FIN515
Homework 3

CHAPTER 5
Problem (p. 164)
5-29 Term Interest Rate Structure
a. Calculate the present value of an investment that pays $1000 in two years and $2000 in five years for certain.
PV = (C1/1+r2) ^2+(C1/1+r5) ^5
PV = 1,000/(1 + 0.0241)^2 + (2,000/(1 + 0.0332)^5= $2,652.15

b. Calculate the present value of receiving $500 per year, with certainty, at the end of the next five years. To find the rates for the missing years in the table, linearly interpolate between the years for which you do know the rates. (For example, the rate in year 4 would be the average of the rate in year 3 and year 5.) r4 = (2.74 + 3.32)/2= 3.03
PV = 500/(1 + 0.0199)^1 + 500/(1 + 0.0241)^2 + 500/(1 + 0.0274)^3 +500/(1 + 0.0303)^4+500/(1 + 0.0332)^5 = $2,296.43

*c. Calculate the present value of receiving $2300 per year, with certainty, for the next 20 years. Infer rates for the missing years using linear interpolation. (Hint: Use a spreadsheet.)

Term yrs | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | Rate (EAR, %) | 1.99 | 2.41 | 2.74 | 3.03 | 3.32 | 3.54 | 3.76 | 3.88 | 4 | 4.13 | 1+rate | 1.0199 | 1.0241 | 1.0274 | 1.0303 | 1.0332 | 1.0354 | 1.0376 | 1.0388 | 1.04 | 1.0413 | 2300/C^A | 2255.1 | 2193 | 2120.9 | 2041.1 | 1953.5 | 1866.7 | 1776.3 | 1695.8 | 1616 | 1534.5 | | | | | | | | | | | | Term yrs | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | Rate (EAR, %) | 4.21 | 4.29 | 4.37 | 4.45 | 4.53 | 4.61 | 4.64 | 4.77 | 4.85 | 4.93 | 1+rate | 1.0421 | 1.0429 | 1.0437 | 1.0445 | 1.0453 | 1.0461 | 1.0464 | 1.0477 | 1.0485 | 1.0493 | 2300/C^A | 1461.3 | 1389.4 | 1319 | 1250.3 | 1183.4 | 1118.3 | 1063.8 | 994.18 | 935.25 | 878.49 |

PV = 30,646.10

5-31 The Yield Curve
What is the shape of the yield curve given the term structure in Problem 29? What expectations are investors likely to have about future interest rates?
The yield