1. GEK2507 1 Frederick H. Willeboordse frederik@chaos.nus.edu.sg Compound & Prosper!

2. GEK2507 2 Values Lecture 8

3. GEK2507 3 What kinds of values are there? Religion Politics Art In business, this is not really how we categorize value. Today’s Lecture

4. GEK2507 4 General Value Book Value Intrinsic Value Market Value Liquidation Value Time Value of Money These are the most common types of value in business Value

5. GEK2507 5 In very general terms one could call the value of a business the amount a purchaser and a seller agree upon during the sale of the business. In this sense, the value of the asset is equal to its price. This is, however, not always the case. The price of an asset can also be higher than its (or one of its types of) value(s) or lower than its (or one of its types of) value(s). General Value

6. GEK2507 6 Book value of an asset: This is simply the purchase price of an asset minus its accumulated depreciation. This is important for accounting but often a poor reflection of the true value of an asset. Book value of a stock: This is the amount of owner’s equity per share. Be aware that this is very different from Market Value. Book Value

7. GEK2507 7 Intrinsic value is the value an investor assigns to an asset. This is a highly individual matter and hence the intrinsic value of an asset is different for each investor. Generally, an investor would look at the cash flows of an investment (e.g. the dividends plus the proceeds of the sale of the stock at the end of the expected holding period), discount them with an expected rate of return and thus determine its intrinsic value. The differences in perception are an important ingredient for the functioning of the financial markets. Intrinsic Value

8. GEK2507 8 The market value of an asset is the price one would pay for that asset in a competitive market place. The same, of course, is true for a stock with the market place being the stock market. Boom or Gloom? Market Value

9. GEK2507 9 This is how much a business would fetch in a fire-sale. The liquidation value of certain assets can be extremely low since those assets may not be of any use to other parties. Liquidation Value

10. GEK2507 10 Pokemon Card: General Value: 12 dollars. The price you just bought it for from a friend. Book Value: 12 dollars. Not much depreciation in a Pokemon card. Intrinsic Value: 30 dollars. It was the only card you were missing! Market Value: 8 dollars. Actually, at the fair, many people turned out to have this card. Liquidation Value: 0.01 cents. The paper isn’t worth much Examples

11. GEK2507 11 Pokemon Card: You don’t agree with my reasoning here? Excellent! That’s exactly the point. Opinions on what constitutes value are diverse. Always keep that in mind when considering value statements. Examples

12. GEK2507 12 Coffee Shop: General Value: 500K. The price someone has just offered. Book Value: 200K. Your 250K investment minus 50K depreciation. Intrinsic Value: 250K. You didn’t like the idea of running a shop and you just want your money back. Market Value: 100K. Enough Starbucks already! Liquidation Value: 20K. Won’t get anything back for the renovation … Only little for the rest. Examples

13. GEK2507 13 Coffee Shop: Again … much to debate. Numbers themselves do not lie but the question is of course: What do they mean? Examples

14. GEK2507 14 The core of this lecture is actually quite similar to what we will do for bonds. We say that money has a “Time Value” because it can be invested and thus become more. In other words, if we have a dollar today, we expect/hope that we will have more than a dollar in the future. The Time Value of money is an essential concept when deciding on an investment. Time Value

15. GEK2507 15 The are a few terms important to know as with regards to the time value of money: Present Value: This is just the monetary value of the investments we have right now Future Value: This is the value of our investment in the future Compounding: Reinvesting the interest received, in other words, receiving interest on interest Time Value

16. GEK2507 16 The present and future values can easily be calculated in Excel We assume 10% interest So we see that 1000 dollars now will be 1610 dollars in 5 years Future Value Future value of 1000 dollars (in five years time).

