23) Case wall Street journal Dow Jones & Company has given you an aray of subscr

ID: 2809192 • Letter: 2

Question

23) Case wall Street journal Dow Jones & Company has given you an aray of subscription options for the wll Stree Joumal A one year subscription costs $75 a three year subscription costs $200 and a five year subscription costs 3330 Subscriptions poyments are due at the beginning of the subscription You expect that luture subscription rates will remain the same in real Be. intiation adjusted terms The nominal rate of interest is 7 12% ond infionon is expected to b630. Anurme that you are a "long term subscriber fie you will be subscribing to the wall Sheet Joumal torever) Which subscription period is the best valuel

Explanation / Answer

As per Fischer effect, nominal interest rate = real interest rate + expected inflation rate

Given that nominal interest rate is 7.12% and expected inflation rate is 3.0%, real interest rate is 4.12%.

For a one year subscription, the real interest rate is 4.12%. Therefore, for a 3 year subscription period, the real interest rate corresponding to the 3 year period is 12.88% = {(1 + 4.12%)3} – 1

Similarly, for a 5 year subscription period, the real interest rate corresponding to the 5 year period is 22.37% = {(1 + 4.12%)5} – 1

The net present values of each subscription period viz. 1 year, 3 year or a 5 year period, assuming a perpetuity for each subscription plan are calculated below:-

No. of years of subscription (A)

Initial subscription amount paid upfront (B)

Real Interest Rate (C)

Net Present Value of the Perpetuity (D) = B/C

$75.0

4.12%

$1,820.4

$200.0

12.88%

$1,553.3

$330.0

22.37%

$1,475.3

The 5 year period’s subscription value has the lowest net present value and hence a minimum cash outlay for a long term subscriber. Therefore, the 5 year subscription period is of the best value to a long term subscriber.