Question

Capital Budgeting Analysis

A firm is planning a new project that is projected to yield cash flows of -$515,000 in Year 1, $586,000 per year in Years 2 through 3, and $678,000 in Years 4 through 6, and $728,000 in Years 7 through 10. This investment will cost the company $2,780,000 today (initial outlay). We assume that the firm's cost of capital is 9.65%.

(1) Draw a timeline to show the cash flows of the project.

(2) Compute payback period, net present value (NPV), profitability index (PI), internal rate of return (IRR), and modified internal rate of return (MIRR).

(3) Discuss whether the project should be taken.

Answer 1

1- Timeline of the Cash Flows:

Particulars/Year	0	1	2	3	4	5	6	7	8	9	10
Initial Outlay	2780000
Cash Flows		-515000	586000	586000	678000	678000	678000	728000	728000	728000	728000

2- Calculation of Different Metrics

A- Payback Period

Particulars/Year	0	1	2	3	4	5	6	7	8	9	10
Initial Outlay	2780000
Cash Flows		-515000	586000	586000	678000	678000	678000	728000	728000	728000	728000
Cumulative Cash Flows		-515000	71000	657000	1335000	2013000	2691000	3419000	4147000	4875000	5603000

Payback period is defined as the period after which we receive our Initial Outlay. This is a normal payback period so we dont discount the cash flows.

Here we can see that in the 7th year our Cash Flows go above and beyond the Initial Outlay.

So Payback period = 7 + (2780000-2691000) / 728000 = 7+0.12 = 7.12 Years.

In this calculation we have basically calculated how much amount do we need in order to cover our initial cost after the 6th year and divided it by the 7th years total cash flows.

B- Net Present Value (NPV)

Particulars/Year	0	1	2	3	4	5	6	7	8	9	10
Initial Outlay	2780000
Cash Flows		-515000	586000	586000	678000	678000	678000	728000	728000	728000	728000
Present Value of Cash Flows		-469676	487394.2	444499.9	469024.1	427746.5	390101.7	382006.7	348387.3	317726.7	289764.4
Total Present Value	3086975
Net Present Value	306975.2

NPV is calculated as = Present Value of Inflows- Present Value of Outflows. In the above table I have calculated them.

NPV = $ 306975.2

C- Profitability Index

Profitability Index is calculated as= Total present Value of Inflows / Total Present Value of Outflows

Using the numbers from the table given in NPV=

Total Present Value of Inflows = 3086975

Total Present Value of Outflows = 2780000

Profitability Index = 3086975 / 2780000 = 1.11

A Profitability Index above 1 shows that the Project is profitable and viable.

D- IRR and MIRR

IRR and MIRR are both calculated by pegging Cash Inflows against Cash Outflows. IRR is the discount amount priced in making the PV of cash inflows equal to the Cash Outflows. MIRR is the price in the Investment plan making the PV of Cash Inflows equal to the PV of Cash Outflows.

IRR = Present Value of Cash Inflows = Present Value of Cash Outflows.

Here in both the case we solve for the Interest rate. Using the same formula as NPV we just dont put in Interest rate and solve for the same.

Solving for R we get

IRR = 11.50%

MIRR = 10.64%

3- Whether the Project should be Taken

Yes, The project should be taken. The Net present value is positive and we earn approximately 11% on our investment which is a good return. The only concern here is that the payback period is very long otherwise since the project is profitable it should be taken.