STUDENT NAME
: CASSANDRA RABAI AK GORDON LUTA (56-2079-013)
THERESA MARIA AK ALBERT BANGAU (56-2074-013)
ELYSHA EJJAH AK MAXSON GALAU (56-2073-013)
NATRA CARLISSA BINTI ABDILLAH (56-2088-014)
NAME OF LECTURER
: MR. KOBE
COURSE
: DIPLOMA IN BUSINESS ADMINISTRATION
SUBMISSION DATE
: 28TH OCTOBER 2019
1
Table of Contents
Contents
Pages
1.0 Question 1, The Energy Company’s 2017 and 2018 financial statements
follow, along with some industry average ratios.
A) Assess Energy Company’s liquidity position, and determine how it
9 – 10
compares with peers and how the liquidity position has changed over
time.
B) Assess Energy Company’s asset management position, and
11
determine how it compares with peers and how its asset management
efficiency has changed over time.
C) Assess Energy Company’s debt management position, and
12
determine how it compares with peers and how its debt management
has changed over time.
D) Assess Energy Company’s profitability ratios, and determine how
13 – 14
they compare with peers and how its profitability positions has
changed over time.
E) What do you think would happen to its ratios if the company
15
initiated cost-cutting measures that allowed it to hold lower levels of
inventory and substantially decreased the cost of goods sold? No
calculations are necessary, Think about which ratios would be affected
by changes in these two accounts.
2.0 Question 2
a) Assuming a rate of 10% annually, find the future value of
16
RM1,000 after 5 years.
b) Find the present value RM1,000 due in 5 years if the discount rate
16
is 10%.
c) What is the rate of return on a security that costs RM1,000 and
16
returns RM2,000 after 5 years?
2
d) Suppose Malaysia’s population is 36.5 million people and its
17
population is expected to grow by 2% annually. How long will it take
for the population to double?
e) Find the present value of an ordinary annuity that pays RM1,000
17
each of the next 5 years if the interest rate is 15%?
f) Find the future value of an ordinary annuity that pays RM1,000 each
17
of the next 5 years if the interest rate is 15%?
g) How will the present value and future value of the annuity in part
18
(f) and (g) change if it is an annuity due?
h) What will the future value and the present value be for RM1,000
18
due in 5 years if the interest rate is 10%, semi-annual compounding?
i) What will annual payments be for an ordinary annuity for 10 years
19
with a present value of RM1,000 if the interest rate is 8%?
j) What will the annual payments be for an annuity due for 10 years
19
with a present value of RM1,000 if the interest rate is 8%?
k) Find the present value and the future value of an investment that
20
pays 8% annually and makes the following end-of-year payments:
l) Five banks offer nominal rates of 6% on deposits, but A pays interest
annually, B pays semi-annually, C pays quarterly, D pays monthly, and
E pays daily.
i) What effective annual rate does each bank pay?
20 – 21
ii) If you deposit RM5,000 in each bank today, how much will
21 – 22
you have in each bank at the end of 1 year?
iii) If you deposit RM5,000 in each bank today, how much will
22 – 23
you have in each bank at the end of 2 year?
iv) If all of the banks are insured by the government (the PIDM)
23 – 24
and thus are equally risky, will they be equally able to attract
funds? If not (and the TVM is the only consideration), what
nominal rate will cause all the banks to provide the same
effective annual rate as Bank A?
3
v) Suppose you don’t have the RM5,000 but need it at the end
24 – 26
of 1 year. You plan to make a series of deposits – annually for
A, semi-annually for B, quarterly for C, monthly for D, and
daily for E – with payments beginning today. How large must
the payments be to each bank?
m) Suppose you borrow RM15,000. The loan’s annual interest rate is
27 – 30
8%, and it requires four equal end-of-year payments. Set up an
amortization schedule that shows the annual payments, interest
payments, principal repayments, and beginning and ending loan
balances.
4
1.0 Question 1, The Energy Company’s 2017 and 2018 financial statements follow, along
with some industry average ratios.
