1. GEM2508 1 A Finance Survival Kit GEM2508 Frederick H. Willeboordse frederik@chaos.nus.edu.sg

2. GEM2508 2 Bonds Lecture 8

3. GEM2508 3 Today’s Lecture Excel What are Bonds in finance How can we use Excel to calculate a reasonable bond price. A bond from 1863

4. GEM2508 4 Excel Basics – Date Math Calculating the number of days between two dates or doing math on dates is tricky. Hence Excel stores dates to ‘number of days since Jan 1, 1900’. This is done with the DATE function. How the date is displayed in a cell depends on how the cell is formatted. In the top picture it is formatted as a ‘date’ and in the bottom picture it is formatted as a number. Syntax:

5. GEM2508 5 Excel Basics – Date Math This allows us to easily calculate the number of days from one date to another.

6. GEM2508 6 Excel Basics – Series Fill 1) Enter the first value 2) Select a range to fill 3) Go to the Fill-Series Menu 4) Choose how you want to do the fill Result

7. GEM2508 7 In finance, a bond is a loan contract where an investor lends a government or a company a certain amount of money and then receives interest at regular intervals for some period of time. The contract has a certain length and the originally stated loan amount is paid back in full at the end of the contract. The US Treasury Bonds

8. GEM2508 8 The are some terms one should be familiar with: Face Value: This is also called “Par Value”, “Maturity Value” or “Principal”. This is the amount that needs to be paid back at the end. Maturity Date: The date on which the principal needs to be returned. Coupon Rate: The percentage of the regular interest. Bonds

9. GEM2508 9 Bonds also have certificates like stocks. And also just like stocks, bonds can be traded. Hence the prices of bonds can fluctuate quite a bit. In fact because there’s a fixed regular interest on the bond and because market interest rates can change, the calculation of a reasonable price for a bond is not trivial. More on this later… Even when the bonds are issued, one does not necessarily have to pay exactly the principal amount. There can be a premium or a discount. Bonds

10. GEM2508 10 An important concept in finance is that of a/the discount rate. In the case of bonds this equals the interest rate that the Federal Reserve charges other banks on short term loans. The discount rate is an important reference rate for other interest rates. Why is it called the discount rate? It has to do with the present value of an investment that will pay off in the future. Bonds

11. GEM2508 11 If e.g. we know that we will get 1000 dollars for a bond next year, and if the current interest rate is 5%, how much would the bond be worth now. If the interest rate is 5%, the investment will be worth 105% in one year. Hence: 1000 dollars (the end value of our investment) = 105% of current value. In other words current value = 1000/105% = 952 dollars. How about if we get 1000 dollars in two years? Bonds

12. GEM2508 12 Time for Excel! Why the 1? Bonds

13. GEM2508 13 Hence, for a bond which will give us 1000 dollars in 10 years time, 614 dollars is a reasonable price. Technically speaking, this is a zero coupon bond since we are not getting any interest paid each year. Let’s do the calculation again for the case that we get a yearly interest payment. Bonds

14. GEM2508 14 The face value of the bond is 1000 dollars and at the end of the year we get 50 dollars interest (the interest rate is 5%). This is a bit trivial so don’t think about it too much! In one year our investment will be worth 105% but we will also have 1050 dollars. As before: current value = (end value)/105% = 1050/105%. This is of course just 1000 dollars! The same would be true for ten years. Bonds

15. GEM2508 15 Hence: 10 year 1000 dollar bond with 5% interest paid yearly: Current Value 1000. 10 year 1000 dollar bond with no interest paid yearly: Current Value 614. Perhaps this makes it a bit clearer why it’s called the ‘discount rate’. And now … bang … the big point: Bonds

16. GEM2508 16 Interest rates change!!!!! When a bond is issued, it’s interest rate is set to the prevailing rate of that moment. It should come as no surprise that the value of a bond will also be influenced by the difference between it’s originally set (and let me stress fixed) coupon rate and the currently prevailing rate. Bonds

17. GEM2508 17 Let us first illustrate this with an extreme example: During freak-year 1, the interest rate is 50%. A 1000 dollar 10-year bond is issued and it will pay 500 dollars a year in interest. A year later we’re in ‘Japan during the nineties’ mode and interest has dropped to 1%. Since a new bond will only give us 1% a year (1 dollar vs the 500 dollars of the freak-bond), the freak-bond must be worth a lot. Roughly: 9 (the remaining years) * 500 + principal = 5500 dollars. Bonds

18. GEM2508 18 Let us look at this a bit more carefully: We have a bond that will give us 1000 dollars in 9 years time that will also pay us 500 dollars of interest a year. Since the interest received can be reinvested at the end of the nine years we should have a bit more than the 5500 dollars. Naturally bonds can be traded. The CBOT in action. Bonds

19. GEM2508 19 With Excel we find that at the end we have: Interest on Bond Cash from previous year + current interest This is the cash we end up with Bonds

20. GEM2508 20 Now we can discount this back to today And we find that the current value is 5,197 dollars. Bonds

21. GEM2508 21 Excellent! Again, a conceptually far from trivial problem could be solved with Excel by “UNDERSTANDING” it. Of course we can also put this in equations: Present Value of Coupons Present Value of Face Value Bond Value With T = Maturity Date and r = Current Interest Rate Bonds

22. GEM2508 22 Let’s try that out: This is straightforwardly calculated in Excel: (Excel is a great general purpose calculator) Bonds

23. GEM2508 23 Now we can discount this back to today And we find that the current value is 5,197 dollars. Hey! That is the same value we found before. Bonds

24. GEM2508 24 Good to know that the Math works! Excel has a large number of built-in functions. Hence if one tries to do something that appears to be quite standard, it’s always a good idea to try and see whether there’s a corresponding Excel function. And indeed: the function is called PV Presumably standing for Present Value Bonds

25. GEM2508 25 Using the Excel built-in function And we find that the current value is …. 5,197 dollars. Yes, we did it again! Note the minus, an Excel convention PV() Bonds

26. GEM2508 26 Understand the problem and use simple Excel functions Use Math Use the ‘black-box’ Excel built-in function Hence we have found three ways to solve our problem: Which one is the best? Bonds

27. GEM2508 27 Thus far we have determined the current value of the bond based on the present and past interest rates. However, on the bond market one does not directly trade in yields but in bonds. This basically reverses the problem as: If I buy a bond at certain price, what is its yield? Bonds

28. GEM2508 28 We can again use the Solver to do the job: The key thing to realize is that the Premium is 0 at the correct yield. Bonds

29. GEM2508 29 And (should I say naturally) there’s also an Excel function that can do the job: Number of years left Coupon Purchase Price Face Value RATE() Bonds

30. GEM2508 30 Bonds Discount Rate Using Excel to Understand and Calculated Yields and Values Key Points of the Day