Hi guys,

Need some help in explain the answer for this question as I don't understand what they means...

Here is the question:

A project costs £100,000 and has an operating cash flow of £10,000 in the first two years and £40,000 in the following three years. The project stops at the end of year 5. The expected return on the market index is 12% and the risk free rate is 5%.

(b) Suppose the operating cash flow consists of both revenues and costs, and suppose the expected revenue each year is 120% of the net expected operating cash flow given above, while the expected costs each year are 20% of the net expected operating cash flow. You should assume that the costs are uncorrelated with the movements of the market index. The revenues have a beta of 0.75. Work out the NPV of the project.

And the answer give is:

The cost of discount rate for the costs is 5 per cent. The discount rate for revenues is 5% + 0.75(12%−5%) = 10.25%. The costs are 2, 2, 8, 8, and 8; and the revenues are 12, 12, 48, 48, and 48.
The present value of the costs is 2/1.05 + 2/1.052 +... = 23.5; the
present value of the revenues is 12/1.1025 + 12/1.10252 +... = 118.5
The present value of future cash flow is 118.5 – 23.5 = 95. The net present value is therefore −100 + 95 = −5, and the project should be rejected.

From my understanding
I believe the cost of discount rate for the cost is 5% is due to uncorrelated with the movement of the market index therefore the discount rate should be the risk free rate but I don't understand on the part for the discount rate of the revenue and how did they get the cost of 2... and revenues of 12...

I like this one on a couple of fronts. For one, I appreciate how you've structured your post--nice partitioning into the three sections making it very easy to follow. Nicely organized post.

I also like the concept illuminated by the question itself. It's an important one that's not seen often enough in the literature. Real world, it's frequently the case that a period's cash flow is actually comprised of separate 'component' cash flows. Once you've acknowledged that, it usually follows that each component CF requires a separate discount rate in your PV work.

Expenses, for example, are much easier to forecast than Revenues. Thanks to the lease I've signed, I know precisely what rent my factory will pay this year. I can only guess, though, at how much product will be demanded by my customers over the same coming 12 months.

Generally, then, the cash outflows represented by Expenses should be discounted at a lower rate than the rate used for discounting the less-predictable Revenues. And that's what your question is doing here--it's separating each year's CF into a Revenue and Expense component, and discounting them separately at their appropriate rates.

As stated, Rev is 120% of the net, which leaves Expense--by default--at 20% of the net. (Remember that Net = Revenue minus Expense) For example, given these percentages, it's easy to see that a net of 10K is produced by Revenue of 12K, less Expenses of 2K. Similarly, a net of 40K, using those same percentages, implies that Revenue is 48K and Expense is 8K.

All that's left, then, is to determine the discount rates appropriate to each CF stream. You're given that the Expense stream should be hit with the risk-free rate (presumably because there's practically no uncertainty involved in their forecasting--not always a reasonable assumption, but it'll do for now).

Revenues, on the other hand, are assigned a beta of 0.75. That means that it's been decided that their discount rate should be the risk-free rate, plus 75% of the market's risk premium (which is given as 12 - 5 = 7%).

Handing it back to you now, amigo... good luck!

Hi, thanks for your great explanation. I have to admit that it's a great question asked.