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?
Loan repayment computation
Cost of house = $ 666,000
Downpayment for the house = $ 61,000
Hence, total loan assumed = 66600061000 = $ 605,000
Total period of repayment = 25 years or (25*12) = 300 months
Nominal rate of interest = 6.5% p.a. or (6.5/12) = 0.5417% per month
 The monthly repayment can be computed using the following formula.
EMI = [P*R*(1+R)^{N}]/[(1+R)^{N} 1]
Hence, monthly repayment = 605000*0.005417*(1.005417)^{300}/(1.005417^{300}1) = $ 4,085
 The amortisation schedule for the loan in the attached excel sheet. The relevant interest payment in the 104^{th}payment would be $2,676 as indicated in the following screenshot.
 The amount that Rex and Rhonda would owe the bank before the 200^{th}repayment is $319,484 which is indicated in the excel shown below.
The future value of the annuity payments at t=15 must be equal to $ 123,750. The applicable interest rate is 5.35% p.a. Let the annuity payment be $ X.
Based on the above, 19.0814X = 123750
Solving the above, X = $6,485.36
The yearly annuity would be $ 6,485.
 Days to maturity = 90
Face value of bond = $ 100,000
Current price of bond = $98.980
Let the nominal annual yield be x% p.a.
100000 = 98980 (1+(x/100)^{(90/365)}
Solving the above, x = 4.24% p.a.
The effective yield can be computed as shown below.
Effective annual yield = (1+ (4.24*90/36500))^{365/90} – 1 = 4.31% p.a.
The effective annual yield is different from the nominal annual yield since it considers the effect of compounding which is not cot considered by nominal yield computation.
 Annual rate of return on All Ordinaries Price Index= [(62235528)/5528]*100 = 12.57%
Annual return of return on Accumulation Index = [(65103 – 56123)/56123]*100 = 16% p.a.

 The present value of bonds would be discounted value of the future cash inflows expected during the maturity period of bond. The discount rate used would be 7% which is the market interest rate.
Bond A
Annual coupon = 8% of 100 = $ 8
Term of maturity = 3 years
The current price of bond can be estimated as follows.
Bond B
Annual coupon = 10% of 100 = $ 10
Term of maturity = 4 years
The current price of bond can be estimated as follows.
Bond C
Annual coupon = 12% of 100 = $ 12
Term of maturity = 5 years
The current price of bond can be estimated as follows.
 The duration computation of the three bonds is indicated below.
Bond A
Relevant computation is shown below.
Duration = 285.93/100 = 2.86 years
Bond B
Relevant computation is shown below.
Duration = 386.98/100 = 3.87 years
Bond C
Relevant computation is shown below.
Duration = 497.46/100 = 4.97 years
 The present value of bonds would be discounted value of the future cash inflows expected during the maturity period of bond. The discount rate used would be 8% which is the market interest rate.
Bond A
Annual coupon = 8% of 100 = $ 8
Term of maturity = 3 years
The current price of bond can be estimated as follows.
Bond B
Annual coupon = 10% of 100 = $ 10
Term of maturity = 4 years
The current price of bond can be estimated as follows.
Bond C
Annual coupon = 12% of 100 = $ 12
Term of maturity = 5 years
The current price of bond can be estimated as follows.
IRR or Internal Rate of Return is defined as the underlying discount rate which results in NPV of the project to come out as zero. It is a popular tool used for the evaluation of projects so as to allow prudent allocation of scarce capital assets. The reliable evaluation of these projects is of utmost importance considering the long term nature of these projects and also the immense amount of capital and other resources that are involved (Arnold, 2015).
While there is a plethora of methods for evaluation of capital projects but one of the most reliable methods is IRR. One of the key attributes that contributes to this aspect is that it takes into consideration the time value of money. Taking this into consideration is quite imperative especially for long term projects since time value of money is a significant factor. This is because a particular incremental cost or incremental revenue which would be realised after 10 to 15 years cannot be considered in absolute terms and need to be adjusted so as to reflect the current value. This is superior in comparison to methods such as payback period which do not take into consideration the time value of money and therefore are not suitable for projects having long duration (Petty et. Al., 2015).
