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.
