Question

6. Implied Real Interest Rates. If the sominal interest rate is the goverament bond rate, and the eurrent change in consumer prices is used as expected inflatios, calculate the implied "real" rates of interest by currency a. Australian dollar "real" rate b. Japanese yen "real" rate e. U.S. dollar "real" rate 7. Delos borrowed 200 million two years ago. The loan agreement, an amortizing loan, was for 5 years at 7.625% interest per annum. Delos has successfully completed two years of debt-service, but now wishes to renegotiate the terms of the loan with the lender to reduce its annual payments. a. What were Delos's annual principal and interest payments under the original loan agreement? b. After two years debt-service, how much of the principal is still outstanding?

Answer 1

QUESTION 6.

The Fisher effect is an economic theory proposed by economist Irving Fisher that describes the relationship between inflation and both real and nominal interest rates.

Mathematically, according to Fischer equation,

(1 + Nominal rate of Return) = (1 + Real rate of return) * (1 + Inflation)

Now, calculating the required values.

a. Australian dollar real rate

(1 + 6.50%) = (1 + R) * (1 + 2.1%), where R is the real rate

R = (1.0650/1.021) - 1

R = 4.31%

b. Japanese real rate

(1 + 1.65%) = (1 + R) * (1 - 0.2%), where R is the real rate

R = (1.0165/0.998) - 1

R = 1.85%

c. US Dollar real rate

(1 + 4.40%) = (1 + R) * (1 + 2.8%), where R is the real rate

R = (1.044/1.028) - 1

R = 1.56%

QUESTION 7

a. Now this question involves application of time value of money concept - annuities.

Here, the loan is borrowed and is repaid in 5 annual installments with interest rate of 7.625%.

First, let us calculate the annual payments. We can do that by using the formula for PV of annuity, where PV is equal to

Now,

$200 = P * [\frac{1 - (1 + 0.07625)^{-5}}{0.07625}]$

P = €49.59719946 mil

P = €49,597,199.46

So, annual payments to repay the loan = €49,597,199.46

Total Repayment = 5 * €49,597,199.46 = €247,985,997

Hence total interest = €247,985,997 - €200,000,000 = €47,985,997

Now, in order to calculate the annual interest payable each year, we need to calculate the debt schedule.

For first year, principal = Euro200 mil.

The annualloan re-payment would have a component of interest and principal.

Interest = Principal at start of the year * Interest Rate (7.625%)

So, Principal component of loan repayment installment = Total annual payment - Interest

This principal component would reduce the principal balance at the end of year, which woul become the principal at the start of the next year

Debt Schedule Repayment is as follows:

Year	Principal at Year start	Annual Payment	Interest	Principal Component	Principal at end of Period
1	$200,000,000.00	$49,597,199.46	$15,250,000.00	$34,347,199.46	$165,652,800.54
2	$165,652,800.54	$49,597,199.46	$12,631,026.04	$36,966,173.42	$128,686,627.11
3	$128,686,627.11	$49,597,199.46	$9,812,355.32	$39,784,844.15	$88,901,782.96
4	$88,901,782.96	$49,597,199.46	$6,778,760.95	$42,818,438.51	$46,083,344.45
5	$46,083,344.45	$49,597,199.46	$3,513,855.01	$46,083,344.45	$0.00

*Please ignore currency symbols of $. It is irrelevant (whether it is $ or Euro) in this question.

b. Now, after two years, principal outstanding (as can be seen from above table) = $128,686,627.11

c. Amount remaining after two years = $128,686,627.11

Since, they have been granted a 2 year extension, they have 5 years now to payback this outstanding amount.

Again, using the PV of an annuity concept, we need to calculate P, when

$128,686,627.11 = P * [\frac{1 - (1 + 0.07625)^{-5}}{0.07625}]$

P = Euro 31,912,481.57. New Annual Installment