For problem 1:
seeFor problem 2:
seeFor problems 3 and 4 use the following:
nominal interest rate = real interest rate + inflation premium + default risk premium + maturity risk premium + liquidity risk premium
all of those can be stated in percentage terms
For 5F:
Ok, this problem is a bit more convoluted than I intended. So I’ll just try to explain what it is asking and how to figure it out.
The key point to remember is that we’re trying to solve for expected inflation rates with a bit more precision.
So, if you do E, you should find expected inflations as 1.5%, 3%, 5%, and 5.5%.
Now, let’s interpret these.
Inflation is expected to be 1.5% over the next year.
Inflation is expected to average 3% over the next 5 years.
Inflation is expected to average 5% over the next 10 years.
Inflation is expected to average 5.5% over the next 20 years.
So, if inflation is expected to average 1.5% over year 1 and 3% over years 1 through 5, then what is the expected average for years 2 through 5?
3% average over 5 years would have a cumulative inflation of 15% (3% x 5). Since we expect inflation over year one to be 1.5%, then the cumulative inflation over the 4 year period (2 through 5) would be 15% - 1.5% = 13.5%. Divide 13.5% ÷ 4 = 3.375%. That’s expected inflation (3.375%) for each year 2 through 5, given year 1 is expected to be 1.5%
5% average over 10 years would have a cumulative inflation of 50% (5% x 10). To find expected inflation over years 6 through 10 we can subtract off the expected (cumulative) inflation over the first 5 years, 15% (= 3% x 5), to give us a cumulative inflation over the years 6 – 10 of 35%. Divide that by 5 years. 35% ÷ 5 = 7%. So expected inflation years 6 through 10 is 7% per year, given expected inflation is 3%* on average years 1 through 5. (*previously reported as 7%)
5.5% average over 20 years would have a cumulative inflation of 110% (5.5% x 20). To find expected inflation over years 11 through 20 we can subtract off the expected (cumulative) inflation over the first 10 years, 50% (= 5% x 10), to give us a cumulative inflation over the years 11 – 20 of ____%. Divide that by ____ years. ___% ÷ ___ = ____%. (Finish using the examples above.)
For problem 6, your calculation of the discounted value of the revenue stream results in
your valuation. Given those other
market determined prices you should decide if at those prices the bond is over valued or undervalued.
If the market price is greater than your valuation, you will find it overvalued in the market and you will expect the price to fall.
If the market price is less than your valuation you will believe it is undervalued in the market and you will expect its price to rise.
So explain if you'd want to buy it at those prices, given your calculated valuations.