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Question:
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:
a)How much is the monthly repayment? 
b)How much interest will be paid in the 104th repayment?
c)How much would Rex and Rhonda owe the bank immediately before making the 200th repayment?
 
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?
Answer:

Question 1:

  • Part a

The monthly repayment will be $ 4159.87 which is calculated as below:

Cost of House

 $             666,000.00

Deposit Utilised

 $               61,000.00

Loan Required

 $             605,000.00

Terms of Loan (Years)

25

Compounding Frequency per year

12

Total Terms

300

Nominal Rate of Interest

6.50% per annum

Effective Rate Formula

(1 + (r/m))^m-1

 

((1+ (0.65/12))^12)-1

 

6.6972%

Monthly rate

0.005581 or 0.56%

Monthly Instalment

Total Loan Amount/ Cumulative Discounting Rate

Monthly Instalment

 $                 4,159.87

  • Part b

Interest in 104th instalment will be paid for $ 2770.17

  • Part c

Rex and Rhonda would owe the bank immediately before making the 200th repayment:

$ 320503.52

Question 2

Rate of Interest

 

 

5.35%

 

 

FV AT T=15

Year

Formula

Compounding Factor

Cash Flow Amount

Future Value

For 14th cf

1

cf * (1+r)1

1.0535

6485.358

6832.325

For 13th cf

2

cf * (1+r)2

1.109862

6485.358

7197.854

For 12th cf

3

cf * (1+r)3

1.16924

6485.358

7582.939

For 11th cf

4

cf * (1+r)4

1.231794

6485.358

7988.627

For 10th cf

5

cf * (1+r)5

1.297695

6485.358

8416.018

For 9th cf

6

cf * (1+r)6

1.367122

6485.358

8866.275

For 8th cf

7

cf * (1+r)7

1.440263

6485.358

9340.621

For 7th cf

8

cf * (1+r)8

1.517317

6485.358

9840.344

For 6th cf

9

cf * (1+r)9

1.598493

6485.358

10366.8

For 5th cf

10

cf * (1+r)10

1.684013

6485.358

10921.43

For 4th cf

11

cf * (1+r)11

1.774108

6485.358

11505.72

For 3rd cf

12

cf * (1+r)12

1.869022

6485.358

12121.28

For 2nd cf

13

cf * (1+r)13

1.969015

6485.358

12769.77

 

 

 

19.08144

 

123750

Cash Flows

Total Annuity/ Cumulative Factor

 

 

 

 

 

123750

 

 

 

 

 

19.08144

 

 

 

 

 

 

 

 

 

 

Cash Flows

$ 6485.358

 

 

 

 

Annual Cash Flows = $ 6485.358 

Question 3

  • Part a

Par Value

 $   100,000.00

Current Price

                     $  98,980.00

Nominal Rate

4.10%

 

100000-98980

 

98980

Effective Rate

4.25%

The nominal rate is less than the effective rate because of presence of compounding effect in the effective rate. The nominal interest works on the basis of simple interest and does not consider the impact of compounding. The compounding means the calculation of interest on the interest element along with the principle amount and hence it enhances the overall effective rate of interest (Brigham & Houston, 2012).

  • Part b

Rate of Return on Index

Ending Price -Starting Price

 

Starting Price

All Ordinary Prices Index

6223-5528

 

5528

Rate of Return

12.57%

 

 

 

 

Accumulative Index

65103-56123

 

56123

Rate of Return

16.00%

Difference between the ordinaries price index and accumulative index:

The accumulation index is also known as total return index and it assumes that the dividends are reinvested on the date of payment of ex-dividend. However, the ordinaries price index only gauges the changes in the price over a period of time. The ordinaries price index acts as the appropriate benchmark particularly for the traders whereas the accumulative index is the appropriate benchmark measure for the investors (Nicholson, 2018).  

