - $14,000 (A/P,15%,5) - $14,000 + $8,000 (A/F,15%,5)
                     = -$16,990
           AWE2(15%) = -$65,000(A/P,15%,20) - $9,000 + $13,000 (A/F,15%,20)
                     = -$19,260
           Select Alternative E1 to minimize costs.
        (b) Coterminated assumption (5-year study period)
           AWE1(15%) = - $16,990; unchanged from Part (a)
           Imputed market value (MV5) for Alternative E2:
           MV5 = [$65,000(A/P,15%,20) - $13,000 (A/F,15%,20)](P/A,15%,15)
                      + $13,000 (P/F,15%,15) = $61,590
           AWE2(15%) = - $65,000(A/P,15%,5) - $9,000 + $61,590(A/F,15%,5)
                     = -$19,256 (slight difference from Part (a) is due to rounding)
           Select Alternative E1 to minimize costs. The reason AWE2 in Part b is the
           same as in Part a is the annual expenses are the same over the 20-year period in
           Part a as they are over the 5-year period in Part b.

6-38    Assume repeatabillity. Use method described in Section 6.5.1.
        Rank order: DN,Alt. 1, Alt. 3, Alt. 2

        IRR on  (1-DN) = 33% > 20%, so select Alt. 1

        IRR on  (3-1): set AW1(i') = AW3(i') and solve for i'
              - $30,000(A/P, i',5) + $12,000 +$10,000(A/F, i',5)
                    = -$40,000(A/P, i',6) + $13,000 + $10,000(A/F, i',6)

                    i' ≈ ½% << 20%, so select Alt. 1

        IRR on  (2-1): set AW1(i') = AW2(i') and solve for i'
           -$30,000(A/P, i',5) + $12,000 + $10,000(A/F, i',5)
           = -$60,000(A/P, i',5) + $23,500 + $10,000(A/F, i',5)

        i' ≈ 26.5% > 20%, so select Alternative 2

6-40 Design 1 PW1 = -$100,000 + $20,000 (P/A,10%,10) = $22,891.34
     Design 2 PW2 = -$160,000 + $27,000 (P/A,10%,10) + $20,000 (P/F,10%,10)
                  = $13,614.18
     Design 3 PW3 = -$200,000 + $28,000 (P/A,10%,10) + $40,000 (P/F,10%,10)
                  = -$12,530.39
     Design 4 PW4 = -$260,000 + $45,500 (P/A,10%,10) + $10,000 (P/F,10%,10)
                  = $23,433.23

       Select Design 4 by slim margin.

       IRR1 ≈ 15.1%, IRR2 ≈ 12%, IRR3 < 10%, IRR4 ≈ 12%;
       Moral: Do not select Design 1 to maximize IRR!


7-7     From Table 7-2, the GDS recovery period is 3 years.
        (a) Basis = $195,000
                d*3 = $195,000 (0.3333 + 0.4445 + 0.1481) = $180,550.50

        (b)         d4 = 0.0741 ($195,000) = $14,449.50

       (c)          BV2 = $195,000 (1 - 0.3333 - 0.4445) = $43,329



7-16    (a)    Income taxes = $50,000 (0.15) + $25,000 (0.25) + $15,000 (0.34) = $18,850
        (b)    Depreciation + Expenses = $220,000 - $90,000 = $130,000


7-26    Machine A:
                            (A)             (B)           (C) = (A) - (B)   (D) = -t (C)    (E) = (A) + (D)
             EOY           BTCF           Depr                 TI            T (40%)            ATCF
               0       -$20,000             ---                ---              ---               -$20,000
             1-12        $12,000         $1,333.33         $10,666.67          -$4,266.67        $7,733.33
              12          $4,000           ---                0                  0                  $4,000


                                       0.1468                                   0.0468
     (a) AW = -$20,000(A/P,10%,12) + $7733.33 +$4,000(A/F,10%,12) = $4,984.53
                             8.9847
     (b) PW = $4,984.53(P/A,10%,24) = $44,784.51

     (c) IRR see part (c) below

       Machine B:
                     (A)             (B)       (C) = (A) - (B)   (D) = -t (C)      (E) = (A) + (D)
         EOY        BTCF             Depr           TI            T (40%)              ATCF
           0    -$30,000              ---           ---              ---                 -$30,000
          1-8     $18,000             $3,750       $14,250               -$5,700          $12,300


                            0.1874
     (a) AW = -$30,000(A/P,10%,8) + $12,300 = $6,678
                             8.9847
     (b) PW = $6,678(P/A,10%,24) = $60,000
                 Choose Machine B.

     (c) IRR; use qualitative reasoning and ∆ (B-A); by observation from
         differences in PWs, both IRRs > MARRAT = 10% and i'%B > i'%A
          Choose Machine B.

