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Question 1

Now that they have accumulated a deposit of $61,000, Rex and his partner Rhonda wish to use the deposit and take out a housing loan to purchase a home. The house costs $666,000. The loan is to be repaid in equal monthly instalments over a term of 25 years.  Rhonda recalls that the interest rate quoted by the bank is an annual nominal rate of 6.5%pa.  Rex has misplaced the paperwork showing the annual effective rate, so you may need to work this out. Interest is added monthly. They would like to know:

  1. How much is the monthly repayment?
  2. How much interest will be paid in the 104threpayment?
  3. How much would Rex and Rhonda owe the bank immediately beforemaking the 200th repayment?
Question 2
Jara has just been advised of a bequest of a lump sum of $119,750 from his Aunt’s will, but it is not due to be available for him for fifteen years (at t = 15 he will receive $123,750). Jara wants to receive some cash earlier than this. He is investigating using the bequest to purchase an annuity, in exchange, with the first annual cash flow of the annuity to be received at the end of year 2 (thirteen cash flows).  Assume that the annuity and the lump sum are of equivalent risk and 5.35% pa is the appropriate interest rate (opportunity cost of funds for Jara). How much is the annual cash flow associated with the annuity?

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

123,750

 

 

 CF

CF

CF

CF

CF

CF

CF

CF

CF

CF

CF

CF

CF

0

Question 3 (5 marks)

Your supervisor has asked you to do the following calculations:

  • A bank bill with 90 days to maturity has a price of $98,980. What is the effective annual yield implied by this price and maturity? What is the annual nominal yield? Face value is $100,000. Label your answers clearly. Provide a brief explanation of why these rates differ.
  • The All Ordinaries price indexopened the year at 5528 and closed at 6223 by the end of the year. The equivalent accumulation index went from 56123 to 65103. What is the annual rate of return on each of these indices? Explain the difference.
Question 4

Consider the following three bonds:

Bond

Term to maturity (years)

Coupon rate (% p.a.)

A

3.0

8

B

4.0

10

C

5.0

12

Each bond has a face value of $100 and the current yield is 7% p.a.  Assume all bonds pay annual coupons. 

Required:

  1. Calculate the current price of each bond.
  2. Calculate the duration of each bond.
  3. Calculate what would be the price of each bond if market interest rateswere to rise to 8%.
Question 5

“The Internal rate of return (IRR) technique is reputed to be one of the most reliable project evaluation methods there is.” Discuss and compare the attributes that give the IRR method its reliability and assess its capacity to price real options.Your answer should be in long-form, and of approximately 1000 words.  Include 4-5 references where appropriate.

Answer:
Answer 1:
  1. Monthly repayment:

EMI = [P x R x (1+R)^N]/[(1+R)^N-1],

where P = loan amount or principal

R = interest rate per month

N = number of monthly instalments.

Que 1 a)

 

Calculation of monthly payment

 

Loan (P)

 $                  605,000.00

Tenure (months) (N)

300

Interest rate monthly (R)

0.54%

EMI = [605000*0.54%*(1+054%)^300]/[(1+0.54%)^300-1]

= [605000*0.54%*5.03]/4.03

                      = $ 4085

EMI

$4,085


  1. Interest amount after 104th payment:

Que 1 b)

After the 104th EMI, the interest would be

EMI No.

Opening balance loan

EMI

Interest

Closing balance loan

104

 $                  493,969.31

 $      4,085.00

 $      2,675.67

 $ 492,559.97

  1. Total loan amount after 200th repayment:

Que 1 c)

Owed money from bank after 200th payment

EMI No.

Closing balance loan

200

 $                  314,762.32

 

 
Answer 2:

0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

123,750

 

 

-$1,138.26

-$1,199.15

-$1,263.31

-$1,330.90

-$1,402.10

-$1,477.11

-$1,556.14

-$1,639.39

-$1,727.10

-$1,819.50

-$1,916.84

-$2,019.39

-$2,127.43

0

 

EMI No.

