Question

1. If you are evaluating a project with the following cash flows, for what range of costs of capital would you accept the project?

	Year 0	Year 1	Year 2	Year 3
Project CF	$1,000	-$700	-$600	-$500

2. You are considering two mutually exclusive projects with the following cash flows. The appropriate cost of capital for Project A is 10%. The appropriate cost of capital for Project B is 14%.

	Year 0	Year 1	Year 2	Year 3
Project A	-$1,000	$500	$600	$700
Project B	-$10	$10	$20	$30

1. Write the equation used to find IRR of each project. Find the IRR of each project. Based solely on IRR, what is your capital budgeting decision?
2. Find the Profitability Index of each project. Based solely on PI, what is your capital budgeting decision?
3. Find the Payback Period of each project. Based solely on Payback, what is your capital budgeting decision

Answer 1

1) IRR is the rate where NPV of the project is 0

​​​​​​0=NPV= C(t)/(1+IRR)t​​​​​​- initial investment

t = time period( i.e. 1,2,3)

C(t) = cash inflow during the period t

Initial investment =1000 inflow in this case

So 0= (-700)/(1+IRR)+(-600)/(1+IRR)2+(-500)/(1+IRR)3 +1000

Solving the above we get IRR= 39.0262%

Hence the range of cost of capital will be 39.0262% to infinity

2)a) As IRR formula is shared above

For Project A IRR=0={500/(1+IRR)1+600/(1+IRR)2+700/(1+IRR)3} - 1000

IRR=33.875%

For Project B IRR =0={10/(1+IRR)1+ 20/(1+IRR)2+30/(1+.IRR)3 } - 10

Therefore IRR= 137.4424%

Based solely on IRR we should select Project B.

b) Profitability index (PI) ={ present value of cash flow/ initial investment}

For Project A PI = {500/1.1 + 600/(1.1)2+ 700/(1.1)3}/1000 =1.4763

Similarly Project B PI= {10/1.14 + 20/(1.14)2+ 30/(1.14)3}/ 10 =4.441

Base on PI we should select Project B

c) Payback period is the period to get back the initial investment amount.

Hence Payback period of protect A =1 year + 500/600

= 1.833 years

Payback period of project B = 1 year.

Based on payback period we should select Project B.