Question

our 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		7,000,000

1. 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: $  

2. 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:     %

Answer 1

NPV is given by:

NPV = L Rt/(1 + i) ,t varies from 1 ton where Rt = Cash flow netted (Inflow - Outflow) during the period "t" i = Discount rate t = number of periods

For Project A

Discount rate = 5%

NPV = [ 5,000,000 / (1 + 5%)^1 ] + [ 10,000,000 / (1 + 5%)^2 ] + [ 20,000,000 / (1 + 5%)^3 ] - Initial Investment  

NPV = 4761904.76 + 9070294.78 + 17276751.97 - 17,000,000

NPV = $ 14,108,951.52

IRR

Discount rate at which NPV = 0 is known as IRR

NPV = 0 = [ 5,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 20,000,000 / (1 + r%)^3 ] - Initial Investment  

0 = [ 5,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 20,000,000 / (1 + r%)^3 ] - 17,000,000

Solving for r

r = 36.12%

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Discount rate = 10%

NPV = [ 5,000,000 / (1 + 10%)^1 ] + [ 10,000,000 / (1 + 10%)^2 ] + [ 20,000,000 / (1 + 10%)^3 ] - Initial Investment  

NPV = 4545454.55 + 8264462.81 + 15026296.02 - 17,000,000

NPV = $ 10,836,213.37

IRR

Discount rate at which NPV = 0 is known as IRR

NPV = 0 = [ 5,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 20,000,000 / (1 + r%)^3 ] - Initial Investment  

0 = [ 5,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 20,000,000 / (1 + r%)^3 ] - 17,000,000

Solving for r

r = 36.12%

----------------------

Discount rate = 15%

NPV = [ 5,000,000 / (1 + 15%)^1 ] + [ 10,000,000 / (1 + 15%)^2 ] + [ 20,000,000 / (1 + 15%)^3 ] - Initial Investment  

NPV = 4347826.09 + 7561436.67 + 13150324.65 - 17,000,000

NPV = $ 8,059,587.41

IRR

Discount rate at which NPV = 0 is known as IRR

NPV = 0 = [ 5,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 20,000,000 / (1 + r%)^3 ] - Initial Investment  

0 = [ 5,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 20,000,000 / (1 + r%)^3 ] - 17,000,000

Solving for r

r = 36.12%

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For Project B

Discount rate = 5%

NPV = [ 20,000,000 / (1 + 5%)^1 ] + [ 10,000,000 / (1 + 5%)^2 ] + [ 7,000,000 / (1 + 5%)^3 ] - Initial Investment  

NPV = 19047619.05 + 9070294.78 + 6046863.19 - 17,000,000

NPV = $ 17,164,777.02

IRR

Discount rate at which NPV = 0 is known as IRR

NPV = 0 = [ 20,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 7,000,000 / (1 + r%)^3 ] - Initial Investment  

0 = [ 20,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 7,000,000 / (1 + r%)^3 ] - 17,000,000

Solving for r

r = 67.46%

-----------------------

Discount rate = 10%

NPV = [ 20,000,000 / (1 + 10%)^1 ] + [ 10,000,000 / (1 + 10%)^2 ] + [ 7,000,000 / (1 + 10%)^3 ] - Initial Investment  

NPV = 18181818.18 + 8264462.81 + 5259203.61 - 17,000,000

NPV = $ 14,705,484.60

IRR

Discount rate at which NPV = 0 is known as IRR

NPV = 0 = [ 20,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 7,000,000 / (1 + r%)^3 ] - Initial Investment  

0 = [ 20,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 7,000,000 / (1 + r%)^3 ] - 17,000,000

Solving for r

r = 67.46%

-----------------------

Discount rate = 15%

NPV = [ 20,000,000 / (1 + 15%)^1 ] + [ 10,000,000 / (1 + 15%)^2 ] + [ 7,000,000 / (1 + 15%)^3 ] - Initial Investment  

NPV = 17391304.35 + 7561436.67 + 4602613.63 - 17,000,000

NPV = $ 12,555,354.65

IRR

Discount rate at which NPV = 0 is known as IRR

NPV = 0 = [ 20,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 7,000,000 / (1 + r%)^3 ] - Initial Investment  

0 = [ 20,000,000 / (1 + r%)^1 ] + [ 10,000,000 / (1 + r%)^2 ] + [ 7,000,000 / (1 + r%)^3 ] - 17,000,000

Solving for r

r = 67.46%

-----------------------

SUMMARY

Project A	Discount Rate
	5%	10%	15%
NPV	1,41,08,951.52	1,08,36,213.37	80,59,587.41
IRR	36.12%	36.12%	36.12%
Project B	Discount Rate
	5%	10%	15%
NPV	1,71,64,777.02	1,47,05,484.60	1,25,55,354.65
IRR	67.46%	67.46%	67.46%