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  1. 1. MACROECONOMICSTutorial
  2. 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. 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. 4. FIRST OFF… Calculate the revenue stream in real terms
  5. 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. 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. 7. WHY APPROXIMATE? The Fisher formula for the real interest rate is:re = {(1+i) / (1+ πe)} – 1Which means that: (1+re) = (1+i) / (1+ πe)
  8. 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.