•
YEAR 2017
Current Ratio
Current Assets
1,206,000
=
= 2.11 times
Current Liabilities
571,500
Inventory Turnover
Cost of Goods Sold 2,980,000
=
= 3.67 times
Inventory
813,000
Days Sales Outstanding
Account Receivable
328,000
=
= 32.9 days
Sales
3,635,000
(
)
(
)
365 days
365 days
Fixed Assets Turnover
Sales
3,635,000
=
= 9.00 times
Net Fixed Assets
404,000
Total Assets Turnover
Sales
3,635,000
=
= 2.18 times
Total Assets 1,667,000
Return on Assets
Net Income
95,970
=
= 0.0576 ≈ 5.76%
Total Assets
1,667,000
Return on Equity
Net Income
95,970
=
= 0.1669 ≈ 16.69%
Common Equity 575,000
5
Profit Margin
Net Profit
95,970
=
= 0.0264 ≈ 2.64%
Sales
3,635,000
Debt Ratio
Total Debt
1,092,000
=
= 0.6550 ≈ 65.50%
Total Assets 1,667,000
6
•
YEAR 2018
Current Ratio
Current Assets
1,405,000
=
= 2.33 times
Current Liabilities
602,000
Inventory Turnover
Cost of Goods Sold 3,680,000
=
= 4.21 times
Inventory
894,000
Days Sales Outstanding
Account Receivable
439,000
=
= 37.79 days
4,240,000
Sales
(
)
(
)
365 days
365 days
Fixed Assets Turnover
Sales
4,240,000
=
= 11.46 times
Net Fixed Assets
370,000
Total Assets Turnover
Sales
4,240,000
=
= 2.31 times
Total Assets 1,836,000
Return on Assets
Net Income
18,408
=
= 0.0498 ≈ 4.98%
Total Assets
370,000
Return on Equity
Net Income
18,408
=
= 0.0320 ≈ 3.20%
Common Equity 575,000
7
Profit Margin
Net Profit
18,408
=
= 0.00434 ≈ 0.43%
Sales
4,240,000
Debt Ratio
Total Debt
1,261,000
=
= 0.6868 ≈ 68.68%
Total Assets 1,836,000
The Energy Company’s Financial Ratio Analysis (2017 and 2018)
Financial Ratios
The Energy
The Energy
Industry
Indicator
Company’s
Company’s
Financial Ratio (Good/Poor)
2017
2018
2018
Current Ratio
2.11 times
2.33 times
2.70 times
Poor
Inventory Turnover
3.67 times
4.12 times
7.0 times
Poor
Days Sales
32.9 days
37.7 days
32.0 days
Poor
9.00 times
11.46 times
13.0 times
Poor
2.18 times
2.31 times
2.6 times
Poor
Return on Assets
5.76%
4.98%
9.1%
Poor
Return on Equity
16.69%
3.20%
18.2%
Poor
Profit Margin
2.64%
0.43%
3.5%
Poor
68.68%
50.0%
Poor
Outstanding
Fixed Assets
Turnover
Total Assets
Turnover
Debt-to-capital-ratio 65.5%
8
Question 1 (A):
Based on The Energy Company’s liquidity position, the difference of them between its
peers and how the liquidity position has changed over time is by through its current ratio,
difference between The Energy Company’s current ratio, it is 2.33 times and its peers is by 2.70
times. Through this, it shows that their indicator for The Energy Company’s current ratio is poor.
However, in the year 2017, the company managed increased their current ratio in 2018, which was
2.11 times in 2017 and increased to 2.33 times in 2018.
Through The Energy Company’s inventory turnover, the difference of them between its
peers is that the company’s inventory turnover is 4.12 times while its peers rate is at a 7.0 times.
This is indicating that The Energy Company’s has a poor inventory turnover than the Industry
Financial Ratio. However, in year 2017, The Energy Company has managed to increase its
inventory turnover in year 2018 which was from 3.67 times to 4.12 times. Even though among its
peers, they are doing poorly but have managed to increase and be better in their own company
inventory turnover.
Days sales outstanding is also in one of The Energy Company’s liquidity position. The
difference of the company’s days sales outstanding between its peers is that it has a higher days
sales outstanding than its peers. The Energy Company manages to have 37.7 days outstanding
rather than its peers who has 32.0 days. This indicates that The Energy Company’s days sales
outstanding is poor from its peers. The changes however in The Energy Company’s itself on their
days sales outstanding in year 2017 was 32.9 days which was much better than in 2018 because
they have increased their days to 37.7 days.
There are a few ways on how The Energy Company can improve their liquidity position to
become better. One of the ways they can do to improve it is by reducing overhead. Overhead refers
to all non-labor expenses required to operate the business. These expenses are either fixed expenses
or variable expenses. By reducing overhead, objectively evaluating regular expenses such as rent,
utilities and insurance may provide opportunities to cut costs. For example, a regular analysis of
insurance needs is a smart practice to employ. Situations can change, assets also changes and thus
coverage needs changing too. Contracting multiple types of insurance, such as vehicle, liability
and business insurance, through one provider often makes the policyholder eligible for discounts.
