1. MACROECONOMICS
Tutorial 3
Raj.Chande@bristol.ac.uk

2. 1) MUCH IMPROVED…
 Real interest rate is the nominal rate minus
inflation.
 Some confusion about when to use expected and
when to use actual inflation.
 Actual, past tense. Expected, future. So when
someone lends money, they consider the expected
real rate. Once they’ve been paid pack, they
calculate the real rate itself.
 So potential decisions are based on an expected
inflation rate, but the real rate of interest can be
known once inflation for that period is known.

3. 2) NOT EASY
 But some good answers and good explanations
(some, not so good).
 Could work out manually, or using a clever trick
 Everyone knows the Fisher approximation, could
have used this to answer manually.
 re = i – πe

4. FIRST OFF…
 Calculate the revenue stream in real terms

5. THE LONG BORING MANUAL WAY
 Calculate the revenue stream in real terms:
100/1.1 + 200/1.12 + 150/1.13
= £90.91 + £165.29 + £112.70 (which is £369ish)
Then calculate how much the firm SHOULD borrow at
the real rate to earn that much each year:
90.91/1.05 + 165.29/1.052 + 112.7/1.053
= £86.58 + £149.92 + £97.35
Which is around £333.85

6. NOW, WITH EXPECTED INFLATION OF 5%
 Do we think the firm should be prepared to pay:
a) the same?
b) more?
c) less?
Let’s work it out, then we’ll see the trick which
saves you all this trouble.

7. WHY APPROXIMATE?
 The Fisher formula for the real interest rate is:
re = {(1+i) / (1+ πe)} – 1
Which means that:
(1+re) = (1+i) / (1+ πe)

8. WHAT DID WE DO MANUALLY?
 Effectively for each year, we discounted for
inflation, then again for the real interest rate.
 So… we discounted by (1+r)(1+ πe) for year 1, for
year 2 ((1+r)(1+ πe))2, and then ((1+r)(1+ πe))3
 But…
(1+re) = (1+i) / (1+ πe)
So we are just discounting by (1+i) for year 1 etc
because everything else cancels out.