NPV profiles: timing differences An oil drilling company must choose between two
ID: 2648817 • Letter: N
Question
NPV profiles: timing differences
An oil drilling company must choose between two mutually exclusive extraction projects, and each costs $12.4 million. Under Plan A, all the oil would be extracted in 1 year, producing a cash flow at t = 1 of $14.88 million. Under Plan B, cash flows would be $2.2034 million per year for 20 years. The firm's WACC is 11.4%.
Construct NPV profiles for Plans A and B. Round your answers to two decimal places. Enter your answers in millions. For example, an answer of $10,550,000 should be entered as 10.55.
Identify each project's IRR. Round your answers to two decimal places.
Project A %
Project B %
Find the crossover rate. Round your answer to two decimal places.
%
Explanation / Answer
SOLUTION Calculation of NPV at Discount Rate 0% Year Cash Flows Plan A Cash Flows Plan B FVIF @ 0% PV of Cash Flows Plan A PV of Cash Flows Plan B 0 ($12,400,000) ($12,400,000) 1 ($12,400,000) ($12,400,000) 1 $14,880,000 $2,203,400 1 $14,880,000 $2,203,400 2 $2,203,400 1 $2,203,400 3 $2,203,400 1 $2,203,400 4 $2,203,400 1 $2,203,400 5 $2,203,400 1 $2,203,400 6 $2,203,400 1 $2,203,400 7 $2,203,400 1 $2,203,400 8 $2,203,400 1 $2,203,400 9 $2,203,400 1 $2,203,400 10 $2,203,400 1 $2,203,400 11 $2,203,400 1 $2,203,400 12 $2,203,400 1 $2,203,400 13 $2,203,400 1 $2,203,400 14 $2,203,400 1 $2,203,400 15 $2,203,400 1 $2,203,400 16 $2,203,400 1 $2,203,400 17 $2,203,400 1 $2,203,400 18 $2,203,400 1 $2,203,400 19 $2,203,400 1 $2,203,400 20 $2,203,400 1 $2,203,400 NPV $2,480,000 $31,668,000 Calculation of NPV at Discount Rate 5% Year Cash Flows Plan A Cash Flows Plan B FVIF @ 5% PV of Cash Flows Plan A PV of Cash Flows Plan B 0 ($12,400,000) ($12,400,000) 1 ($12,400,000) ($12,400,000) 1 $14,880,000 $2,203,400 1.05 $14,171,428.57 $2,098,476.19 2 $2,203,400 1.1025 $1,998,548.75 3 $2,203,400 1.1576 $1,903,379.76 4 $2,203,400 1.2155 $1,812,742.63 5 $2,203,400 1.2763 $1,726,421.56 6 $2,203,400 1.3401 $1,644,211.00 7 $2,203,400 1.4071 $1,565,915.24 8 $2,203,400 1.4775 $1,491,347.85 9 $2,203,400 1.5513 $1,420,331.29 10 $2,203,400 1.6289 $1,352,696.46 11 $2,203,400 1.7103 $1,288,282.35 12 $2,203,400 1.7959 $1,226,935.57 13 $2,203,400 1.8856 $1,168,510.06 14 $2,203,400 1.9799 $1,112,866.73 15 $2,203,400 2.0789 $1,059,873.07 16 $2,203,400 2.1829 $1,009,402.93 17 $2,203,400 2.2920 $961,336.12 18 $2,203,400 2.4066 $915,558.21 19 $2,203,400 2.5270 $871,960.20 20 $2,203,400 2.6533 $830,438.29 NPV $1,771,428.57 $15,059,234.27 Calculation of NPV at Discount Rate 10% Year Cash Flows Plan A Cash Flows Plan B FVIF @ 10% PV of Cash Flows Plan A PV