ECONOMICS 0281
HANDOUT #1: INDEXATION

1. Indexation: Preserves the real purchasing power of lenders.   Example: Suppose you want to purchase a 2 year coupon bond which has a coupon rate of 5% and a face value of \$5000.

a. If the inflation rate is zero and the interest rate is 4%, then the price of the bond is

PV =     \$250/ (1.04)  + \$250/(1.04)2  + \$5,000/(1.04)2

=      \$240.38  +  \$231.15  +  \$4,622.77

=   \$5,094.30
b. Now suppose inflation is 4% each year. Note that we know the inflation rate for a year at the end of the year. Given that bond payments are also made at the end of the year, this payment can then be adjusted by the appropriate inflation rate.
Nominal Value of                      Real Value of
Year             CPI              Coupon Payment                 Coupon Payment

1              104.00                  \$260.00                              \$250.00

2              108.16                   \$270.40                             \$250.00

2                                         \$5,408.00                          \$5,000.00

PV  =   \$260.00/(1.04) +  \$270.40/(1.04)2  +    \$5,408.00/(1.04)2

=      \$249.99   +    \$250.01   +    \$5,000

=   \$5,500

c. In case you don't know how to adjust nominal values for the inflation rate, use the following formula:
Real \$s   =   (Nominal \$s/CPI)100

Real \$s(CPI/100) = Nominal \$s = \$250(1.04) = \$260

To check your calculations, divide by the appropriate price index to adjust to real \$s.
(\$249.99/1.04)100 = \$240.38

(\$250.01/1.0816)100 = \$231.15

(\$5,000/1.0816)100 = \$4,622.78

Total = \$5,094.31