17. GEK2507 17 Of course this can easily be expressed mathematically, but let’s do it step by step to understand what we are doing: Or: Value after two years = (Present Value + Interest) + Interest 1 st year: Value after one year = Present Value + Interest 2 nd year: Value after two years = Value after one year + Interest Substitute Line 1 This interest needs to be on the entire “Value after one year” Future Value

18. GEK2507 18 Or: 1 st year: Value after one year = PV + PV* r = PV*(1 + r) 2 nd year: Value after two years = PV * (1 + r) + PV * (1 + r) * r Hence we have: FV2 = PV * ( (1+r) + (1+r)*r) ) = PV * ( 1+r+r+r*r) = PV * ( 1 + 2r + r ) = PV * ( 1 + r) 2 2 FV2 = PV * ( 1 + r) 2 Future Value Value after one year

19. GEK2507 19 And thus we obtain the formula: Let’s check this for our example And indeed this is equal to 1610 as before. Future Value

20. GEK2507 20 Surprise! There’s also an Excel function for this: FV =FV(10%,5,0,-1000,0) As expected, the same as before! The interest rate The number of years The present value Note the minus! Unused parameters for this problem Future Value

21. GEK2507 21 Compounding Interest is powerful …. One thousand dollars becomes nearly 2600 after 10 years! That must be too good to be true. Compounding

22. GEK2507 22 Compounding Interest is powerful …. One thousand dollars becomes nearly 120,000 after 50 years if the interest is 10%. Note how the curve bends Upwards! 50-year Chart Compounding

23. GEK2507 23 A closely related topic especially in the context of the time value of money is that of discount. When a business decides to invest a certain sum, it needs to discount the expected future cash flows in order to decide whether the investment is worthwhile. After all, if your return is too small, it would not be wise to make the investment. Discount Let us start with the case of receiving a single lump sum sometime in the future. What would the ‘present value’ of this sum be?

24. GEK2507 24 Surprise! There’s an Excel function for this: PV =PV(3%,10,0,-1000,0) Note the relationship to inflation (see later on) The interest rate The number of years The future value Note the minus! Unused parameters for this problem Present Value

25. GEK2507 25 The problem is now that the cash flow is expected to grow over the years (since the business is hopefully getting better and better). As always, it may be complicated to imagine at first, but if we have an idea of how to get started we can take it from there. The obvious starting point is: The Cash Flows Discount

26. GEK2507 26 Let us assume that we have the following cash flows: What would they be worth? Discounting uneven cash flows

27. GEK2507 27 We can of course just sum them up: Is this a reasonable value for the cash flows? 15,450.- Discounting uneven cash flows

28. GEK2507 28 No! we need to have some return (namely 10% in this case): The sum of each year’s cash flow’s present values! Discounting uneven cash flows

29. GEK2507 29 Thus we obtain: Surprisingly little, isn’t it! Discounting uneven cash flows

30. GEK2507 30 Naturally there also is an Excel function for this: NPV Presumably standing for Net Present Value. Discount Rate Range of Cash Flows Discounting uneven cash flows

31. GEK2507 31 We just used the function NPV with NPV presumably standing for Net Present Value. It would seem that what we have calculated is the ‘Present Value’ and that there is no need for the ‘Net’. Indeed, usually one calls what we have calculated ‘Present Value’. Generally, ‘Net Present Value’ is when we subtract from this the cost of acquiring the cash flow in question. Excel’s NPV

32. GEK2507 32 Of course, often things work the other way around. We bargain to get a certain stream of cash flows and then we wonder what the compounded yield on this asset is going to be. Rate of Return

33. GEK2507 33 The key thing to realize is that at the actual yield, the purchase price equals the present value. In other words, the net present value is zero. Hence we can use the solver. Calculating the Yield

34. GEK2507 34 =D5-D3 Calculating the Yield

35. GEK2507 35 There is also a built in Excel function: IRR Standing for Internal Rate of Return =IRR(C10:C20) This is investment in year 0. Calculating the Yield

36. GEK2507 36 Another useful built in Excel function: XIRR It gives the IRR for non-periodic cash flows. =XIRR(C10:C17,B10:B17) This is investment at the beginning Calculating the Yield A cash flow at a certain date

37. GEK2507 37 There’s of course nothing wrong with this calculation but the determined present value assumes the stream of cash flows to be certain. In real life, one can never be entirely certain of future cash flows and one therefore needs to take risk into account. Risk

38. GEK2507 38 Generally speaking, the expected rate of return should increase when the risk increases and decrease when the risk decreases. Hence, the expected return on US government bonds (very little risk) is lower than than that of stocks (a company might go bankrupt). Risk

39. GEK2507 39 Money has Time Value Interest can compound Discount is an important concept Compound or be poor! Time is your friend! Be patient. Key Points of the Day