9
Be cost effective about travel, and consider whether you could rent instead of buying equipment
to reduce the overhead.
Secondly, The Energy Company can improve their liquidity position by selling unneeded
assets. Whether the asset is land, machinery, equipment, vehicles or office machines, any surplus
assets that the company doesn’t need to represent potential cash. Selling unneeded assets can
increase liquidity as soon as the transaction takes place. That extra cash can then be used to reduce
current liabilities such as short-term debt obligations or property tax bills, for example, improve
solvency. But, The Energy Company has to give careful thought to which assets they sell off.
Lastly, one of the ways The Energy Company can improve their liquidity position is
handling their accounts management well. Both accounts receivable and accounts payable impact
liquidity. To increase liquidity, the company should consistently review accounts receivable to
make sure customers receive and pay bills on time. Delays in sending bills, particularly in
businesses without a fixed billing schedule, can severely inhibit cash flow and damage liquidity.
In terms of accounts payable, vendors sometimes offer a longer payment plan or installments when
dealing with a business. By lowering total payments due or spreading out the payments with longer
intervals between bill, the business can improve its liquidity.
10
Question 1 (B):
Based on Energy Company’s asset management position, the peers generates 13.0 times
more fixed asset compare to Energy Company. Compare to the Energy Company, they only
generates 11.6 times lesser. Which states at the indicator is poor. This means that the Energy
Company utilizes their fixed assets less efficiently than does its peers. Also, the Energy Company’s
asset management position based on year 2017 and 2018 is very different. The difference is that
during 2017, the firm generates 9.00 times while on 2018 the firm generates as high as 11.46 times
more than the last year. This shows that the fixed asset turnover for the company is increasing
within a year.
Next in the asset management, comparing Energy Company and the peers, the peers
generates cash 2.6 times more than the Energy Company. The Energy Company only generates
2.31 times that year. Which states at the indicator that the Energy Company did poorly on their
asset turnover. This shows that the Energy Company utilizes assets less efficiently than their peers.
As for the company’s evaluation based on the year 2017, the company generates 2.18 times. While
on the year 2018, the firm generates 2.31 times which is slightly higher than the last year. In this
term the company did a great job in increasing their asset turnover in a yearly basis.
As for the return on asset, the Energy Company ratio is 4.98% in other words, during the
year they produced $4.98 of net income. Compare to the peers, they produced 9.1% of asset which
is more than what the Energy Company can produce. Hence, the poor results at the indicator table.
In the year 2017, the Energy Company produced 5.76% which is $5.76 of net income. Then it
drops by 4.98% on the year 2018. This means that the Energy Company manage their return on
assets very poorly over the year.
There are many ways for the Energy Company to improve their ways of managing their
assets. One of the ways they can use is they should Identify key performance indicators to highlight
strengths and improvement opportunities and to measure performance and progress over time.
Defining a manageable number of key performance indicators can be a critical first step toward
addressing the daunting challenge of measuring progress in asset management. Basic measures to
track include percentage of devices lost or stolen, and effort spent per week in investigation of
unknown devices.
11
Question 1 (C):
Based on Energy Company’s debt management position, the difference between it and its
peers, also how its debt management has changed over time is by its debt-to-capital ratio. In year
2017, Energy Company’s peer’s debt-to-capital ratio is 65.5% and it increases to 68.68% in the
year 2018. Compared its peers, their debt-to-capital ratio is 50%. This means that the Energy
Company’s debt-to-capital ratio is poor.
By Energy Company’s Return on Equity, the difference between it and its peers is very far
by comparison. In year 2017, Energy Company’s peers return on equity is 16.69% and it decreases
to 3.20% in the year 2018. Compared its peers, their return on equity is 18.2%. This means that
the Energy Company’s return on equity ratio is poor. The owners of Energy Company are
receiving a return on their investment that is very bad when compared to its peers. The peers
company’s ratio is far more profitable in its operations than the Energy Company. It is expected
that the Energy Company would have less return on common equity.
There are a few ways on how the Energy Company can improve their debt management.
From their Debt-to-capital ratio, it can be reduced by increasing sales revenues to generate profits.
This can be achieved by raising prices, increasing sales, or reducing costs and then it can be used
to pay off existing debt. Also, to restructure the debt. If a company is paying relatively high interest
rates on its loans, and current interest rates are significantly lower, the company can seek to
refinance its existing debt. This will reduce both interest expenses and monthly payments and its
cash flow.
