Question

Capital Budgeting Question:

You are considering two mutually exclusive projects for potential investment. The cash flows for the two projects are given. For both projects, the required rate of return is 12%.

Year	Project A	Project B
0	($40,000)	($40,000)
1	$14,400	$0
2	$14,400	$0
3	$14,400	$0
4	$14,400	$70,000

Find the following:

1. The Net Present Value (NPV) .

2. The Internal Rate of Return (IRR) .

3. Use Excel to draw a graph of the NPV of these cash flows as a function of the discount rate (NPV Profile).

4. What is the value of cross over point?

5. What is your recommendation, which project the company shall choose? Explain the basis of your choice.

Answer 1

1=n	2	3=1/1.12^Yr.n	4=2*3	5	6=5*3
Year	Project A	PV F at 12%	PV at 12%	Project B	PV at 12%
0	-40000	1	-40000	-40000	-40000
1	14400	0.89286	12857.14	0	0
2	14400	0.79719	11479.59	0	0
3	14400	0.71178	10249.64	0	0
4	14400	0.63552	9151.46	70000	44486.27
		NPV=	3737.83		4486.27
		IRR=
IRR=	16.37%			15.02%

1.NPV=Sum of the PVs of all cash flows including initial investment at yr.0 , ie. -CF0+(CF1/(1+r)^1)+(CF2/(1+r)^2+(CF3/91+r)^3+(CF4/(1+r)^4

NPV of Project A=-40000+(14400/1.12^1)+(14400/1.12^2)+(14400/1.12^3)+(14400/1.12^4)=

3737.83

NPV of Project B=-40000+(70000/1.12^4)=

4486.27

2. IRR is the discount rate at which the NPV =0

ie.-CF0+(CF1/(1+r)^1)+(CF2/(1+r)^2+(CF3/91+r)^3+(CF4/(1+r)^4=0

so, for Project A, equating the discounted values at r% to 0,we have,

-40000+(14400/(1+r)^1)+(14400/(1+r)^2)+(14400/(1+r)^3)+(14400/(1+r)^4)=0

& solving for r, we get the IRR as

16.37%

for Project B, equating the discounted values at r% to 0,we have,

-40000+(70000/(1+r)^4)=0

& solving for r, we get the IRR as

15.02%

4.Cross over point is the discount rate at which both the NPV s are equal.

ie. Equating both the NPVs & solving for r,

-40000+(14400/(1+r)^1)+(14400/(1+r)^2)+(14400/(1+r)^3)+(14400/(1+r)^4)=-40000+(70000/(1+r)^4)

& solving for r, we get the cross over discount rate as

13.16%

Value/NPV at Cross-over rate=$ 2690 for both Projects A & B

5. Recommendation

At 12% discount rate, Project B is recommended.

&

If the discount rate is less than 15.02% project B isrecommended

If the discount rate is between 15.02% & 16.37% project A is recommended

In addition,

NPV profiles near cross-over rate			Cross-over rate	Recommended
	A	B
13.50%	2391	2180	Above	project A
13.16%	2690	2690	C/O rate	Indifferent
13%	2832	2932	Below	Project B