39. Declining perpetuities and annuities You own an oil pipeline that will gener

Question

39. Declining perpetuities and annuities You own an oil pipeline that will generate a $2 mil lion cash return over the coming year. The pipeline's operating costs are negligible, and it is expected to last for a very long time. Unfortunately, the volume of oil shipped is declining, and cash flows are expected to decline by 4% per year. The discount rate is 10%. a. What is the PV of the pipeline's cash flows if its cash flows are assumed to last forever? b. What is the PV of the cash flows if the pipeline is scrapped after 20 years?

Explanation / Answer

a. Present value = 2,000,000/(0.10 + 0.04) = 14,285,714.29

b.

Present value = 13,347,130.78

Discount rate 10.0000% Cash flows Year Discounted CF= cash flows/(1+rate)^year Cumulative cash flow                                -   0                                            -                                           -          2,000,000.000 1                       1,818,181.82                    1,818,181.82        1,920,000.000 2                       1,586,776.86                 3,404,958.678        1,843,200.000 3                       1,384,823.44                    4,789,782.12        1,769,472.000 4                       1,208,573.18                    5,998,355.30        1,698,693.120 5                       1,054,754.78                    7,053,110.08        1,630,745.395 6                           920,513.26                    7,973,623.35        1,565,515.579 7                           803,357.03                    8,776,980.37        1,502,894.956 8                           701,111.59                    9,478,091.96        1,442,779.158 9                           611,879.20                 10,089,971.17        1,385,067.992 10                           534,003.67                 10,623,974.84        1,329,665.272 11                           466,039.57                 11,090,014.40        1,276,478.661 12                           406,725.44                 11,496,739.84        1,225,419.515 13                           354,960.38                 11,851,700.23        1,176,402.734 14                           309,783.61                 12,161,483.83        1,129,346.625 15                           270,356.60                 12,431,840.44        1,084,172.760 16                           235,947.58                 12,667,788.02        1,040,805.849 17                           205,917.89                 12,873,705.91            999,173.615 18                           179,710.16                 13,053,416.06            959,206.671 19                           156,837.96                 13,210,254.02            920,838.404 20                           136,876.76                 13,347,130.78

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