To improve the Return on Equity ratio, Energy Company should balance revenue growth
with cost management by controlling the costs. To maintain the cost means growth of revenue or
cost cutting. For example, lessen the workforce is in order to do cost cutting, though you must
ensure that the loss of these positions does not reduce any revenue contributions or reducing utility
expenses is another savings strategy. Also, to Improve asset turnover by calculating it and dividing
sales by the company's total assets. The more sales a company produces relative to its assets, the
more profitable it should be, and the higher return on equity it should earn.
12
Question 1 (D):
Based on The Energy Company’s profitability ratios, which is their profit margin, the
difference between them and its peers is that The Energy Company profit margin is only 0.43%
whereas its peers has a 3.5% profit margin which is 3.07 higher than The Energy Company. This
has indicated that The Energy Company is doing very poorly in the profit margin. However, the
profitability position has changed very drastically over time. In the year 2017, The Energy
Company’s profit margin was 2.64% and in the year 2018, it has dropped to 0.43% which is a
difference in 2.21%.
Profit margin is a ratio analysis method used by accountants and financial analysts to gauge
the profitability of a business by comparing to previous records or other businesses within the same
industry. The figures used are taken from an income statement and primarily involve sales as basis
of computation. Profit margin show how much profit is earned from every dollar worth of sales.
Dividing net profit or net loss by sales will result in a net profit margin. A net loss will result in a
negative profit margin.
A few possible reasons as to why The Energy Company has decreased their profit margin
in 2018 could possibly be because of low revenues. Any decrease in revenue will result in a
decrease in profits. Once a company’s sales decrease below the total amount spent for expenses
and cost of goods sold in a given period, a net loss will occur. Poor pricing strategies, ineffective
marketing programs, competition, inability to keep up with market changes and inefficient
marketing personnel are common causes of decreasing revenues. To reverse the negative margin,
management must implement ways to increase market share and revenues.
The next possible reason to why The Energy Company profit margin dropped because of
their cost of goods. High production or purchase costs of merchandise intended for sale can lead
to inadequate funds to cover expenses. Cost of goods sold is directly deducted from sales.
Whatever amount is left after the deduction will be used to pay for business expenses and generate
profit. When cost of goods sold increases to the point that there are not enough funds left to support
all expenses for the period, a net loss will occur. The higher the cost of goods sold, the lower the
net profit margin becomes.
13
In order for The Energy Company to improve their profitability ratio, especially in their
profit margin, The Energy Company can improve it by improving their sales. Increasing sales is
of paramount importance when it comes to improving profit margin. How a company goes about
increasing sales depends on its business model. For instance, a retailer can raise the price of its
merchandise, focusing on items that sells the most. If the company increases the price of an item
from RM10 to RM12 and sells 10,000 units, sales increase by Rm20,000. A retailer can also focus
its attention on selling higher-priced items, while reducing low margin products in its store. The
Energy Company can also focus on lowering costs or providing incentives to increase demand
thereby boosting sales.
Secondly, what The Energy Company can do to increase their profit margin is by handling
their gross profit margin better. Before getting to profit margin, a company should look at its gross
margin, which essentially is the amount of money it makes per each items sold. Gross margin is a
function of sales calculated as sales minus cost of goods sold by sales. Cost of goods sold refers to
the direct costs associated with the production of goods sold by the company and usually the largest
cost component on the income statement. Therefore, managing your company’s cost of goods sold
is another way to improve profit margin. Some companies manage cost of goods sold by finding
cheap sources of raw material or negotiating the cost of production.
Lastly, the company, The Energy Company can increase their profit margin is by managing
their expenses. During the course of doing business, a company will incur numerous operating
expenses and deducts these from the money it takes in to arrive at net income. Operating expenses
include salaries, rent, utilities, depreciation, and other expenses necessary to run the business. High
expenses receives a lot of attention from business owners and is another way to improve profit
margin. Every company approaches the issue of managing operating expenses differently. Cutting
back on work hours is a common practice or downsizing staff. The ultimate goal is to make the
organization as lean as possible without sacrificing productivity and performance.
14
Question 1 (E):
If the Energy Company initiated cost cutting measures, it would improve the profit margin
ratio. Profit margin is one of the commonly used profitability ratios to gauge the degree to which
a company or a business activity makes money. It represents what percentage of sales has turned
into profits. It will also increase its net income. Not to mention it will also improve return on assets.
Return on assets is a financial ratio that tells how much profit a company can generate from its
assets. In general, the higher the return on assets, the better the company is doing because higher
return on assets indicate a company is more effectively using its assets to generate profits. In other
words, they’re earning more money on less investment.
If the Energy Company also reduce its level of inventory, it will improve its current ratio.