  7-39 Use a study period of 3 years

Quotation I
EOY         BTCF BTCF          Depr.   Depr.     Book Gain (Loss)                       in           Cash Flow
           Capital Operating Fact.              Value On Disp.                        Ord. Inc         for IT (Cap)
0       $(180,000)                            $180,000
1            ---   $(28,000) 0.2000 $(36,000) $144,000                                $(64,000)
2            ---   $(28,000) 0.3200 $(57,600) $ 86,400                                $(85,600)
3       $50,000    $(28,000) 0.0960 $(17,280) $ 69,120 $ (19,120)                     $(45,280) $ 7,648
PW of ATCF, Quotation I: $(143,174)
IT = Income Taxes

Quotation II
EOY        BTCF BTCF           Depr.   Depr.     Book Gain (Loss)                       in           Cash Flow
           Capital Operating Fact.              Value On Disp.                        Ord. Inc         for IT (Cap)
0       $(200,000)                            $200,000
1            ---   $(17,000) 0.2000 $(40,000) $160,000                                $(57,000)
2            ---   $(17,000) 0.3200 $(64,000) $ 96,000                                $(81,000)
3       $60,000    $(17,000) 0.0960 $(19,200) $ 76,800 $ (16,800)                     $(36,200) $ 6,720
PW of ATCF, Quotation II: $(136,848)
IT = Income Taxes
Accept Quotation II.



8-12   MARR = ic = 25% per year; Assume f = 8% per year; Let k = 0
       Note that the estimated cash flows are in R$ except for the contract maintenance
       agreement ($3,000 / year). However, the PW of $3,000 per year at ic = 25% per year
       is equal to the PW of the R$ equivalent at ir. Therefore, the PW of the cash flows as
       a function of N is:
              PW = -$50,000 + $18,000 (P/A, ir , N) - $3,000 (P/A, 25%, N)
       and,
                       0.25 - 0.08
               ir                  01574 or 15.74% per year
                                      .
                          1.08
       By trial and error we have:               N         PW
                                                 3      -$15,257
                                                 4        -6,455
                                                 5         1,230
       The life of the computer system must be at least 5 years for it to be economically
       justified.

8-27   f = 4.5% per year; ic (after-tax) = 12% per year; t = 40%; b = 0
       increase rate = 6 % per year (applies to annual expenses, replacement costs, and
       market value)
       Analysis period = 20 years; Useful life = 10 years
       MACRS (GDS) 5-year property class
       Capital investment (and cost basis, B)                   = -$260,000
       Market value (at end of year 10) in year 0 dollars       = $50,000
       Annual expenses (in year 0 dollars) = -$6,000
       Annual property tax = 4% of capital investment (does not inflate)
       Assume like replacement at end of year 10.
       Annual Property                                                       ATCF     ATCF*
EOY   Expenses Taxes            BTCF       Depr.         TI       T(40%)      (A$)      (R$)
 0                            -$260,000                                    -$260,000 -$260,000
 1     -$6,360 -$10,400         -16,760    52,000 -68,760 27,504               10,744    10,281
 2      -6,742 -10,400          -17,142    83,200 -100,342 40,137              22,995    21,057
 3      -7,146 -10,400          -17,546    49,920 -67,466 26,986                9,440     8,272
 4      -7,575 -10,400          -17,975    29,952 -47,927 19,171                1,196     1,003
 5      -8,029 -10,400          -18,429    29,952 -48,381 19,352                  923       741
 6      -8,511 -10,400          -18,911    14,976 -33,887 13,555               -5,356    -4,113
 7      -9,022 -10,400          -19,422         0 -19,422    7,769           -11,653     -8,563
 8      -9,563 -10,400          -19,963         0 -19,963    7,985           -11,978     -8,423
 9     -10,137 -10,400          -20,537         0 -20,537    8,215           -12,322     -8,292
 10    -10,745 -10,400          -21,145         0 -21,145    8,458           -12,687     -8,170
 10                              89,542             89,542 -35,817             53,725    34,595
 10                            -465,620                                     -465,620 -299,826
 11    -11,390      -18,625     -30,015    93,124 -123,139 49,256              19,241    11,856
 12    -12,073      -18,625     -30,698   148,998 -179,696 71,878              41,180    24,282
 13    -12,798      -18,625     -31,423    89,399 -120,822 48,329              16,906     9,540
 14    -13,565      -18,625     -32,190    53,639 -85,829 34,332                2,142     1,157
 15    -14,379      -18,625     -33,004    53,639 -86,643 34,657                1,653       854
 16    -15,242      -18,625     -33,867    26,820 -60,687 24,275               -9,592    -4,743
 17    -16,157      -18,625     -34,782         0 -34,782 13,913             -20,869     -9,875
 18    -17,126      -18,625     -35,751         0 -35,751 14,300             -21,451     -9,713
 19    -18,154      -18,625     -36,779         0 -36,779 14,712             -22,067     -9,562
 20    -19,243      -18,625     -37,868         0 -37,868 15,147             -22,721     -9,421
 20                             160,357            160,357 -64,143             96,214    39,894




       * ATCF(R$) = ATCF(A$)  1/(1.045)k

              012  0.045
               .
       ir =               = 0.0718 or 7.18% per year
                  .
                 1045

               20                                  20
       PW =   
              k0
                    ATCFk (A$) (P/F, 12%, k) =      ATCF
                                                   k0
                                                              k   (R$) (P/F, 7.18%, k) = -$359,665

				
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