Question

You are the head of Corporate Investments for Everspring, Corp., which has a cost of capital (discount rate) of 10%. You are deciding on whether to invest your firm’s money in the three projects below. All cash flows for each project are shown; all projects are abandoned after Year 5.

  Project A Project B   Project C
Initial Investment ($100,000) ($500,000)   ($6,500,000)
Year 1 $30,000 ($100,000) $1,000,000
Year 2 $40,000 $200,000 $1,500,000
Year 3 $50,000 $200,000 $2,000,000
Year 4 $60,000 $200,000 $2,500,000
Year 5 $70,000 $200,000 $3,000,000

1. Assume each year’s cash flows occur evenly over the year. If your required payback period is 30 months, in which projects would you invest?

2. Assume each year’s cash flows occur at the end of the year. What is the net present value (NPV) of Project A?

3. Assume each year’s cash flows occur at the end of the year. What is the internal rate of return (IRR) of Project B?

4. Assume each year’s cash flows occur at the end of the year. What is the profitability index (PI) of Project C?

Answer 1

payback period is the time period in which entire initial cost of investment is recovered.

for Project A

year	cashflows	cumulative cashflows
1	30000	30000
2	40000	70000
3	50000	120000
4	60000	180000
5	70000	250000

initial investment in project A is $100,000 which will be recovered by 3 years ,

Given that the cash flows will evenly accrue for the entire year ie 50000/12= 4167 per month in 3rd year

Pay back period for project A = in 2 years we have recovered 70000 so balance (100000-70000)= 30000 will be recovered in 3rd year , so 30000/4167 = 7.19 ie whithin approximately 7months

Total months = 24 months (2 years) + 7.19 months = 31.19 months

similary for Project B

intiial investment = 500000

cumulative cash flows for 4 years = (100000)+200000+200000+200000 = 500000

therefore payback period for project b is 4 years or 48 months.

Similarly for Project C

intial investment = 6,500,000

cumulative cash flows for 3 years =1000000+1500000+2000000= 4,500,000

remaining balance recovery = 6500000-4500000=2,000,000

since cash flow accrue evenly through out the year ,

4th year = 2500000/12=208333

balance months = 2000000/208333= 9.6 months

total pay back period for project c = 36 months ( 3years) + 9.6 months = 45.6 months

Decision making under Pay back period method :

Project	Payback period
A	31.19 months
B	48 months
C	45.6 months

Since project A is near to 30 months the company shall invest in project A as they can recover their initial in vestment within 31.19 months compared to other projects B & C.

2. NPV of Project A = Present Value of cash inflows - present value of cash outflows

year	cashflows	PVF @10%	discounted cashflows
1	30000	0.909	27270
2	40000	0.826	33040
3	50000	0.751	37550
4	60000	0.683	40980
5	70000	0.621	43470
		PV of cash flows	182310

NPV of project A = 182310-100000 = 82310

Since NPV is Positive we can accept project A.

3. Calculation of IRR for Project B

IRR is the rate at which present value of cash inflow will be equal to present value of cash outflows

ie Present value of cash inflows = present value of cash outflows

year	cashflows	pvf @10%	discounted cashflows	pvf @ 8%	Discounted cashflows
1	(100000)	0.909	(90900)	0.926	(92600)
2	200000	0.826	165200	0.875	175000
3	200000	0.751	150200	0.794	158800
4	200000	0.683	136600	0.735	147000
5	200000	0.621	124200	0.681	136200

present value of cash flows @ 10% = 485300

present value of cash flows @ 8% = 524400

required cash flow = 500000

decrease of discount rate by 2% has increased the cashflow by 524400-458300=39100

required increase in cashflow = 500000-485300 = 14700

by using interpolation method we are finding the IRR

2% decrease - 39100 increase

? - 14700 increase

= (14700 *2) / 39100 =0.75% decrease

therefore IRR of project B = 10% -0.75% = 9.25%

Note: we have taken 8% as an estimate you can solve the above sum with any rate below 10% as the discounted cash flow @ 10% is less then required cashflow of 500000.

4. Profitability index of project C = present value of cash inflows / present value of cash outflows

= {(1000000*0.909)+(1500000*0.826)+(2000000*0.751)+(2500000*0.683)+(3000000*0.621)}/6500000

=1.11

decision ; since Profitability index is above 1 it is profitable to accept the project.