The current ratio is a liquidity ratio that measures a company's ability to pay short-term obligations
or those due within one year. It tells investors and analysts how a company can maximize the
current assets on its balance sheet to satisfy its current debt and other payables. This is because the
higher the current ratio, the more capable a company is of paying its obligations because it has a
larger proportion of short-term asset value relative to the value of its short-term liabilities. This
will also reduce the company’s liabilities as well.
This will also result as improving Energy Company’s Inventory Turnover. Inventory
Turnover is a ratio showing how many times a company has sold and replaced inventory during a
given period. A company can then divide the days in the period by the inventory turnover formula
to calculate the days it takes to sell the inventory on hand. The higher inventory turnover ratio, the
more profitable the company will be. By reducing costs and lowering inventory would also
improve debt ratio where it means a financial ratio that indicates the percentage of a company's
assets that are provided via debt. It is the ratio of total debt and total assets.
Lastly, this will affect Return on Equity (ROE) which means to measure of the profitability
of a business in relation to the equity which also known as net assets or assets minus liabilities. It
improves the ROE in a way where Energy Company can finance themselves with debt and equity
capital by increasing the amount of debt capital relative to its equity capital, a company can
increase its return on equity. Also, increasing profits relative to equity increases a company's return
on equity. Increasing profits does not necessarily have to come from selling more product. It can
15
also come from increasing prices of each product sold, lowering the cost of goods sold, reducing
its overhead expenses, or a combination of each.
QUESTION 2
a) Assuming a rate of 10% annually, find the future value of RM1,000 after 5 years.
FV = PV(1 + r)n
FV = RM1,000(1 + 0.10)5
= RM1,610.51
b) Find the present value RM1,000 due in 5 years if the discount rate is 10%.
FV = RM1,000
n = 5 years
i = 10%
PV =
FV
(1 + r)n
PV =
RM1,000
(1 + 0.10)5
c) What is the rate of return on a security that costs RM1,000 and returns RM2,000 after 5
years?
PV = RM1,000
FV = RM2,000
1
FV [n]
i = [[ ] ] − 1
PV
1
RM2,000 [5]
i = [[
] ]−1
RM1,000
= 1.1487 − 1
= 0.1487 ≈ 14.87%
16
d) Suppose Malaysia’s population is 36.5 million people and its population is expected to
grow by 2% annually. How long will it take for the population to double?
PV = RM36,500,000
FV for double population = 36.5 million × 2 = 73,000,000
i = 2%
n = 1 years
FV
Time will be taken = [
log [PV]
i
log [1 + n]
[
]
RM73,000,000
]
log RM36,500,000
Time will be taken = [
]
0.02
log [1 + n1 ]
log(2)
=
log(1.02)
=
0.3010
= 35 years
0.0006
e) Find the present value of an ordinary annuity that pays RM1,000 each of the next 5 years
if the interest rate is 15%?
1
1−[
]
(1 + i)n
CF × [
]
i
1
1−[
]
(1 + 0.15)5
RM1,000 × [
] = RM3,352.16
0.15
f) Find the future value of an ordinary annuity that pays RM1,000 each of the next 5 years
if the interest rate is 15%?
[1 + i]n − 1
CF × [
]
i
[1 + 0.15]5 − 1
RM1,000 × [
]
0.15
= 6742.38
17
g) How will the present value and future value of the annuity in part (f) and (g) change if it
is an annuity due?
CF/FV ordinary annuity = RM1,000
i = 15%
n = 5 years
[1 + i]n − 1
FV annuity due = CF × [
] [1 + i]
i
[1 + 0.15]5 − 1
RM1,000 × [
] [1 + 0.15]
0.15
= RM1,000 × 6.74238 × 1.15
= RM7,753.74
h) What will the future value and the present value be for RM1,000 due in 5 years if the
interest rate is 10%, semi-annual compounding?
FV/PV = RM1,000
i = 10%
n = 5 years
Present Value
Future Value
FV
i
(1 + m)n×m
RM1,000
PV =
0.10
(1 + 2 )5×2
RM1,000
=
= RM613.91
(1.05)10
FV = PV(1 + m)n×m
PV =
i
FV = RM1,000(1 +
0.10 5×2
)
2
= RM1,000 × (1.05)10
= RM1,628.89
18
i) What will annual payments be for an ordinary annuity for 10 years with a present value
of RM1,000 if the interest rate is 8%?
PV ordinary annuity = RM1,000
i = 8%
n = 10 years
Annual payments for an ordinary annuity for 10 years
=[
(i ×PV ordinary annuity)
=[
=
]
1−(1+i)−n
(0.08 × RM1,000)
]
1 − (1 + 0.08)−10
80
0.5368
= RM149.00
j) What will the annual payments be for an annuity due for 10 years with a present value of
RM1,000 if the interest rate is 8%?
