Question

our division is considering two investment projects, each of which requires an up-front expenditure of $23 million. You estimate that the investments will produce the following net cash flows:

Year	Project A	Project B
1	$  4,000,000	$20,000,000
2	10,000,000	10,000,000
3	20,000,000	8,000,000

What are the two projects' net present values, assuming the cost of capital is 5%? 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%? 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%? Round your answers to the nearest dollar.

Project A $

Project B $

What are the two projects' IRRs at these same costs of capital? Round your answers to two decimal places. Project A     %

Project B     %

Answer 1

For this question, before we begin answering the 4 parts, I will calculate the discounted cashflows at various required rates for each of the project:

Project A:

Year (n)	Cashflows (CF)	Discounted CF (@5%) CF * ( 1 + 5%)^n	Discounted CF (@10%) CF * ( 1 + 10%)^n	Discounted CF (@15%) CF * ( 1 + 15%)^n
0	(23,000,000)	(23,000,000)	(23,000,000)	(23,000,000)
1	4,000,000	3,809,524	3,463,203	3,011,481
2	10,000,000	9,070,295	7,496,111	5,668,137
3	20,000,000	17,276,752	12,980,279	8,534,744
Sum of Discounted CFs		7,156,571	939,594	(5,785,637)

Project B:

Year (n)	Cashflows (CF)	Discounted CF (@5%) CF * ( 1 + 5%)^n	Discounted CF (@10%) CF * ( 1 + 10%)^n	Discounted CF (@15%) CF * ( 1 + 15%)^n
0	(23,000,000)	(23,000,000)	(23,000,000)	(23,000,000)
1	20,000,000	19,047,619	17,316,017	15,057,406
2	10,000,000	9,070,295	7,496,111	5,668,137
3	8,000,000	6,910,701	5,192,112	3,413,898
Sum of Discounted CFs		12,028,615	7,004,240	1,139,441

Now NPV at each discount rate is basically the sum of all discounted cashflows (calculated above). Therefore

@ 5% Discount rate

NPV of Project A: $7,156,571

NPV of Project B: $12,028,615

@10% Discount rate

NPV of Project A: $939,594

NPV of Project B: $7,004,240

@15% Discount rate

NPV of Project A: - $5,785,637

NPV of Project B: $1,139,441

IRR for two projects:

IRR is the discount rate at which NPV is equal to zero. I would suggest using Excel or Financial Calculator to caluclate the same, since it is almost impossible to calculate manually and too time consuming as well.

In Excel, use function IRR, which takes in all associated cashflows as arguments with the appropriate signs associated with them. All outflows should be negative and inflows be positive.

IRR for Project A= 17.45%

IRR for Project B= 37.15%