Black Corporation is planning to buy a new machine that costs $30,000. The machi
ID: 2717413 • Letter: B
Question
Black Corporation is planning to buy a new machine that costs $30,000. The machine will generate additional revenues of $10,000 annually over its ten-year useful like, after which it will have no value. Black Corporation uses straight-line depreciation and pays income taxes at a 50 percent rate. Black’s management wishes to receive at least 10 percent on its investments.
a) Calculate the differential annual after-tax net cash flows from the investment.
b) Evaluate the investment using i) NPV and ii) IRR
c) The expected annual amount of fire damage to this machine is expressed in the following probability distribution:
Probability (%) Damage ($)
75 0
10 1,000
8 10,000
7 20,000
Calculate the annual expected value of the damage.
d) If Black Corporation totally retains these losses, evaluate the investment in the machine by using i) NPV and ii) IRR.
e) Ignoring your answer to the above, if Black implements risk control procedures, the expected value of the losses will $1,000. The annual cost of the procedure is $750. Evaluate the investment in the machine with the use of loss control by using i) NPV and ii) IRR.
f) If Black now buys insurance to fully cover losses to the machine, the premium will be $1,750 per year. Assume conditions described in e). Evaluate the investment in the machine with the use of insurance by using i) NPV and ii) IRR.
g) Would you recommend that Black buy the machine? If so, under which alternative. Explain.
Explanation / Answer
Question a. Cost of Machine 30000 Year of life 10 Annual Depreciation 3000 Aditional Revenue 10000 Less: Depreciation 3000 EBT 7000 Tax @50% 3500 EAT 3500 Add: Depreciation 3000 After tax cashflows 6500 Question b. Present Value using Discount rate of Year Cashflow 10% 15% 16% 17% 17.26% 18% 19% 0 -30000 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 1 6500 5909.09 5652.17 5603.45 5555.56 5543.38 5508.47 5462.18 2 6500 5371.90 4914.93 4830.56 4748.34 4727.55 4668.20 4590.07 3 6500 4883.55 4273.86 4164.27 4058.41 4031.78 3956.10 3857.20 4 6500 4439.59 3716.40 3589.89 3468.73 3438.41 3352.63 3241.35 5 6500 4035.99 3231.65 3094.73 2964.72 2932.37 2841.21 2723.82 6 6500 3669.08 2810.13 2667.87 2533.95 2500.81 2407.81 2288.93 7 6500 3335.53 2443.59 2299.89 2165.77 2132.76 2040.51 1923.47 8 6500 3032.30 2124.86 1982.67 1851.09 1818.88 1729.25 1616.36 9 6500 2756.63 1847.71 1709.19 1582.12 1551.19 1465.46 1358.28 10 6500 2506.03 1606.70 1473.44 1352.24 1322.90 1241.92 1141.42 Total 9939.69 2622.00 1415.98 280.92 0.03 -788.44 -1796.92 Answer: NPV 9939.69 IRR 17.26% Question c. Expected (p) Damages Damage 75% 0 0 10% 1000 100 8% 10000 800 7% 20000 1400 Total 2300 Formula , Expected Damage = probability x Damage Answer: 2300 Question d. After tax cashflow after retaining expected loss = 6500-2300 = 4200 Present Value using Discount rate of Year Cashflow 10% 5% 6% 6.64% 7% 8% 9% 0 -30000 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 1 4200 3818.18 4000.00 3962.26 3938.58 3925.23 3888.89 3853.21 2 4200 3471.07 3809.52 3737.99 3693.43 3668.44 3600.82 3535.06 3 4200 3155.52 3628.12 3526.40 3463.54 3428.45 3334.10 3243.17 4 4200 2868.66 3455.35 3326.79 3247.96 3204.16 3087.13 2975.39 5 4200 2607.87 3290.81 3138.48 3045.80 2994.54 2858.45 2729.71 6 4200 2370.79 3134.10 2960.83 2856.22 2798.64 2646.71 2504.32 7 4200 2155.26 2984.86 2793.24 2678.44 2615.55 2450.66 2297.54 8 4200 1959.33 2842.73 2635.13 2511.73 2444.44 2269.13 2107.84 9 4200 1781.21 2707.36 2485.97 2355.39 2284.52 2101.05 1933.80 10 4200 1619.28 2578.44 2345.26 2208.79 2135.07 1945.41 1774.13 Total -4192.82 2431.29 912.37 -0.10 -500.96 -1817.66 -3045.84 Answer: NPV -4192.82 IRR 6.64% Question e. After tax cashflow after retaining expected loss = 6500-1000-750 = 4750 Present Value using Discount rate of Year Cashflow 10% 8% 9% 9.37% 10% 11% 12% 0 -30000 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 1 4750 4318.18 4398.15 4357.80 4343.25 4318.18 4279.28 4241.07 2 4750 3925.62 4072.36 3997.98 3971.34 3925.62 3855.21 3786.67 3 4750 3568.75 3770.70 3667.87 3631.27 3568.75 3473.16 3380.96 4 4750 3244.31 3491.39 3365.02 3320.32 3244.31 3128.97 3018.71 5 4750 2949.38 3232.77 3087.17 3036.00 2949.38 2818.89 2695.28 6 4750 2681.25 2993.31 2832.27 2776.03 2681.25 2539.54 2406.50 7 4750 2437.50 2771.58 2598.41 2538.31 2437.50 2287.88 2148.66 8 4750 2215.91 2566.28 2383.86 2320.96 2215.91 2061.15 1918.45 9 4750 2014.46 2376.18 2187.03 2122.21 2014.46 1856.89 1712.90 10 4750 1831.33 2200.17 2006.45 1940.48 1831.33 1672.88 1529.37 Total -813.31 1872.89 483.87 0.17 -813.31 -2026.15 -3161.44 Answer: NPV -813.31 IRR 9.37% Question f. Using Insurance instead, Insurance company will cover all loses. Hence company will pay only 1750 as insurance premium. Therefore Result will be same as question e. After tax cashflow = 6500-1750 = 4750 Present Value using Discount rate of Year Cashflow 10% 8% 9% 9.37% 10% 11% 12% 0 -30000 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 -30000.00 1 4750 4318.18 4398.15 4357.80 4343.25 4318.18 4279.28 4241.07 2 4750 3925.62 4072.36 3997.98 3971.34 3925.62 3855.21 3786.67 3 4750 3568.75 3770.70 3667.87 3631.27 3568.75 3473.16 3380.96 4 4750 3244.31 3491.39 3365.02 3320.32 3244.31 3128.97 3018.71 5 4750 2949.38 3232.77 3087.17 3036.00 2949.38 2818.89 2695.28 6 4750 2681.25 2993.31 2832.27 2776.03 2681.25 2539.54 2406.50 7 4750 2437.50 2771.58 2598.41 2538.31 2437.50 2287.88 2148.66 8 4750 2215.91 2566.28 2383.86 2320.96 2215.91 2061.15 1918.45 9 4750 2014.46 2376.18 2187.03 2122.21 2014.46 1856.89 1712.90 10 4750 1831.33 2200.17 2006.45 1940.48 1831.33 1672.88 1529.37 Total -813.31 1872.89 483.87 0.17 -813.31 -2026.15 -3161.44 Answer: NPV -813.31 IRR 9.37%
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