PV ordinary annuity = RM1,000
i = 8%
n = 10 years
Annual payments for an ordinary annuity for 10 years
=[
[
(i ×PV annuity due)
1−(1+i)−n ×(1+i)
]
(0.08 × RM1,000)
]
1 − (1 + 0.08)−10 × (1 + 0.08)
=
80
0.5798
= RM137.99
19
k) Find the present value and the future value of an investment that pays 8% annually and
makes the following end-of-year payments:
0
1
2
3
100
200
400
100
Year 1, Cash flow RM100, (1+0.08)1 = RM92.59
200
Year 2, Cash flow RM200, (1+0.08)1 = RM171.47
400
Year 3, Cash flow RM400, (1+0.08)1 = RM317.53
Total = RM581.59
l) Five banks offer nominal rates of 6% on deposits, but A pays interest annually, B pays
semi-annually, C pays quarterly, D pays monthly, and E pays daily.
i) What effective annual rate does each bank pay?
𝑘
Effective Annual Rate (EAR) = (1 + 𝑚)𝑚 − 1
Nominal Rate = 6%
→ Bank A, m = 1 (annually)
EAR = (1 +
0.06 1
)
𝑚
− 1 = 6%
→ Bank B, m = 2 (semi-annually)
EAR = (1 +
0.06 2
)
2
− 1 = 6.09%
→ Bank C, m = 4 (quarterly)
EAR = (1 +
0.06 4
)
4
− 1 = 6.136%
→ Bank D, m = 1 (monthly)
EAR = (1 +
0.06 12
)
12
− 1 = 6.168%
20
→ Bank E, m = 365 (daily)
0.06
EAR = (1 + 365 )365 − 1 = 6.183%
Bank
Annual Rate
Bank A
6%
Bank B
6.09%
Bank C
6.136%
Bank D
6.168%
Bank E
6.183%
Each banks have the same nominal rate which is 6% but they have different number of
compounding cycle. For Bank A, its number of compounding cycle is 1 which makes its Effective
Annual Rate to be 6%. . For Bank B, its number of compounding cycle is 2 which makes its
Effective Annual Rate to be 6.09%. For Bank C, its number of compounding cycle is 4 which
makes its Effective Annual Rate to be 6.136%. For Bank D, its number of compounding cycle is
12 which makes its Effective Annual Rate to be 6.168%. Lastly, for Bank E, its number of
compounding cycle is 365 which makes its Effective Annual Rate to be 6.183%.
ii) If you deposit RM5,000 in each bank today, how much will you have in each bank
at the end of 1 year?
Future Value, FV = PV (1 + i)n
→ Bank A, i = 6%, n = 1
FV = RM5,000 (1 + 0.06)1 = RM 5,300.00
→ Bank B, i = 6.09%, n = 1
FV = RM5,000 (1 + 0.0609)1 = RM 5,304.50
→ Bank C, i = 6.136%, n = 1
FV = RM5,000 (1 + 0.06136)1 = RM 5,306.80
→ Bank D, i = 6.168%, n = 1
FV = RM5,000 (1 + 0.06168)1 = RM 5,308.40
21
→ Bank E, i = 6.183%, n = 1
FV = RM5,000 (1 + 0.06183)1 = RM 5,309.15
Bank
Future Value
Bank A
RM 5300.00
Bank B
RM 5304.50
Bank C
RM 5306.80
Bank D
RM 5308.40
Bank E
RM 5309.15
Each of the bank has different future value since each interest for each bank is different but
they have the same amount for their years which is only 1 years. Bank A has an interest of 6%
which makes its future value to be RM 5,300.00. Bank B has an interest of 6.09% which makes its
future value to be RM 5,304.50. Bank C has an interest of 6.136% which makes its future value to
be RM 5,306.80. Bank D has an interest of 6.168% which makes its future value to be RM 5,306.80.
And lastly, Bank E has an interest of 6.183% which makes its future value to be RM 5,309.15
iii) If you deposit RM5,000 in each bank today, how much will you have in each bank
at the end of 2 year?
