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Investment: the importance of timing

We have already discussed the fact that in comparing investments, what we get and when we get it are two of the three key factors. We have talked about how returns can come as income, lump sum, or both. Let’s talk a bit more about the timing.

Time is money

Imagine this situation. A well-known bank is offering £1,000 to be collected in cash one year from today. Anyone can bid for it, and the highest bidder by 5pm today gets it. There is no risk. If you are the highest bidder, you will get it for certain. How much would you bid? Let’s look at some possible bids you could make. Nobody in their right mind will bid more than £1,000. There isn't much point in paying £1,000 to get £1,000, so it has to be less. If you bid, say, £500 you can be pretty sure that someone will bid higher. What you are trying to decide is how much £1,000 in a year’s time is worth to you now. Putting it another way, what we want to know is the present value (that means the value now) of an amount of cash that we expect to get one year from now.

Let’s turn the problem on its head, and see what £1,000 now would be worth in a year’s time. We look in the newspaper or on the web and see that the best rate of interest we could get in a savings account with a bank or building society is a little over 5%. Interest rates might go up or down over the next 12 months, but probably not by very much. If we took a stab at 5% (we will forget about tax for this example), then we would expect to earn 5p interest on every pound we've saved by this time next year. Our £1 becomes £1 plus 5p (£1.05). If we save £100, we get back 100 times £1.05: if we save £1,000 then it becomes 1,000 times £1.05.

Using present value

Turning that back again, if we want exactly £1,000 this time next year, we would have to save £1,000 divided by 1.05. The present value of £1,000 one year from now is £952.38. If we wanted to know the present value of our £1,000 in two years time, we simply divide the £952.38 by 1.05 again (assuming we think our 5% interest rates won’t change significantly). That would be £907.03. What we are doing is to discount future cash flows using 5% as our discount rate. We can use the same formula to calculate the value now of any sums of cash that we expect to get in the future. That means that we can compare investments that return cash to us in different ways, and at different times. If the present value of the cash flows from the investment is greater than the amount we have to invest, then the investment is said to have a positive net present value (NPV). Naturally, we want all our investments to have a positive NPV!

NPV and rate of return

Suppose we invest £1,000 today and we expect to get back £1,102.50 in two years' time. Is that a good investment? By using the idea of discounting future cash we can ask what discount rate we would have to use to give us a present value that is equal to the amount of money we expect to invest. In other words, what discount rate gives us an NPV of zero? We can calculate that rate. In the example, it is 5%. It is the rate of return on the investment (usually referred to as the internal rate of return or IRR). Investments that give us the highest IRR for the same risk are the most attractive.

Time to take another look at risk.

 

  9 October, 2008 © 2008 K.R.Wade and Co Ltd prev page next page