of Cash Flows Plan B 0 ($12,400,000) ($12,400,000) 1 ($12,400,000) ($12,400,000) 1 $14,880,000 $2,203,400 1.1 $13,527,272.73 $2,003,090.91 2 $2,203,400 1.21 $1,820,991.74 3 $2,203,400 1.331 $1,655,447.03 4 $2,203,400 1.4641 $1,504,951.85 5 $2,203,400 1.6105 $1,368,138.04 6 $2,203,400 1.7716 $1,243,761.86 7 $2,203,400 1.9487 $1,130,692.60 8 $2,203,400 2.1436 $1,027,902.36 9 $2,203,400 2.3579 $934,456.69 10 $2,203,400 2.5937 $849,506.08 11 $2,203,400 2.8531 $772,278.26 12 $2,203,400 3.1384 $702,071.14 13 $2,203,400 3.4523 $638,246.49 14 $2,203,400 3.7975 $580,224.09 15 $2,203,400 4.1772 $527,476.44 16 $2,203,400 4.5950 $479,524.04 17 $2,203,400 5.0545 $435,930.94 18 $2,203,400 5.5599 $396,300.86 19 $2,203,400 6.1159 $360,273.51 20 $2,203,400 6.7275 $327,521.37 NPV $1,127,272.73 $6,358,786.30 Calculation of NPV at Discount Rate 12% Year Cash Flows Plan A Cash Flows Plan B FVIF @ 12% PV of Cash Flows Plan A PV of Cash Flows Plan B 0 ($12,400,000) ($12,400,000) 1 ($12,400,000) ($12,400,000) 1 $14,880,000 $2,203,400 1.12 $13,285,714.29 $1,967,321.43 2 $2,203,400 1.2544 $1,756,536.99 3 $2,203,400 1.4049 $1,568,336.60 4 $2,203,400 1.5735 $1,400,300.53 5 $2,203,400 1.7623 $1,250,268.33 6 $2,203,400 1.9738 $1,116,311.01 7 $2,203,400 2.2107 $996,706.26 8 $2,203,400 2.4760 $889,916.30 9 $2,203,400 2.7731 $794,568.13 10 $2,203,400 3.1058 $709,435.83 11 $2,203,400 3.4785 $633,424.85 12 $2,203,400 3.8960 $565,557.90 13 $2,203,400 4.3635 $504,962.41 14 $2,203,400 4.8871 $450,859.30 15 $2,203,400 5.4736 $402,552.94 16 $2,203,400 6.1304 $359,422.27 17 $2,203,400 6.8660 $320,912.74 18 $2,203,400 7.6900 $286,529.23 19 $2,203,400 8.6128 $255,829.67 20 $2,203,400 9.6463 $228,419.35 NPV $885,714.29 $4,058,172.08 Calculation of NPV at Discount Rate 15% Year Cash Flows Plan A Cash Flows Plan B FVIF @ 15% PV of Cash Flows Plan A PV of Cash Flows Plan B 0 ($12,400,000) ($12,400,000) 1 ($12,400,000) ($12,400,000) 1 $14,880,000 $2,203,400 1.15 $12,939,130.43 $1,916,000.00 2 $2,203,400 1.3225 $1,666,086.96 3 $2,203,400 1.5209 $1,448,771.27 4 $2,203,400 1.7490 $1,259,801.10 5 $2,203,400 2.0114 $1,095,479.22 6 $2,203,400 2.3131 $952,590.62 7 $2,203,400 2.6600 $828,339.67 8 $2,203,400 3.0590 $720,295.37 9 $2,203,400 3.5179 $626,343.80 10 $2,203,400 4.0456 $544,646.78 11 $2,203,400 4.6524 $473,605.90 12 $2,203,400 5.3503 $411,831.21 13 $2,203,400 6.1528 $358,114.10 14 $2,203,400 7.0757 $311,403.57 15 $2,203,400 8.1371 $270,785.71 16 $2,203,400 9.3576 $235,465.83 17 $2,203,400 10.7613 $204,752.90 18 $2,203,400 12.3755 $178,046.00 19 $2,203,400 14.2318 $154,822.61 20 $2,203,400 16.3665 $134,628.35 NPV $539,130.43 $1,391,810.97 Calculation of NPV at Discount Rate 17% Year