Opening balance loan

EMI

Interest

Closing balance loan

1

119750

6406.625

$5,404.90

$114,345.10

2

$114,345.10

$6,117.46

$5,694.07

$108,651.03

3

$108,651.03

$5,812.83

$5,998.70

$102,652.33

4

$102,652.33

$5,491.90

$6,319.63

$96,332.70

5

$96,332.70

$5,153.80

$6,657.73

$89,674.97

6

$89,674.97

$4,797.61

$7,013.92

$82,661.05

7

$82,661.05

$4,422.37

$7,389.16

$75,271.88

8

$75,271.88

$4,027.05

$7,784.48

$67,487.40

9

$67,487.40

$3,610.58

$8,200.95

$59,286.45

10

$59,286.45

$3,171.82

$8,639.70

$50,646.74

11

$50,646.74

$2,709.60

$9,101.93

$41,544.81

12

$41,544.81

$2,222.65

$9,588.88

$31,955.93

13

$31,955.93

$1,709.64

$10,101.89

$21,854.04

14

$21,854.04

$1,169.19

$10,642.34

$11,211.70

15

$11,211.70

$599.83

$11,211.70

$0.00

 

EMI No.

Opening balance loan

EMI

Interest

Closing balance loan

1

123750

 

 

$123,750.00

2

$123,750.00

$6,620.63

$6,832.32

$116,917.68

3

$116,917.68

6255.09563

$7,197.85

$109,719.82

4

$109,719.82

5870.01043

$7,582.94

$102,136.88

5

$102,136.88

5464.32318

$7,988.63

$94,148.26

6

$94,148.26

5036.93166

$8,416.02

$85,732.24

7

$85,732.24

4586.67469

$8,866.28

$76,865.96

8

$76,865.96

4112.32897

$9,340.62

$67,525.34

9

$67,525.34

3612.60576

$9,840.34

$57,685.00

10

$57,685.00

3086.14736

$10,366.80

$47,318.19

11

$47,318.19

2531.52343

$10,921.43

$36,396.77

12

$36,396.77

1947.22712

$11,505.72

$24,891.05

13

$24,891.05

1331.67096

$12,121.28

$12,769.77

14

$12,769.77

683.182545

$12,769.77

$0.00

 

 
Answer 3:
  1. Annual nominal yield:

Que 3 a)

Calculation of rate

 

 

Maturity Price

98980

Time (days)

90

Face value

100000

Rate

4.25%


Effective annual yield = (1+r/n)^n-1

= ((1.0425)^4)-1

= 18.11%

Price = (10000 * 18.11%)

= 18,117.48

Nominal annual yield=( Price * time / 365)/100

=(((18114.78)*90/365)/100)

= 44.67%

The effective annual yield of the business is 18.11% whereas the nominal annual yield is 18.11%. The main reason behind the difference among both the rate is that it explains about the different concept of the business. For instance, effective annual yield brief about the annual rate of the proposal whereas the nominal yield takes the concern till the maturity date of the proposal.

  1. Return and the differences:

Que 3 b)

Calculation of annual rate of return

 

AORD

Accumulation index

 

 

 

Opening price

5528

56123

Closing price

6223

65103

 

 

 

Return (Closing price – Opening price) / Opening price

12.57%

16.00%

The annual rate of return of AORD is 12.57% whereas the annual rate of return of accumulation index is 16%. The main reason behind the difference among both the return is that the AORD stock prices are affected by few stock whereas the accumulated stock price is affected by the total stock which are registered at the stock exchange and thus the prices are different and the return are also different.

