FINANCIAL ECONOMICS – MAY 2013

SECTION A(60 MARKS)

QUESTION 1

(a)Differentiate between simple and compound interest. (4 marks)

It is the type of interest which does not take into account the time value of money. Simple interest is computed on the principle for the entire term of the loan and is due at the end of the term. It does not take into account the fact that interest can be calculated on interest, usually used on periods of less than a year. There is also an array of conversions for bills, deposits and bonds, etc. within the financial markets.

Compound interest is the interest which is calculated not only on the initialprincipal but also the accumulated interest of prior periods. Compound interest differs from simple interest in that simple interest is calculated solely as a percentage of the principal sum.

(b)Mr. Ashford plans to invest $200,000 for 6 years at a compoundinginterest rate of 10% per year. How much is Mr. Ashford expecting to receive at the end of 6thyear? (6 marks)

Answer: $354,312.20

(c)Suppose that a Treasury Bill with face value of K100 is issued on 8th September 2006 and matures on 15th December, 2006. Given that the price of the Treasury Bill is K99.27076, find the annual rate of interest. (5 marks)

QUESTION 2

(a)Differentiate between simple and compound interest. (4 marks)

  1. Graphics, such as maps, graphs and diagrams, are mostly used to represent large volume of data. They are necessary in that, if the information is presented in tabular form or in a descriptive record, it becomes difficult to draw results.
  2. Graphical form makes it possible to easily draw visual impressions of data.
  3. Enhances understanding of the learners.
  4. Makes comparison much easier and creates an imprint in mind for a longer time.
  5. At times drawing inferences about whatever is being presented in a non graphical form may be a time consuming task hence graphical representation presents characteristics in a simplified way.
  6. Makes patterns of population growth, distribution and the density, sex ratio, age-sex composition and occupation structure to be easily understood.

(b)You invest $400 today in an account that earns interest at a rate of 12% per year compounded monthly. What will be the future value at the end of 2 years? (10 marks)

Because the interest is compounded monthly, we convert 2 years to 24 months, and the annual rate of 12% to the monthly rate of 1%.

Calculation using an FV factor:

FV = PV x [FV factor for n = 24, i = 1%]
FV = $400 x [1.270] ← FV factor from FV of 1 Table
FV = $508

At the end of 2 years, you will have $508 in your account.

QUESTION 3

(a)What is a loan amortisation schedule? (2 marks)

A loan amortizationschedule is a common tool that borrowers use to keep track of how much of the principal balance they have paid so far.

A few crucial details are needed to have an accurate result in a loanamortization schedule. The loan amount, annual interest rate, and number of years that the loan will last are typically the first numbers that are required to calculate a schedule. The typical loanamortizationschedule offers a summary of the interest paid, and the number of months left on the loan.

For example, some schedules also work for loans that are paid bimonthly, quarterly, weekly, or some other frequency, instead of just monthly.

(b)Suppose a debt of $100,000 with an interest rate of 4% compounded annually is amortised by equal monthly payment over 7 years;

Loan Summary
Principal: / $100000
Interest Rate: / 4%
Loan Term: / 7 years
/ Payment Summary
Number of Payments: / 84
Monthly Payment: / $1,366.88
Total Principal Paid: / $100,000.00
Total Interest Paid: / $14,817.97
Total Paid: / $114,817.97

(i)Find the value of each monthly payment (2 marks)

$1,366.88

(ii)What will be the total interest to be paid(2 marks)

$14,817.97

(iii)Construct an amortisation schedule (9 marks)

Yearly Amortization Schedule

Payments / Yearly Total / Principal Paid / Interest Paid / Balance
Year 1 (1-12) / $16,402.57 / $12,632.49 / $3,770.07 / $87,367.51
Year 2 (13-24) / $16,402.57 / $13,147.16 / $3,255.41 / $74,220.35
Year 3 (25-36) / $16,402.57 / $13,682.80 / $2,719.77 / $60,537.55
Year 4 (37-48) / $16,402.57 / $14,240.25 / $2,162.31 / $46,297.29
Year 5 (49-60) / $16,402.57 / $14,820.42 / $1,582.14 / $31,476.87
Year 6 (61-72) / $16,402.57 / $15,424.23 / $978.34 / $16,052.64
Year 7 (73-84) / $16,402.57 / $16,052.64 / $349.93 / $0.00
Totals / $114,817.97 / $100,000.00 / $14,817.97