Question 4

  • Part a

Bond A

Years

Cash Flows per year

DCF@7%

PV of Cash Flows

1

8

0.935

7.48

2

8

0.873

6.99

3

8

0.816

6.53

3

100

0.816

81.63

Current Price of Bond

 

 

20.99

 

Bond B

 

 

 

 

Years

Cash Flows per year

DCF@7%

PV of Cash Flows

1

10

0.935

9.35

2

10

0.873

8.73

3

10

0.816

8.16

4

10

0.763

7.63

4

100

0.763

76.29

Current Price of Bond

 

 

110.16

 

Bond C

 

 

 

 

Years

Cash Flows per year

DCF@7%

PV of Cash Flows

1

12

0.935

11.21

2

12

0.873

10.48

3

12

0.816

9.80

4

12

0.763

9.15

5

12

0.713

8.56

5

100

0.713

71.30

Current Price of Bond

 

 

120.50

  • Part b

Bond A

Years

Cash Flows per year

DCF@7%

PV of Cash Flows

Weights of bond value

Years* Weight

1

8

0.935

7.48

0.073

0.07

2

8

0.873

6.99

0.068

0.14

3

8

0.816

6.53

0.064

0.19

3

100

0.816

81.63

0.795

2.39

 

 

 

102.62

1.000

2.79

 

Duration = 2.79 years

 

Bond B

 

 

 

 

 

 

Years

Cash Flows per year

DCF@7%

PV of Cash Flows

 

 

1

10

0.935

9.35

0.085

0.08

2

10

0.873

8.73

0.079

0.16

3

10

0.816

8.16

0.074

0.22

4

10

0.763

7.63

0.069

0.28

4

100

0.763

76.29

0.693

2.77

 

 

 

110.16

1.000

3.51

 

Duration= 3.51 years

 

Bond C

 

 

 

 

 

 

Years

Cash Flows per year

DCF@7%

PV of Cash Flows

 

 

1

12

0.935

11.21

0.093

0.093

2

12

0.873

10.48

0.087

0.174

3

12

0.816

9.80

0.081

0.244

4

12

0.763

9.15

0.076

0.304

5

12

0.713

8.56

0.071

0.355

5

100

0.713

71.30

0.592

2.958

 

 

 

120.50

1.000

4.128

Duration = 4.13 Years

  • Part c

Bond A

Years

Cash Flows per year

DCF@8%

PV of Cash Flows

1

8

0.926

7.41

2

8

0.857

6.86

3

8

0.794

6.35

3

100

0.794

79.38

Current Price of Bond

 

 

20.62

Bond B

Years

Cash Flows per year

DCF@8%

PV of Cash Flows

1

10

0.926

9.26

2

10

0.857

8.57

3

10

0.794

7.94

4

10

0.735

7.35

4

100

0.735

73.50

Current Price of Bond

 

 

106.62

Bond C

Years

Cash Flows per year

DCF@8%

PV of Cash Flows

1

12

0.926

11.11

2

12

0.857

10.29

3

12

0.794

9.53

4

12

0.735

8.82

5

12

0.681

8.17

5

100

0.681

68.06

Current Price of Bond

 

 

115.97

Question 5

Internal Rate of Return

Every business involves decision making in the course of its normal operations. Undertaking of right decisions at the right time leads to the success of the business. To reach at a prudent decision, a firm has to use various tools and techniques. Capital budgeting is also a part of decision making process which involves financial planning for generally a longer period of time and involves the investment of large sums of money. These decisions are usually irrevocable in nature due to the deployment of huge amount of funds. To evaluate the projects that are long term in nature there are various techniques available under financial management studies. These techniques are Net Present Value (NPV), Payback Period, Average Accounting Rate of Return (ARR), Profitability Index, Internal Rate of Return etc.

Internal rate of return is the key technique of project evaluation as it involves the determination of such rate of return at which the net present value of the project is zero because of the fact that the total cash inflows of the project is equal to the total cash outflows of such project (Shinoda, 2010). Net present value is the sum of all the cash flows of the project since year 0 to the end of useful life of project. Present value of cash flows is calculated using the discounting rate.  The IRR technique is recognised with different names such as yield on investment, marginal efficiency of capital, time-adjusted rate of return, rate of return etc. IRR totally depends on the initial investment of the project and its cash proceeds to evaluate whether the project is accepted or rejected. An IRR of the project is typically the rate of return that it will earn if the required investment is made in such project and it receives the specific cash inflows.

