Your division is considering two investment projects, each of which requires an up-front expenditure of $17 million. You estimate that the investments will produce the following net cash flows:
| Year | Project A | Project B | ||
| 1 | $ 5,000,000 | $20,000,000 | ||
| 2 | 10,000,000 | 10,000,000 | ||
| 3 | 20,000,000 | 6,000,000 | ||
What are the two projects' net present values, assuming the cost of capital is 5%? Do not round intermediate calculations. Round your answers to the nearest dollar.
Project A: $
Project B: $
What are the two projects' net present values, assuming the cost of capital is 10%? Do not round intermediate calculations. Round your answers to the nearest dollar.
Project A: $
Project B: $
What are the two projects' net present values, assuming the cost of capital is 15%? Do not round intermediate calculations. Round your answers to the nearest dollar.
Project A: $
Project B: $
What are the two projects' IRRs at these same costs of capital? Do not round intermediate calculations. Round your answers to two decimal places.
Project A: %
Project B: %
(a) NPV = Present value of all Cash inflows – Initial Investments
NPV @ 5%:
Project A:
Present value of all cash inflows – Initial Investments
= $5,000,000 / (1+.05) + $10,000,000 / (1+.05)2 + $20,000,000 / (1+.05)3 - $17,000,000
= $5,000,000*0.9524+$10,000,000*0.9070+$20,000,000*0.8638-$17,000,000
= $4,761,904.76+$9,070,294.78+$17,276,751.97-$17,000,000
= $31,108,951.52-$17,000,000
= $14,108,952
Project B:
Present value of all cash inflows – Initial Investments
= $20,000,000 / (1+.05) + $10,000,000 / (1+.05)2 + $6,000,000 / (1+.05)3 - $17,000,000
= $20,000,000*0.9524+$10,000,000*0.9070+$6,000,000*0.8638-$17,000,000
= $19,047,619.05+$9,070,294.78+$5,183,025.59-$17,000,000
= $33,300,939.42-$17,000,000
= $16,300,939
NPV @ 10%:
Project A:
Present value of all cash inflows – Initial Investments
= $5,000,000 / (1+.10) + $10,000,000 / (1+.10)2 + $20,000,000 / (1+.10)3 - $17,000,000
= $5,000,000*0.9091+$10,000,000*0.8264+$20,000,000*0.7513-$17,000,000
= $4,545,454.55+$8,264,462.81+$15,026,296.02-$17,000,000
= $27,836,213.37-$17,000,000
= $10,836,213
Project B:
Present value of all cash inflows – Initial Investments
= $20,000,000 / (1+.10) + $10,000,000 / (1+.10)2 + $6,000,000 / (1+.10)3 - $17,000,000
= $20,000,000*0.9091+$10,000,000*0.8264+$6,000,000*0.7513-$17,000,000
= $18,181,818.18+$8,264,462.81+$4,507,888.81-$17,000,000
= $30,954,169.80-$17,000,000
= $13,954,170
NPV @ 15%:
Project A:
Present value of all cash inflows – Initial Investments
= $5,000,000 / (1+.15) + $10,000,000 / (1+.15)2 + $20,000,000 / (1+.15)3 - $17,000,000
= $5,000,000*0.8696+$10,000,000*0.7561+$20,000,000*0.6575-$17,000,000
= $4,347,826.09+$7,561,436.67+$13,150,324.65-$17,000,000
= $25,059,587.41-$17,000,000
= $8,059,587
Project B:
Present value of all cash inflows – Initial Investments
= $20,000,000 / (1+.15) + $10,000,000 / (1+.15)2 + $6,000,000 / (1+.15)3 - $17,000,000
= $20,000,000*0.8696+$10,000,000*0.7561+$6,000,000*0.6575-$17,000,000
= $17,391,304.35+$7,561,436.67+$3,945,097.39-$17,000,000
= $28,897,838.42-$17,000,000
= $11,897,838
(b) Project’s IRR:
|
IRR= |
IRR is the rate whether NPV = 0 |
Project A:
So, $17,000,000 = $5,000,000 / (1+r) + $10,000,000 / (1+r)2 + $20,000,000 / (1+r)3
NPV @ 36%
= $5,000,000 / (1+.36) + $10,000,000 / (1+.36)2 + $20,000,000 / (1+.36)3 - $17,000,000
=$33889.68
NPV @ 37%
= $5,000,000 / (1+.37) + $10,000,000 / (1+.37)2 + $20,000,000 / (1+.37)3 - $17,000,000
=$(2,44,424.24)
IRR = R1+NPV1*(R2-R1)/(NPV1-NPV2)
= 36+33889.68*(37-36)/(33889.68-(-244424.24))
= 36+0.12
IRR = 36.12%
Project B:
So, $17,000,000 = $20,000,000 / (1+r) + $10,000,000 / (1+r)2 + $6,000,000 / (1+r)3
NPV @ 65%
= $20,000,000 / (1+.65) + $10,000,000 / (1+.65)2 + $6,000,000 / (1+.65)3 - $17,000,000
= $129977.46
NPV @ 66%
= $20,000,000 / (1+.66) + $10,000,000 / (1+.66)2 + $6,000,000 / (1+.66)3 - $17,000,000
= $(11,156.25)
IRR = R1+NPV1*(R2-R1)/(NPV1-NPV2)
= 65+129977.46*(66-65)/(129977.46-(-11156.25))
= 65+0.92
IRR = 65.92%
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