QUESTION 4

In a country called Timberstone, there are more graduates exceeding the industry’s demand for workers, whose average wage stands at 250 dollars. But the industry is willing to offer lower wages so that the work force is fully employed.With an aid of Classical theory, clearly define how the economy would return to the natural level of real GDP. (15 marks)

The economy is in equilibrium at Y1 with labour supplied by SAS1 while demand is along AD1, at which point 250 dollars is offered. This however creates voluntary unemployment from the graduates entering the labour market.

The immediate, short-run effect is that the economy moves down along the SAS curve labeled SAS1, causing the equilibrium price level to fall from P1 to P2, and equilibrium real GDP to fall below its natural level of Y1 to Y2. If real GDP falls below its natural level, the economy's workers and resources are not being fully employed. When there are unemployed resources, the classical theory predicts that the wages paid to these resources will fall. With the fall in wages, suppliers will be able to supply more goods at lower cost, causing the SAS curve to shift to the right from SAS1 to SAS2. The end result is that the equilibrium price level falls to P3, but the economy returns to the natural level of real GDP.

SECTION B(40 MARKS)

QUESTION 5

(a)Congratulations!!! You have won a cash prize! You have two payment options: A - Receive $10,000 now OR B - Receive $10,000 in three years. Which option would you choose? Illustrate with a timeline. (5 marks)

By receiving $10,000 today, you are poised to increase the future value of your money by investing and gaining interest over a period of time. For Option B, you don't have time on your side, and the payment received in three years would be your future value.

Timeline illustration:

If you are choosing Option A, your future value will be $10,000 plus any interest acquired over the three years. The future value for Option B, on the other hand, would only be $10,000. So how can you calculate exactly how much more Option A is worth, compared to Option B?

(b)If you choose Option A and invest the total amount at a simple annual rate of 7.5%, calculate the future value of your investment at the end of five years? (5 marks)

$14,356.29

(c)Zanga Investment intends to lease sugarcane field for the next 20 years, over which period you plan to harvest 5,000 Kilograms every year. The current price per Kilogram is K300, but it is expected to increase 3% a year. The appropriate discount rate is 10%. What is the present value of the sugarcane that Zanga Investment is expected to be harvested from the field?(10 marks)

A

PV of harvested paprika = K300*5000*(1.03)= K16,145,980

The present value of the paprika expected to be harvested from this field is K16.146 million.

QUESTION 6

(a)What do you understand by the term statistical analysis? (2 marks)

Statistical analysis is actually the processing of raw data with a focus on measures of central tendency and measures of dispersion to yield probabilities of occurrences of future events.

(b)Discuss with the aid of a diagram under the Moderate Monetarists how the economy would behave in the short run and in the long run. Discuss. (10 marks)

Short run

In the short run any increase in the money supply may lead to an increase in aggregate demand. This may, in turn, lead to more employment, but before long people's expectations will catch up and as we saw with the expectations augmented Phillips Curve the effects of the boost will only be short-lived. Inflation picks up and wipes out any short-term gains. The following diagram shows this:

Output grows a bit, but inflation is pushed up and once the inflation is in the system people will begin to anticipate it.

Long-run

In the long run, any attempts to reduce unemployment below its natural rate will result in inflation. This means that there is no long-run trade-off between unemployment and inflation, and the long-run aggregate supply curve will be vertical.