Future Value, FV = PV (1 + i)n
→ Bank A, i = 6%, n = 2
FV = RM5,000 (1 + 0.06)2 = RM 5,618.00
→ Bank B, i = 6.09%, n = 2
FV = RM5,000 (1 + 0.0609)2 = RM 5,627.54
→ Bank C, i = 6.136%, n = 2
FV = RM5,000 (1 + 0.06136)2 = RM 5,632.43
→ Bank D, i = 6.168%, n = 2
FV = RM5,000 (1 + 0.06168)2 = RM 5,635.82
22
→ Bank E, i = 6.183%, n = 2
FV = RM5,000 (1 + 0.06183)2 = RM 5,637.41
Bank
Future Value
Bank A
RM5,618.00
Bank B
RM5,627.54
Bank C
RM5,632.43
Bank D
RM5,635.82
Bank E
RM5,637.41
Each of the bank has different future value since each interest for each bank is different but
they have the same amount for their years which is only 2 years. Bank A has an interest of 6%
which makes its future value to be RM5,618.00. Bank B has an interest of 6.09% which makes its
future value to be RM5,627.54. Bank C has an interest of 6.136% which makes its future value to
be RM5,632.43. Bank D has an interest of 6.168% which makes its future value to be RM5,635.82.
And lastly, Bank E has an interest of 6.183% which makes its future value to be RM5,637.41.
iv) If all of the banks are insured by the government (the PIDM) and thus are equally
risky, will they be equally able to attract funds? If not (and the TVM is the only
consideration), what nominal rate will cause all the banks to provide the same
effective annual rate as Bank A?
Nominal rate =
i
m
, m = number of compounding cycle
→ Bank B, i = 6%, m = 2 (semi-annually)
Nominal rate =
6
= 3%
2
→ Bank C, i = 6%, m = 4 (quarterly)
Nominal rate =
6
= 1.5%
4
→ Bank D, i = 6%, m = 12 (monthly)
23
Nominal rate =
6
= 0.5%
12
→ Bank E, i = 6%, m = 365 (daily)
Nominal rate =
6
= 0.0164%
365
Bank
Nominal Rate
Bank B
3%
Bank C
1.5%
Bank D
0.5%
Bank E
0.0164%
These four banks have different values of number of compounding cycle but the same value
of interest which is 6%. Bank B number of compounding cycle is 2 which makes its nominal rate
to be 3%. Bank C number of compounding cycle is 4 which makes its nominal rate to be 1.5%.
Bank D number of compounding cycle is 12 which makes its nominal rate to be 0.5%. Lastly,
Bank E number of compounding cycle is 365 which makes its nominal rate to be 0.0164%.
v) Suppose you don’t have the RM5,000 but need it at the end of 1 year. You plan to
make a series of deposits – annually for A, semi-annually for B, quarterly for C,
monthly for D, and daily for E – with payments beginning today. How large must the
payments be to each bank?
→ Bank A
n = 1 (annually)
i = 6% ≈ 0.06
FV annuity due = CF [
(1+i)n −1
i
] [1 + i]
(1 + 0.06)1 − 1
RM5,000 = CF [
] [1 + 0.06]
0.06
RM5,000 = CF × 1 × 1.06
CF =
RM5,000
= RM4,716.98
1.06
24
→ Bank B
n = 2 (semi-annually)
i=
6%
= 3% ≈ 0.03
2
FV annuity due = CF [
(1+i)n −1
i
] [1 + i]
(1 + 0.03)2 − 1
RM5,000 = CF [
] [1 + 0.03]
0.03
RM5,000 = CF × 2.03 × 1.03
CF =
RM5,000
= RM2,391.32
2.0909
→ Bank C
n = 4 (quarterly)
i=
6%
= 1.5% ≈ 0.015
4
FV annuity due = CF [
(1+i)n −1
i
] [1 + i]
(1 + 0.015)4 − 1
RM5,000 = CF [
] [1 + 0.015]
0.015
RM5,000 = CF × 4.09 × 1.015
CF =
RM5,000
= RM1,204.82
4.15
→ Bank D
n = 12 (monthly)
i=
6%
= 0.5% ≈ 0.005
12
FV annuity due = CF [
(1+i)n −1
i
] [1 + i]
(1 + 0.005)12 − 1
RM5,000 = CF [
] [1 + 0.005]
0.005
RM5,000 = CF × 12.33 × 1.005
CF =
RM5,000
= RM403.55
12.39
25
→ Bank E
n = 365 (daily)
i=
6%
= 0.016% ≈ 0.00016
365
FV annuity due = CF [
(1+i)n −1
i
] [1 + i]
(1 + 0.00016)365 − 1
RM5,000 = CF [
] [1 + 0.00016]
0.00016
RM5,000 = CF × 375.84 × 1.00016
CF =
RM5,000
= RM13.30
375.90
For Bank A, since it is annually, and the interest for Bank A is 6%, the amount of payment
they have to make is around RM 4,716.98. For Bank B, it is semi-annually, and the interest for
Bank B is 3%, the amount of payment they have to make is around RM 2,391.32. For Bank C, it
is quarterly, and the interest for Bank C is 1.5%, the amount of payment they have to make is
around RM 1,204.82. For Bank D, it is monthly, and the interest for Bank D is 0.5%, the amount
of payment they have to make is around RM 403.55. Lastly, for Bank E, it is daily, and the interest
for Bank E is 0.016%, the amount of payment they have to make is around RM 13.30.