Annuity and future value computation
Another positive aspect of IRR is that it considers all the cash flows over the life of the project. As a result, it provides a complete picture of the given project. This is in contrast with evaluation techniques such as payback period (Both discounted and undiscounted) which consider the cash flows till the time the initial investment is recovered. Thus, while choosing between two projects, the assessment using payback period might not be reliable but it is not the case with IRR (Damodaran, 2015).
Yet another positive aspect of IRR is that the computation does not require to consider the cost of capital. This is a significant advantage of IRR over measures such as NPV which are highly sensitive to changes in cost of capital. Also, the reliable prediction of cost of capital determination in a plethora of projects is quite difficult owing to the varying risk levels of the projects compared to the risk level of the firm and also the underlying funding. This leads to reliable computation of IRR. Further, interpretation of IRR is also quite simple since it requires comparison between the IRR and the hurdle rate (also called as discount rate or cost of capital) (Brealey, Myers and Allen, 2014).
Despite the attributes of IRR which contribute to reliability, there are certain shortcomings that also need to be highlighted. One of these is the underlying assumption that reinvestment can happen at IRR which is rarely true. This is because in case of IRR being on the lower side, the assumed reinvestment rate might be lower. On the other hand if IRR is quite high, then the assumed reinvestment rate might be higher than realistically expected. An additional problem with usage of IRR arises in cases where there are both positive and negative cashflows associated with the project after the initial investment. In such projects, multiple values of IRR are obtained which can lead to confusion. Another situation where reliability of IRR is questionable when one has to compare two or more projects with different project lives. IRR may not give the correct conclusion in such cases and an annualised measure would lead to better results (Parrino and Kidwell, 2014).
Considering the significant rise in external factors that tend to impact project viability, it has become a useful practice to insert real options in the projects especially where the duration is long term. A useful example of this can be indicated in the form of mining project concerned with iron ore mining. It might be possible that owing to economic slowdown after six months or an year, there might be decrease in the iron ore demand which would adversely impact the price and hence the viability of the project. To meet with such contingencies, real options are inserted which provide management the options to either postpone the project or abandon the same. These options are very useful for minimising the losses considering the huge investments in such projects (Damodaran, 2015).
With regards to valuation of real options, the valuation techniques used are similar to those that are used for financial options valuation. The traditional capital budgeting techniques such as IRR are not suitable for these real options considering that the pricing is dependent on the host of factors ranging from the underlying volatility in price, strike price and duration. With this underlying uncertainty, measures like IRR are not suitable since they are deployed when the underlying cash flows are definite and thereby lack volatility. As a result, for real options valuation, techniques such as BlackScholes option pricing model, binomial lattice along with simulation methods are used which consider the wide range of possible scenarios and capture the same in the form of mathematical model (Petty et. Al., 2015).
Based on the above discussion, it is apparent that IRR is a quite reliable measure for evaluation of long term capital projects. There are a number of attributes which contribute in this regards. These include time value of money, nonrequirement of discount rate and considers all cash flow. However, there are certain situations when IRR is not a reliable measure, which have been included and one needs to be considerate of these scenarios. Also, the real options which are widely used in evaluation of capital projects are not reliably valued by IRR and require techniques that are used for valuation of financial options.
References
Arnold, G. (2015) Corporate Financial Management. 3^{rd} ed. Sydney: Financial Times Management.
Brealey, R. A., Myers, S. C., & Allen, F. (2014) Principles of corporate finance, 2nd ed. New York: McGrawHill Inc.
Damodaran, A. (2015). Applied corporate finance: A user’s manual 3rd ed. New York: Wiley, John & Sons.
Parrino, R. and Kidwell, D. (2014) Fundamentals of Corporate Finance, 3rd ed. London: Wiley Publications
Petty, J.W., Titman, S., Keown, A., Martin, J.D., Martin, P., Burrow, M., & Nguyen, H. (2015). Financial Management, Principles and Applications, 6^{th} ed.. NSW: Pearson Education, French Forest Australia
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