Cash Flows Plan A Cash Flows Plan B FVIF @ 17% PV of Cash Flows Plan A PV of Cash Flows Plan B 0 ($12,400,000) ($12,400,000) 1 ($12,400,000) ($12,400,000) 1 $14,880,000 $2,203,400 1.17 $12,717,948.72 $1,883,247.86 2 $2,203,400 1.3689 $1,609,613.56 3 $2,203,400 1.6016 $1,375,738.08 4 $2,203,400 1.8739 $1,175,844.52 5 $2,203,400 2.1924 $1,004,995.31 6 $2,203,400 2.5652 $858,970.35 7 $2,203,400 3.0012 $734,162.69 8 $2,203,400 3.5115 $627,489.48 9 $2,203,400 4.1084 $536,315.80 10 $2,203,400 4.8068 $458,389.57 11 $2,203,400 5.6240 $391,785.96 12 $2,203,400 6.5801 $334,859.79 13 $2,203,400 7.6987 $286,204.95 14 $2,203,400 9.0075 $244,619.62 15 $2,203,400 10.5387 $209,076.60 16 $2,203,400 12.3303 $178,697.94 17 $2,203,400 14.4265 $152,733.29 18 $2,203,400 16.8790 $130,541.27 19 $2,203,400 19.7484 $111,573.74 20 $2,203,400 23.1056 $95,362.17 NPV $317,948.72 $222.55 Calculation of NPV at Discount Rate 20% Year Cash Flows Plan A Cash Flows Plan B FVIF @ 20% PV of Cash Flows Plan A PV of Cash Flows Plan B 0 ($12,400,000) ($12,400,000) 1 ($12,400,000) ($12,400,000) 1 $14,880,000 $2,203,400 1.2 $12,400,000.00 $1,836,166.67 2 $2,203,400 1.44 $1,530,138.89 3 $2,203,400 1.728 $1,275,115.74 4 $2,203,400 2.0736 $1,062,596.45 5 $2,203,400 2.4883 $885,497.04 6 $2,203,400 2.9860 $737,914.20 7 $2,203,400 3.5832 $614,928.50 8 $2,203,400 4.2998 $512,440.42 9 $2,203,400 5.1598 $427,033.68 10 $2,203,400 6.1917 $355,861.40 11 $2,203,400 7.4301 $296,551.17 12 $2,203,400 8.9161 $247,125.97 13 $2,203,400 10.6993 $205,938.31 14 $2,203,400 12.8392 $171,615.26 15 $2,203,400 15.4070 $143,012.72 16 $2,203,400 18.4884 $119,177.26 17 $2,203,400 22.1861 $99,314.39 18 $2,203,400 26.6233 $82,761.99 19 $2,203,400 31.9480 $68,968.32 20 $2,203,400 38.3376 $57,473.60 NPV $0.00 -$1,670,368.02 Calculation of Crossover Rate Year Cash Flows Plan A Cash Flows Plan B Cumulative Cash Flows 0 ($12,400,000) ($12,400,000) $0 1 $14,880,000 $2,203,400 $12,676,600 2 $2,203,400 ($2,203,400) 3 $2,203,400 ($2,203,400) 4 $2,203,400 ($2,203,400) 5 $2,203,400 ($2,203,400) 6 $2,203,400 ($2,203,400) 7 $2,203,400 ($2,203,400) 8 $2,203,400 ($2,203,400) 9 $2,203,400 ($2,203,400) 10 $2,203,400 ($2,203,400) 11 $2,203,400 ($2,203,400) 12 $2,203,400 ($2,203,400) 13 $2,203,400 ($2,203,400) 14 $2,203,400 ($2,203,400) 15 $2,203,400 ($2,203,400) 16 $2,203,400 ($2,203,400) 17 $2,203,400 ($2,203,400) 18 $2,203,400 ($2,203,400) 19 $2,203,400 ($2,203,400) 20 $2,203,400 ($2,203,400) Crossover Rate 16.41% Yes. Since the crossover rate is higher than the WACC this project is accepted Yes. The WACC is the correct reinvestment rate assumption for a projects cash flows.
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