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	$ 4,000,000		$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:     %

Answer 1

Year	Project A		Project B
	Cash Flow	PV of Cash Flow	Cash Flow	PV of Cash Flow
0	-17000000	-17000000	-17000000	-17000000
1	4000000	4000000/(1+r)1	20000000	20000000/(1+r)1
2	10000000	10000000/(1+r)2	10000000	10000000/(1+r)2
3	20000000	20000000/(1+r)3	6000000	6000000/(1+r)3

Where r=cost of capital

N=time of project

a) r=5%=0.05

NPV_{Project A}

= 4000000/(1+0.05)¹ + 10000000/(1+0.05)² + 20000000/(1+0.05)³ -17000000

= 3809523.81 + 9070294.785 + 17276751.97 -17000000

= 13156570.57

Rounding to the nearest dollar, NPV_{Project A}=$ 13156571

NPV_{Project B}

= 20000000/(1+0.05)¹ + 10000000/(1+0.05)² + 6000000/(1+0.05)³ -17000000

= 19047619.047619 + 9070294784581 + 5183025.591189-17000000

= 33300939.4234-17000000

= 16300939.42

Rounding to the nearest dollar, NPV_{Project B}= $33300939

b)

r=10%=0.1

NPV_{Project A}

= 4000000/(1+0.1)¹ + 10000000/(1+0.1)² + 20000000/(1+0.1)³ -17000000

= 3636363.636364 + 8264462.809917 + 15026296.018032-17000000

= 26927122.464313 -17000000

= 9927122.46

Rounding to the nearest dollar, NPV_{Project A}=$ 9927122.46

NPV_{Project B}

= 20000000/(1+0.1)¹ + 10000000/(1+0.1)² + 6000000/(1+0.1)³-17000000

= 18181818.181818 + 8264462.809917 + 4507888.805409-17000000

= 30954169.797145-17000000

= 13954169.79

Rounding to the nearest dollar, NPV_{Project B}= $ 13954169.79

c)

r=15%=0.15

NPV_{Project A}

= 4000000/(1+0.15)¹ + 10000000/(1+0.15)² + 20000000/(1+0.15)³ -17000000

= 3478260.869565+7561436.672968+13150324.64864 -17000000

= 24190022.191173-17000000

= 7190022.19

Rounding to the nearest dollar, NPV_{Project A}=$ 7190022

NPV_{Project B}

= 20000000/(1+0.15)¹ + 10000000/(1+0.15)² + 6000000/(1+0.15)³-17000000

= 17391304.347826+7561436.672968+3945097.394592-17000000

= 28897838.415386-17000000

= 11897838.41

Rounding to the nearest dollar, NPV_{Project B}= $ 11897838

d)

For IRR, consider that the NPV at IRR equals to zero

therefore

Thus,

For Project A,

4000000/(1+r)¹ + 10000000/(1+r)² + 20000000/(1+r)³ -17000000 = 0

=> 4/(1+r)¹ + 10/(1+r)² + 20/(1+r)³ -17=0

For Project B,

20000000/(1+r)¹ + 10000000/(1+r)² + 6000000/(1+r)³ -17000000 = 0

=> 20/(1+r)¹ + 10/(1+r)² + 6/(1+r)³ -17 = 0

Because the cash flows are uneven, we calculate manually by trial & error or using solver in excel

For project A, Observe that if r=100 i.e 100%, then the NPV= 2+5+10=0

For Project B, we solve using excel as

Therefore IRR for Project A is 100% and Project B is 111.76%