Question

Please show and explain work- simplified

3. Your division is considering two investment projects, each of which requires an up-front expenditure of 20 million. You estimate that the investment 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 a. What are the two project’s net present values, assuming the cost of capital is 5%? 10%? 15%? b. What are the two projects’ IRRs at these same costs of capital? Show your work.

Answer 1

NPV of Project A:

When cost of capital(k) = 5%

5,000,000 A's NPV = (1 + 0.05)1 10,000,000 20,000,000 (1+0.05)2 + (1+0.05)3 - 20,000,000

by solving,

A's NPV = $11,108, 951.52

When cost of capital(k) = 10%

A's NPV = 5,000,000 (1 +0.10) 1 10,000,000 (1+0.10)2 20,000,000 (1+0.10)3 - 20,000,000

A's NPV = $7,836, 213.37

When cost of capital(k) = 15%

A's NPV = 5,000,000 (1 +0.15)1 10,000,000 (1+0.15)2 20,000,000 (1+0.15)3 - 20,000,000

A's NPV = $5,059,587.41

NPV of Project B:

When cost of capital(k) = 5%

20,000,000 B's NPV = (1 +0.05)1 10,000,000 6,000,000 (1+0.05)2 + (1+0,05)3 13 - 20,000,000

B's NPV = $13,300,939.42

When cost of capital(k) = 10%

B's NPV = 20,000,000 (1 + 0.10)1 10,000,000 (1+0.10)2 6,000,000 (1 + 0.10)3 - 20,000,000

B's NPV = $10,954,169.80

When cost of capital(k) = 15%

20,000,000 B's NPV = (1 + 0.15) 1 10,000,000 (1+0.15)2 6,000,000 (1+0.15)3 M3 - 20,000,000

B's NPV = $8,897,838.42

Internal rate of return (IRR) is the rate at which present value of future cash flows equals to the initial cost.

IRR of Project A:

IRR = i

20,000,000 = 5,000,000 10,000,000 20,000,000 (1+1" (14:12 十一 (1 + i) |

by solving with trial and error method,

iA = 26.73%

IRR of Project A:

IRR = i

20,000,000 = 20,000,000 10,000,000 (1+1T) (1+ 2 6.000,000 (14)

using trail and error method,

iß = 47.63%

We can also solve above problem in excel.

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

B year 0 1 2 3 Project A -$20,000,000 $5,000,000 $10,000,000 $20,000,000 26.73% Project B -$20,000,000 $20,000,000 $10,000,000 $6,000,000 47.63% b) IRR 7 8 10 a) 11 Cost of capital 5% 10% NPV-A $11,108,951.52 $7,836,213.37 $5,059,587.41 NPV-B $13,300,939.42 $10,954,169.80 $8,897,838.42 15%

Cell reference -

ДА В D Project A Project B =C3 2 year 3 o 41 5 2 6 3 7 b) IRR 8 Cost of capital 10 a) 0.05 0.1 12 0.15 -20000000 5000000 10000000 20000000 =IRR(C3:C6) 20000000 10000000 6000000 =IRR(D3:06) NPV-A =NPV(B10, $C$4:$C$6)+$C$3 =NPV(B11,$C$4:$C$6)+$C$3 =NPV(B12,$C$4:$C$6)+$C$3 NPV-B =NPV(B10,$D$4:$D$6)+$D$3 =NPV(B11,$D$4:$D$6)+$D$3 =NPV(B12, $D$4:$D$6)+$D$3

Hope this will help, please do comment if you need any further explanation. Your feedback would be highly appreciated.