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# Fisher Effect, Time Value of Money

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1) Fisher Effect
Year Expected rate
of inflation Observed rate
of inflation Expected real interest rate
2008 5% XX 1.5%
2007 4% 3.5% 3%

a. Define the Fisher Effect and explain why expected inflation should have an impact on the nominal rate of interest?
b. Today is January 1, 2008. What is the one-year nominal rate of interest that will prevail in the financial market today?
c. Suppose that the one-year nominal interest rate was 7% one year ago on January 1, 2007. Was real income redistributed between borrowers and lenders over the course of 2007? Derive the percentage amount of the redistribution for the borrowers and the lenders.
d. Suppose the observed rate of inflation in 2007 had been 5%. Was real income redistributed between borrowers and lenders over the course of 2007? Derive the percentage amount of the redistribution for the borrowers and the lenders.

2. Today is t=0 and you learn that you will be admitted to College at t=1. You expect to graduate in four years at t=5. College informs you that tuition will remain unchanged at \$11,000 per year over the four-year period while you are attending. Tuition payments are due in t=1, t=2, t=3 and t=4.
To finance your education, your parents invested \$30,000 in a savings account in t= -4 (i.e., four years prior to t=0). The interest rates for this account are as follows:

Time period t= -4 to t= -3
t= -3 to t= -2 t= -2 to t= -1
t= -1 to t= 0
t= 0 to t=1 t=1 to t=2
t=2 to t=3
t=3 to t=4
t=4 to t=5
Interest Rate 6% 4% 3%

a. Your friend Michael tells you that you will need to borrow \$14,000 since the total tuition cost will be \$44,000 and you will have only \$30,000 in cash. Is Michael's calculation correct? Explain your answer.
b. Derive the amounts that you will have to borrow (if any) at t=1, t=2, t=3 and t=4.
Assume that interest on borrowed amounts will not accrue until you have graduated.

3. You own a coal mining company and are considering opening a new mine in South Africa. Your financial adviser gives you the following analysis on two possible mining opportunities:
Investment A: The mine requires an initial investment (t=0) of \$120 million. Once the investment is made, the mine is expected to produce revenues of \$40 million per year from t=1 to t=4. After t=4, the coal will be depleted but the site must be cleaned in t=5 at a cost of \$10 million.
Investment B: The coal is buried more deeply in this mine. It will have a cost of \$50 million in t=0, \$100 million in t=1 and \$50 million in t=2. The mine will produce the following revenues:
t=1: \$ 0 million; t=2: \$ 40 million; t= 3: \$ 40 million; t= 4: \$ 100 million; t= 5: \$80 million
After t= 5, the site will run out of coal. It will, however, need to be cleaned in t=6 at a cost of \$12 million.

Suppose that the alternative interest rate is 6%.

a. What is the net future value of investment A at t=4?
a. What is the net future value of investment B at t=4?
b. Suppose the alternative interest rate is 10%. Do you invest in the shallow (A) or deep (B) mine? Why?

4. Today is t=0 and you have an outstanding bank loan. It requires you to make four annual payments of \$6,000 each at t=0, t=1, t=2, and t=3. Your bank offers you the opportunity to convert the t=0, t=1 and t=2 payments into one balloon payment at t=3.

a. Derive the amount of the balloon payment if the interest rate on the loan is 4%?
b. Derive the amount of the balloon payment if the interest rate on the loan is 7%?