(c)The following are the possible returns and associated probabilities of security X:

Rate of ReturnProbability

15%25%

17.5%25%

10%12%

22%10%

Calculate the mean return and standard deviation of security X (8 marks)

Solution 8.1

Mean return (ř)

0.15 x 0.25 = 0.0375

0.175 x 0.25 = 0.04375

0.1 x 0.12 = 0.012

0.22 x 0.1 = 0.022

0.11525 = 11.525%

Following the rest of the formula:

(0.015 – 0.11525)2 x 0.25 = 0.00030189

(0.175 - 0.11525)2 x 0.25 = 0.00089252

(0.1 - 0.11525)2 x 0.12 = 0.00002791

(0.22 – 0.11525)2 x 0.1 = 0.00109726

0.00231957

√0.00231957 = 4.81619%

Comment:

The standard deviation of your asset portfolio is almost 5 per cent, and a mean return is 11.525%. The 5% is a reflection of the risk inherent in your portfolio. It is a measure of the extent to which the possible outcomes are likely to be different from the mean outcome, and finance assumes that this is risk.

QUESTION 7

(a)Define effective interest rate with a clear example. (4 marks)

This is the interest rate that makes allowance for inflation and is the actual rate paid (or received) after accounting for compounding that occurs during the year. If you want to compare two alternative investments with different compounding periods you need to compute the effective interest rate also known as effective annual rate (EAR) and use that for comparison.

Example:Let's assume a nominal interest rate of 6% per annum, which is credited as of = 0.5% every month.

After one year, the initial investment is increased by the factor (1+0.005)12 ≈ 1.0616. As a result, this nominal interest rate of 6%is equivalent to an effective interest rate of 6.16%.

(b)Suppose that a principal of K560 million is invested in football production factory at the beginning of the year, and the interest is accumulated at nominal annual rate of 37%, compounded monthly.

(i)What is the accumulated amount at the end of the year? (8 marks)

(ii)What is the annual effective rate of interest? (8 marks)

Solution (i) accumulated amount

Each month, the amount function grows by .Therefore, the accumulated amount at the end of the year is:

  • Mathematically:

A(n) = A0· (1+i)n = 560 · (1+0.0308)12 = 560 ·=560 x 1.4391

Answer: K805,899,609.91

Solution (ii) annual effective rate of interest

The effective annual interest i satisfies the equation:

  • Mathematically: 1+ i =

from above we know:

1+ i =1.4391

Therefore:

i =43.91%

QUESTION 8

(i)What is stagflation? (2 Marks)

This is the situation in which both unemployment and inflation go up at the same time.

(ii)Discuss the circumstances under which the Natural Rate of Unemployment is achieved. (18 marks).

Say the economy starts at point U with expected inflation at 0%, and the government decide that they want to lower the level of unemployment because it is too high. They therefore decide to boost demand by 5%. The attempt to reduce unemployment would primarily be through boosting aggregate demand (AD) in some way. In the short run, the increase in AD would lead to a rise in national income and subsequently we might expect unemployment to fall. This is represented by a movement along the Philips curve to point V.

However, the adjustment period would also mean that there would be shortages in the economy which would 'pull' prices up. The increase in these prices leads people to seek wage demands that give them a 'real' increase, i.e. is above inflation. Since inflation has risen, people could reasonably be expected to build an anticipated inflation rate into their wage demands. If these wage demands were granted (and in the days of powerful trade unions and without the emphasis on global competition as there is now this was very likely), the result would be increased costs for businesses. The increased costs caused the AS curve to shift to the left and the economy would be at point W.

Firms would push up prices to maintain their profit margins or shed labour in response to the additional demand and higher costs and the net result would be that the economy would be back to the unemployment level it started with (U) but with a higher level of inflation (5%). (Note how we have used the framework of AS/AD to explain the Phillips Curve - this shows how closely related the two things are!) The increase in demand for goods and services will fairly soon begin to lead to inflation, and so any increase in employment will quickly be wiped out as people realise that there hasn't been a real increase in demand.

So having moved along the Phillips curve from U to V, the firms now begin to lay people off once again and unemployment moves back to W. Next time around the firms and consumers are ready for this, and anticipate the inflation.

If the government insist on trying again to reduce the unemployment the economy will do the same thing (W to X to Y), but this time at a higher level of inflation. In future wage negotiations they may not push just for a 5% increase in wages but 5% + ! They might think that given that inflation had risen by 5% last year it might rise by 8% next and so put in for a wage rise of 11% to ensure they get a real pay increase plus cover themselves for any anticipated inflation.

For this reason the rate U is often known as the Natural Rate of Unemployment.

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