 
Answer 4:
  1. Current price of bond:

Bond A = 8 [1-((1+7%)^-3)/0.07]+ 100 / [1+0.07]^3

Bond B=  10 [1-((1+7%)^-4)/0.07]+ 100 / [1+0.07]^4

Bond C = 12 [1-((1+7%)^-5)/0.07]+ 100 / [1+0.07]^5

Calculation of Current price of Bond A

1

8.0000

0.935

7.476636

2

8.0000

0.873

6.98751

3

108.0000

0.816

88.16017

Current price

102.6243

 

Calculation of Current price of Bond B

1

10.00

0.935

9.345794

2

10.00

0.873

8.734387

3

10.00

0.816

8.162979

4

110.00

0.763

83.91847

5

 

 

 

Current price

110.1616

 

Calculation of Current price of Bond C

1

12.00

0.935

11.21495

2

12.00

0.873

10.48126

3

12.00

0.816

9.795575

4

12.00

0.763

9.154743

5

112.00

0.713

79.85445

Current price

120.501

  1. Duration of bond:

Calculation of total duration of Bond A

 

Amount

P. V factor

Present value

Total amount = Present value * number of years

1

8.0000

0.935

7.476636

7.476636

2

8.0000

0.873

6.98751

13.97502

3

108.0000

0.816

88.16017

264.4805

 

 

 

102.6243

285.9322

Duration of bond (Total amount – present value)

2.786203

 

Calculation of duration of Bond B

 

Amount

P. V factor

Present value

Total amount = Present value * number of years

1

10.00

0.935

9.345794

9.345794

2

10.00

0.873

8.734387

17.46877

3

10.00

0.816

8.162979

24.48894

4

110.00

0.763

83.91847

335.6739

5

 

0.713

 

 

 

 

 

110.1616

386.9774

Duration of bond

3.512815

 

Calculation of duration of Bond C

 

Amount

P. V factor

Present value

Total amount = Present value * number of years

1

12.00

0.935

11.21495

11.21495

2

12.00

0.873

10.48126

20.96253

3

12.00

0.816

9.795575

29.38672

4

12.00

0.763

9.154743

36.61897

5

112.00

0.713

79.85445

399.2723

 

 

 

120.501

497.4554

Duration of bond

4.128227

  1. Price of each bond:

Bond A = 8 [1-((1+8%)^-3)/0.08]+ 100 / [1+0.08]^3

Bond B=  10 [1-((1+8%)^-4)/0.08]+ 100 / [1+0.08]^4

Bond C = 12 [1-((1+8%)^-5)/0.08]+ 100 / [1+0.08]^5

Calculation of Current price of Bond A

1

8.0000

0.926

7.407407

2

8.0000

0.857

6.858711

3

108.0000

0.794

85.73388

Current price

100

 

Calculation of Current price of Bond B

1

10.00

0.926

9.259259

2

10.00

0.857

8.573388

3

10.00

0.794

7.938322

4

110.00

0.735

80.85328

 

 

0.681

 

Current price

106.6243

 

Calculation of Current price of Bond C

1

12.00

0.926

11.11111

2

12.00

0.857

10.28807

3

12.00

0.794

9.525987

4

12.00

0.735

8.820358

5

112.00

0.681

76.22532

Current price

115.9708

If the yield price would be increased than the current price of the bond would be decreased.

 
Answer 5:

The report brief that "The Internal rate of return (IRR) technique is reputed to be one of the most reliable project evaluation methods there is.”  The IRR is one of the huge tools of capital budgeting which is used by the business to evaluate various approaches or the business projects. The process of IRR is more crucial as it takes the concern on all he related factors and the assumption level of the technique is lower than the other evaluation techniques (Peterson and Fabozzi, 2012). The main factors of IRR are that it only takes the help of one single discount rate to evaluate the project or the proposal of an organization.

Internal rate of return (IRR) is basically calculated through a metric which helps the business to measure the total profitability from the investment project of an organization. Through the evaluation of IRR on the potential project of the business, a discount rate is calculated which converts the total net present value of cash inflow and cash outflow of business zero (Frank and Goyal, 2009). There is no specific formula of IRR method as it is calculated through trial method. However, the below formula could be used to calculate the IRR of the company:

The formula says that the different rates must be applied in the formula to evaluate that on which rate of return, the NPV of the business would be zero. That rate of return is internal rate of return which explains that the business proposal would offer that much return to the business. If the internal rate of return of the business is higher than the total cost of capital of an organization than the project should be accepted by the business as it explains the total return from the proposal would be higher than the total cost of the business which would lead to the business towards the profitability level.

