Question

NPV Your division is considering two projects with the following cash flows (in millions): 0 2 3 Project A Project B $29 -$16 $15 $8 $13 $3 $3 $6 a. what are the projects' NPVs assuming the WACC is 5%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A $ Project B $ what are the projects' NPVs assuming the WACC is 10%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A$ Project B $ what are the projects' NPVs assuming the WACC is 15%? Round your answer to two decimal places. Enter your answer in millions. For example, an answer of $10,550,000 should be entered as 10.55. Project A $ million million million million million Project B $ million

Answer 1

a)

For the Calculations of NPV, we will find out the present value of all cash outflows and inflows. If the resulting figure is in positive, it is PV of Net Cash Inflows. If the amount is in negative, it is PV of net Cash Outflows. NPV can be positive or negative.

Calculation of NPV for Project A @ WACC 5%

Year	Cash Flows	Discounting Factor @ 5%	Present Value of Cash Flows ($)
0	-29000000	1	-29000000
1	15000000	0.95238095	14285714.29
2	13000000	0.90702948	11791383.22
3	3000000	0.8638376	2591512.796
		TOTAL ($)	-331389.6987
		TOTAL ( $ Million)	-0.33

Calculation of NPV for Project B @ WACC 5%

Year	Cash Flows	Discounting Factor @ 5%	Present Value of Cash Flows ($)
0	-16000000	1	-16000000
1	8000000	0.95238095	7619047.619
2	3000000	0.90702948	2721088.435
3	6000000	0.8638376	5183025.591
		TOTAL ($)	-476838.3544
		TOTAL ( $ Million)	-0.48

Calculation of NPV for Project A @ WACC 10%

Year	Cash Flows	Discounting Factor @ 10%	Present Value of Cash Flows ($)
0	-29000000	1	-29000000
1	15000000	0.9090909	13636363.64
2	13000000	0.8264463	10743801.65
3	3000000	0.7513148	2253944.403
		TOTAL ($)	-2365890.308
		TOTAL ( $ Million)	-2.37

Calculation of NPV for Project B @ WACC 10%

Year	Cash Flows	Discounting Factor @ 10%	Present Value of Cash Flows ($)
0	-16000000	1	-16000000
1	8000000	0.90909091	7272727.273
2	3000000	0.82644628	2479338.843
3	6000000	0.7513148	4507888.805
		TOTAL ($)	-1740045.079
		TOTAL ( $ Million)	-1.74

Calculation of NPV for Project A @ WACC 15%

Year	Cash Flows	Discounting Factor @ 15%	Present Value of Cash Flows ($)
0	-29000000	1	-29000000
1	15000000	0.8695652	13043478.26
2	13000000	0.7561437	9829867.675
3	3000000	0.6575162	1972548.697
		TOTAL ($)	-4154105.367
		TOTAL ( $ Million)	-4.15

Calculation of NPV for Project B @ WACC 15%

Year	Cash Flows	Discounting Factor @ 15%	Present Value of Cash Flows ($)
0	-16000000	1	-16000000
1	8000000	0.86956522	6956521.739
2	3000000	0.75614367	2268431.002
3	6000000	0.65751623	3945097.395
		TOTAL ($)	-2829949.864
		TOTAL ( $ Million)	-2.83

To summarise the above workings,

Amount in $ Million	WACC @ 5%	WACC @ 10%	WACC @ 15%
NPV of A	-0.33	-2.37	-4.15
NPV of B	-0.48	-1.74	-2.83

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b)

Internal Rate of Return (IRR) of a Project is a rate of return at which NPV = 0. Thus, IRR is indifferent of the WACC.

So, IRR is simply the rate, which when applied to all cash inflows and outflows, results in NPV = 0

Calculation of IRR for Project A

Let, IRR be i

At IRR,

NPV = 0

=> NPV = -29,000,000/ (1+i)⁰ + 15,000,000/(1+i)¹ + 13,000,000/(1+i)² + 3,000,000/(1+i)³

=> NPV = -29,000,000/ (1+i)⁰ + 15,000,000/(1+i)¹ + 13,000,000/(1+i)² + 3,000,000/(1+i)³

You may use Trial and error and / or interpolation to find the IRR.

At i = 4% = 0.04, NPV = $ 0.11 Million

At i = 4.25% = 0.0425, NPV = $ 0.00 Million

Therefore IRR of Project A is 4.25%

You may also calculate IRR using excel function as shown below

Year Cash Flows 29000000 15000000 13000000 3000000 0 4 IRRrr(C3:C6) 10 12

It will give IRR = 4.2455 % = 4.25% (Rounded off)

IRR for Project B

Making similar calculations as above for Project B, IRR for Project B = 3.2964% = 3.30% (Rounded off)

IRR of Project A at WACC @ 5% or 10% or 15% = 4.25%

IRR of Project B at WACC @ 5% or 10% or 15% = 3.30%