## Monday, August 22, 2011

### Intrinsic Value and Bond Valuation

This is Part 1 of a Series

The intrinsic value of an asset is only worth the sum of the present values of all the future cash flows it provides. This is the assumption of bond analysis and valuation. When you buy a bond, you are offered interest or coupon payments which you receive in varying intervals (e.g. monthly, quarterly, semi-annually, annually, etc.). You pay upfront for the principal, receive interest payments, and finally receive that principal you initially paid for upon maturity (i.e. expiration date of the bond). Coupon Bonds. In bond analysis, a bond is only worth the sum of the present values of all its coupon payments and principal upon maturity.
What is Present Value? It is the discounted value of a cash you’d be receiving in the future. It is based on the premise that as rational capitalists, we give more value to cash we can hold, spend, or invest now (at the present time) than the same cash amount we would receive in the future. It does make sense if we observe an extreme example: were you offered a million pesos, would you rather have it now or have it 10 years later? Most definitely, that Php1M is worth more to you now than it is (at the same amount) 10 years after!

How about Discounting? Discounting is a technical, finance-slang term akin to your more familiar, layman’s interest rate. Say you have a Php100 and you offered it to me as a loan with 10% interest per annum. After a year, assuming I stay true and make good our original terms, your Php100 would be worth Php110.

In algebra, this is expressed as:

FV = PV x (1+i)^n
Where:
FV = Future Value
PV = Present Value
i = interest rate
n = period in years

Using the formula, this is how we solve our above example (where the unknown is FV):
110 = 100 x (1+10%)^1

In a similar manner but now coming from a different angle, say I would pay you Php110 after a year, how much money would you loan me now? That depends on how much do you value that Php110 you’d be receiving from me a year later. Hence, if you say you value it today at Php100, then effectively you’re discounting that future Php110 at a 10% discount rate.

The unknown this time is PV, so we would have to transpose above formula to arrive at this equation:

PV = FV / (1+i)^n
Where: i = discount rate

100 = 110 / (1+15%)^1

So you see, the discount rate is just the same as the concept of interest rate; it’s just coming from a different point of view where the given is the future cash amount you’re anticipating and the unknown is the price or cash you have to pay now to receive that future cash.

Mentioned formulas shall be two cornerstone equations in evaluating the present cash value of an asset.

Now let me ask: what is the worth of a 5-year bond whose principal is Php100 and has an annual coupon or interest rate of 10%?

Let’s recast the cash flows:
Year 1 = Php10 (interest/coupon payment)
Year 2 = 10
Year 3 = 10
Year 4 = 10
Year 5 = Php10 + 100 (coupon + principal payment) Required Rate of Return. The worth of a bond is primarily determined by the discount rate which is synonymous to your required rate of return.
Before trying to answer this question, let me tell you: do you know it’s actually worth whatever price you want to pay for it? I mean, you can pay Php110 for it, even Php120. But if you are first most sensitive to how much rate of return you’d want to earn from this deal, then you’d definitely want to discount its cash flows at that rate. Thus, the starting point is by first asking: how much rate of return do you require and intend to achieve? Or to ask simply: what is your required rate of return?

In a similar note, as a return-conscious investor, instead of saying: The price you pay determines your rate of return, we're more interested in: Your required rate of return determines the price you shall pay.

Let’s say we want to earn 15%. Given that 15% required rate of return (discount rate), we can now appropriately answer how much the bond is worth.

Discounted Cash Flows
Year 1 = 10/(1+15%)^1 = Php8.70
Year 2 = 10/(1+15%)^2 = 7.56
Year 3 = 10/(1+15%)^3 = 6.58
Year 4 = 10/(1+15%)^4 = 5.72
Year 5 = 110/(1+15%)^5 = 54.69
Sum of Present Values = Php83.24

At a 15% discount rate, the bond is worth Php83.24. It’s actually the same as saying: If you want to earn 15% on this bond deal, you would have to buy that bond for Php83.24. The discount rate is your required rate of return (many analysts, however, would try to insist for a more accurate discount rate, but in my opinion, it's a matter of personal preference; it's you investing anyway, not them, so it's a dictate of your required rate of return, not theirs). Continue to Part 2: Intrinsic Value and the Equity Bond Theory

## Disclaimer

The information presented here is for educational purposes only. Under no circumstances should it be construed as a recommendation to buy, sell, or hold any stocks. If you choose to use this information, you do so at your own risk.

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