IRR method is one of the reliable method of capital budgeting tools because it does not take the help of various assumptions to reach over a result as well as it focuses on the single internal rate of return to reach over a conclusion that the project must be accepted by the business or not (Lord, 2007). Further, it considers the time value of factors as well to evaluate the present value of future cash outflow and inflow of the business which make it more reliable.

The Kaplan and Atkinson, (2015) has presented into his study that there are twp mostly used tools of capital budgeting which are internal rate of return and net present value. Net present values explain about the total profit from the investment proposal but the main disadvantage of this tool is that it does not take the concern of total cost of the business. Sometimes the profit of a project is higher but it is lower than the cost of the company. Thus, IRR is the best approach as it also takes the concern on the cost of capital of the business. It measures the actual rate of return of the business where the NPV of the business would be zero and compares it with the cost of capital of the business. It explains that if the cost of capital of the business is higher than the net present value of the business than the project should not be accepted by the business as it would ultimately lead to the business towards the loss.

Higgins (2012) has further brief into the research paper that IRR approach is one of the most reliable approach in price real options in the capital budgeting process due to the below topics:

Hurdle rate:

Hurdle rate brief about a minimum rate which is expected by the company to earn when company invests into a particular project. It is a subjective rate to explain. In the internal rate of return, it is not important to identify the hurdle rate due to the fact that it is simple for a business to believe on the factors and results of the business. The outcome from the business makes it simple for the management to make better decisions.

Simplicity:

It is one of the most attractive things about the IRR approach that it is simple to calculate and interprets. The IRR approach makes it simple for the business to make base for the managers to make a better decision about the acceptance of the project (Hillier, Grinblatt and Titman, 2011). It measures all the related aspect of the business to reach over a conclusion stage about the investment proposal.

Reliability:

IRR method is one of the reliable method of capital budgeting tools because it does not take the help of various assumptions to reach over a result as well as it focuses on the single internal rate of return to reach over a conclusion that the project must be accepted by the business or not.

Time value of money:

Further, it considers the time value of factors as well to evaluate the present value of future cash outflow and inflow of the business which make it more reliable. It makes it simple for the business to make base for the managers to make a better decision about the acceptance of the project (Gapenski, 2008).

Required rate of return:

The IRR approach calculates different rates which are applied in the formula of NPV to evaluate that on which rate of return, the NPV of the business would be zero. It calculates the single rate of return to measure the investment proposal’s performance.

IRR is the one of the best approaches as it also takes the concern on the cost of capital of the business. It measures the actual rate of return of the business where the NPV of the business would be zero and compares it with the cost of capital of the business. It explains that if the cost of capital of the business is higher than the net present value of the business than the project should not be accepted by the business as it would ultimately lead to the business towards the loss.

 
References:

Frank, M.Z. and Goyal, V.K., 2009. Capital structure decisions: which factors are reliably important?. Financial management, 38(1), pp.1-37.

Gapenski, L.C., 2008. Healthcare finance: an introduction to accounting and financial management. Health Administration Press.

Higgins, R. C., 2012. Analysis for financial management. McGraw-Hill/Irwin.

Hillier, D., Grinblatt, M. and Titman, S., 2011. Financial markets and corporate strategy. McGraw Hill.

Kaplan, R.S. and Atkinson, A.A., 2015. Advanced management accounting. PHI Learning.

Lee.C.F and Lee, A, C,.2006. Encyclopedia of finance, Springer science, new York.

Lord, B.R., 2007. Strategic management accounting. Issues in Management Accounting, 3.

Peterson, P,P and Fabozzi,F,J,. 2012, Capital budgeting: theory and practice, John Wiley & sons, Canad

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