Case 026Capital budgetingWarm up

Anantam Packaging can add a production line for Rs 100 crore. Build its NPV at a 12% WACC as a cash flow vector times a discount factor vector, and say whether to go ahead.

Moody'sNew York · 2018

The situation

Anantam Packaging makes corrugated boxes. It can add a new line for Rs 100 crore, paid today. The line is expected to produce after-tax cash flows of Rs 20 crore in year 1, Rs 28 crore in year 2 and Rs 32 crore in each of years 3, 4 and 5. At the end of year 5 the machinery can be sold for Rs 20 crore, also after tax.

The finance team uses a 12% weighted average cost of capital for projects of this kind. The interviewer hands you a blank sheet and says: build it as two vectors.

Your task

Set up the NPV as one vector multiplied by another, give the answer, and say what it means for the decision.

Quick check

Undiscounted, the inflows add up to Rs 164 crore against Rs 100 crore spent. Roughly what is the NPV at 12%?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

NPV is about Rs 12.8 crore, so the line clears the 12% hurdle. Put the five cash flows in one row and the five discount factors, 1 over 1.12 raised to each year, in the row below. Multiply them pair by pair and add: Rs 112.8 crore. Subtract the Rs 100 crore outlay. The IRR is about 16.4%, and without the salvage value the NPV nearly vanishes.

Step 1Why does the interviewer want two vectors rather than a formula?

Because that is how a model is built and checked. Think of a shopping bill: one column of quantities, one column of prices, and the total is each quantity times its price, added up. An NPV is the same bill: a row of cash flows times a row of discount factors, summed, less the outlay. In a sheet that is one SUMPRODUCTA spreadsheet function that multiplies two ranges cell by cell and adds the results. over two ranges, and anyone reviewing it can see every year's contribution rather than trusting one long nested formula.

NPV is one row times another, then summed: Anantam's new line, Rs croreCash flowthe first vector20283232salvage52Year 1Year 2Year 3Year 4Year 5x Discount factor1 / 1.12 to the year0.8930.7970.7120.6360.567= Present valuethe products17.922.322.820.329.5Sum of products112.8less outlay 100NPV +12.8croreIn a sheet: =SUMPRODUCT(cash flow row, discount factor row) - 100
Anantam's cash flows of Rs 20, 28, 32, 32 and 52 crore, multiplied by discount factors from 0.893 down to 0.567, give present values summing to Rs 112.8 crore, an NPV of Rs 12.8 crore after the Rs 100 crore outlay.
Step 2How do you build each vector?

The cash flow vector is the five years, with the salvage value added to year 5 rather than left out. That is the most common slip: the Rs 20 crore resale is real cash, and leaving it off understates the project. The discount factor vector is 1 divided by 1.12 raised to the year number, so year 1 is 0.893 and year 5 is 0.567. Writing the factors out as their own row lets you check them at a glance: each is the one before divided by 1.12.

YearCash flowDiscount factorPresent value
0(100.0)1.000(100.0)
120.00.892917.86
228.00.797222.32
332.00.711822.78
432.00.635520.34
552.00.567429.51
NPV64.012.80
Rs crore. Year 5 carries Rs 32 crore of operating cash plus Rs 20 crore of salvage. The present values add to Rs 112.80 crore, and after the Rs 100 crore outlay the NPV is Rs 12.80 crore.
The relationship
NPV=∑t=15CFt×1(1.12)t  −  100=112.8−100=12.8\text{NPV} = \sum_{t=1}^{5} CF_t \times \frac{1}{(1.12)^t} \; - \; 100 = 112.8 - 100 = 12.8
CF_tafter-tax cash flow in year t, including salvage in year 5
1/(1.12)^tthe discount factor for year t at a 12% WACC
100the outlay today, which needs no discounting
What it says in wordsMultiply each year's cash by what a rupee of that year is worth today, add them up, and take off what you spend now.
Step 3What does the answer tell you, and where is it fragile?

A positive NPV means the line earns more than the 12% the capital costs, by Rs 12.8 crore in today's money. The IRR of about 16.4% says the same thing in a rate. The cushion is thin: without the salvage value the NPV falls to about Rs 1.4 crore. So the first question to ask is how firm that resale figure is, and the second is what happens if years 3 to 5 come in at Rs 28 crore instead of 32.

Close the way a reviewer would. The line creates value on these numbers, the result leans on the last two years and the salvage, and the two-vector layout lets a manager change any one assumption and watch the total move. That last point is what the interviewer asked about when they said vectors.

Where candidates lose it

The commonest loss is leaving the salvage value out, or discounting it as if it arrived in year 1. It arrives in year 5 with the last operating cash flow, so it gets the year 5 factor.

The second is an off-by-one in the factor row: discounting year 1 cash by 1.12 squared because the outlay was counted as year 1. The outlay is today, year 0, with a factor of exactly 1.

What the interviewer asks next

  • What WACC makes the NPV exactly zero, and how would you find it in a sheet?
  • How would you add a Rs 5 crore working capital investment that is recovered in year 5?
  • If the cash flows arrive evenly through each year rather than at year end, how does the factor row change?

Asked at Moody's, Analytics, New York, 2018 (Wall Street Oasis): Construct an NPV formula using 2 vectors and show me your thought process.

Company names and figures are illustrative.