- 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 |
- 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 |
- 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 |
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 |
- 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.
- 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.
- 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 |
- 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 |
- 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.
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 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.
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.
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.
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).
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.
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