26
m) Suppose you borrow RM15,000. The loan’s annual interest rate is 8%, and it requires
four equal end-of-year payments. Set up an amortization schedule that shows the annual
payments, interest payments, principal repayments, and beginning and ending loan balances.
Year 1
PV = RM15,000
n = 4 years
i = 8%
m=1
1−[
Present Value annually = CF × [
RM15,000 = CF × [
RM15,000 = CF × [
CF =
1−[
1
]
(1+0.08)4
0.08
1
]
(1+i)n
i
]
]
1−0.73502
0.08
]
RM15,000
3.312125
CF = RM4,528.81
Interest payments
i
FV = PV × (1 + m)n×m
FV = RM15,000 × (1 +
0.08 1×1
)
1
FV = RM16,200 – RM15,000
FV = RM1,200
Beginning of year 1 balance (Annuity payment – Interest)
= [RM15,000 – (RM4,528.81 – RM1,200)]
= RM15,000 – RM3,328.81
=RM1,1671.19
End of Year 2 payment = RM1,1671.19
27
Year 2
PV = RM15,000
n = 4 years
i = 8%
m=1
1−[
Present Value annually = CF × [
RM15,000 = CF × [
RM15,000 = CF × [
CF =
1−[
1
]
(1+0.08)4
0.08
1
]
(1+i)n
i
]
]
1−0.73502
0.08
]
RM15,000
3.312125
CF = RM4,528.81
Interest payments
i
FV = PV × (1 + m)n×m
FV = RM1,1671.19× (1 +
0.08 1×1
)
1
FV = RM12,604.89 – RM1,1671.19
FV = RM933.70
Beginning of year 1 balance (Annuity payment – Interest)
= [RM1,1671.19 – (RM4,528.81 – RM933.70)]
= RM1,1671.19 – RM3,595.12
= RM8,076.07
End of Year 3 payment = RM8,076.07
Year 3
PV = RM15,000
n = 4 years
i = 8%
m=1
28
1−[
Present Value annually = CF × [
RM15,000 = CF × [
RM15,000 = CF × [
CF =
1−[
1
]
(1+0.08)4
0.08
1
]
(1+i)n
i
]
]
1−0.73502
0.08
]
RM15,000
3.312125
CF = RM4,528.81
Interest payments
i
FV = PV × (1 + m)n×m
FV = RM8,076.07× (1 +
0.08 1×1
)
1
FV = RM8,722.16 – RM8,076.07
FV = RM646.09
Beginning of year 1 balance (Annuity payment – Interest)
= [RM8,076.07 – (RM4,528.81 – RM646.09)]
= RM8,076.07 – RM3,882.72
= RM4,193.35
End of Year 4 payment = RM4,193.35
Year 4
PV = RM15,000
n = 4 years
i = 8%
m=1
29
1−[
Present Value annually = CF × [
RM15,000 = CF × [
RM15,000 = CF × [
CF =
1−[
1
]
(1+0.08)4
0.08
1
]
(1+i)n
i
]
]
1−0.73502
]
0.08
RM15,000
3.312125
CF = RM4,528.81
Interest payments
i
FV = PV × (1 + m)n×m
FV = RM4,193.35× (1 +
0.08 1×1
)
1
FV = RM4,528.818 – RM4,193.35
FV = RM335.47
Beginning of year 1 balance (Annuity payment – Interest)
= [RM4,193.35– (RM4,528.81 – RM335.47)]
= RM4,193.35– RM4,193.34
= RM0.00
Amortization Table
Year Beginning
Balance
Annual
Interest
Principal
Ending Loan
Payment
Payment
Payment
Balance
1
RM15,000.00
RM4,528.81
RM1,200.00
RM3,328.81
RM11,671.19
2
RM11,671.19
RM4,528.81
RM933.70
RM3,595.12
RM8,076.07
3
RM8,076.07
RM4,528.81
RM646.09
RM3,882.73
RM4,193.34
4
RM4,193.34
RM4,528.81
RM335.47
RM4,193.34
RM0.00
30