For any project proposal to be accepted under IRR technique, the rate of discounting must exceed the cost of capital of the project which is commonly termed as hurdle rate or the cut off rate. The IRR which is lower than the hurdle rate represents the cost to the shareholders of the project whereas the IRR which is higher than the hurdle rate represents the return on the investment made by the shareholders of the project and it maximises their wealth. Therefore, to decide whether a particular project must be accepted or rejected, it is necessary to compare the cost of capital with the internal rate of return. If the IRR is higher than the cost of capital, then the proposed project must be accepted and if the IRR is less than the project’s cost of capital, then it must not be accepted (Rossi, 2015).

The use of IRR technique of project evaluation enables the project manager to have a clear picture of the value of the project and also the associated risk with it. As IRR method takes into account the time value of money, it allows the project managers to know the actual return from the investment made in the project. The internal rate of return is often called as the project’s break-even financing rate. Unlike other techniques of capital budgeting such as payback period, IRR considers the project’s profitability across its entire economic life and not merely till the particular period of time.

The discounting rate at which the capital outlay of the project is equated with its cash flows is shown in the percentage terms and hence this method offers the uniform ranking and also the quick comparison of the related efficiency of alternative project proposals. Generally, the decisive results under both the techniques of capital budgeting i.e. NPV and IRR are same but there are certain circumstances where the cash flows are non-conventional in nature, mutually exclusive projects etc. The assumptions relating to reinvestment rate are different under both the methods.  Under NPV method, it is assumed that the cash flows would be reinvested at or around the cost of capital of the project while IRR method works on the assumption that the cash flows of the project can be reinvested at its IRR (Bierman & Smidt, 2012). In theoretical view, project’s manager usually finds NPV as the better technique to evaluate the worthiness of the project. However from the practical view point, IRR is more accepted technique of project evaluation due the general disposition of business executives towards the rate of return than the returns expressed in actual dollar terms. Since, all the interest rates, profitability ratios are often expressed as the annual rate of returns, the application of IRR technique makes more sense to the financial decision makers. The main strength of IRR method is that it has the ability to measure the benefits related to the invested funds in the project. Therefore, in case of individual projects, use of IRR technique is more beneficial as this method will provide the project managers with ultimate results that are more sophisticated and reliable in nature. The interpretation of results of IRR is more convenient for the financial analysts.

Investment in the real assets involves a certain set of real options that can be exercise to enhance the value of assets as well as to limit the losses. Real option evaluation eliminates the potential losses by way of project abandonment in the circumstances that are unfavourable in nature. Traditional methods such as NPV, IRR and discounted cash flows cannot capture the flexibility in managerial decision making (Bennouna, Meredith & Marchant, 2010). Rather, the decision trees serves as the more appropriate approach to identify the value of real options under which average expected cash flows are determined considering the probabilities linked to the cash flows. In situations that are quite dynamic or uncertain in nature, traditional techniques of capital budgeting fails to offer realistic results (Santos, Soares, Mendes & Ferreira, 2014).

It can now be concluded that, though the application of internal rate of return as a technique of project evaluation provides the project managers with realistic and sophisticated results but there are certain loopholes in this technique which makes it unable to serve its basic purpose of decision making. This technique cannot be used in the dynamic environment and hence such circumstances require use of more advanced tools such as decision tree analysis to evaluate the project’s worth.

References:

Bennouna, K., Meredith, G.G. and Marchant, T., 2010. Improved capital budgeting decision making: evidence from Canada. Management decision, 48(2), pp.225-247.

Bierman Jr, H. and Smidt, S., 2012. The capital budgeting decision: economic analysis of investment projects. US: Routledge.

Brigham, E.F. and Houston, J.F., 2012. Fundamentals of financial management. US: Cengage Learning.

Nicholson, C., 2018. How is a Total Return (accumulation) index different to a price index? Available at: < https://www.bwts.com.au/index.cfm/resources/ask-colin/1163-how-is-a-total-return-accumulation-index-different-to-a-price-in/> Accessed on 18.08.2018

Rossi, M., 2015. The use of capital budgeting techniques: an outlook from Italy. International Journal of Management Practice, 8(1), pp.43-56.

Santos, L., Soares, I., Mendes, C. and Ferreira, P., 2014. Real options versus traditional methods to assess renewable energy projects. Renewable Energy, 68, pp.588-594.

Shinoda, T., 2010. Capital budgeting management practices in Japan: a focus on the use of capital budgeting methods. Economic Journal of Hokkaido University, 39, pp.39-50.

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