Concept of time value of money
Answer a: Fundamentals of time value concepts
The Concept of time value of money indicates that value of money depreciates year after year. It further reflects that at the present value of money is more than the future value. As per Chan and Rate (2018), time value of money refers to the concept that the value of money at present is more than the value the amount of money would have in the future. This is due to the potential earning capacity of money. A certain amount of money would earn more amount of interest if it is deposited at an earlier phase provided the rate of interest remains the same (Burns and Walker 2015).
For example, if $1000 is deposited at 10 percent interest for 1 year on 01.01.2018, it would earn an interest of $100 and the total amount combining the principal and interest would come to $1100 on 01.01.2019. Again, if the same amount of $1000 is deposited for 6 months on 01.07.2018, at 10 percent it would only yield at interest of 50. This means that the total amount would come to $ 1050 on 01.01.2019.
The above example shows that money used earlier would bear more utility than used in the future. One can point out that for same amount of money, the value of disbursement remains the same but the utility or benefit that can be availed or purchased with that money will be less in future. This difference is known as opportunity cost which a person incurs because he used a certain amount of money in the future. The value of time value of money is as follows:
FV=PV*[1+ (i/n)] ^ (n*t)
FV=Future value of money
PV=Present value of money
i=interest rate
n=number of compounding periods per year
t=number of years
PV |
n |
T |
i |
n*t |
i/n |
1+(i/n) |
[1+(i/n)]^(n*t) |
PV*[1+(i/n)]^(n*t) |
FV |
1000 |
4 |
1 |
10 |
4 |
2.5 |
3.5 |
150 |
150063 |
150063 |
1000 |
4 |
2 |
10 |
8 |
2.5 |
3.5 |
22519 |
22518754 |
22518754 |
Calculation of FV of money
The above shows compares the present value of money and the increment one can earn. If the money is deposited now, two years from now the value would be $ 22518754. If the same amount is deposited a year later, the value would be $ 150063. This analysis shows that value of money decreases with late investment and that is what is known as time value of money.
- Discounting and compounding process and their uses (what is the rational for using discounting process rather than compounding process in decision making?)
Brooks (2015 opines that both discounting and compounding process is useful in their own ways. The rational for using discounting rates rather than compounding process is as follows:-
Discounting rate |
Compounding rate |
It helps to ascertain the percentage of amount to be invested today to get a particular amount in future. |
It helps to ascertain the future value of a particular amount invested today. |
It is known as the future value of the project |
It is known as the present value of the project |
Discounting factors are used in order to ascertain discounting rates |
Compounding interest rates are used |
Table: Difference between discounting rate and compounding rate
From the above table, it can be inferred that discounting rates are more suitable for decision making purpose. An investor will get to know what amount he should invest in order to meet his future long-term goals, which cannot be done while using compounding rate of interest.
- Discount rate and main components of the discount rate (why do we use different discount rates for evaluating different decisions?).
Calculation of FV of money
The two basic components of discount rate is risk free rate and weighted average cost of capital. Cost of capital is used in order to calculate different forms of capital budgeting techniques for any particular project. There are different types of discounting rates use for different purpose. In order to ascertain future value of an investment, different discounting rates are used (Brooks 2015).On the other hand, single discounting values are used to ascertain value of future cash flows. On the other various discounting techniques, which are as follows:-
- Discounted cash flows
- Net Present Value
- Internal rate of return
All the above types are suitable for different purposes. Net present value is used to ascertain the excess of future inflows versus outflows. On the other hand, internal rate of return is used to ascertain the rate of return from a particular project. In addition to this, payback period is used to determine the time frame to get back the initial investment amount.
- Use of time value in valuation of financial instruments such as bonds, equity and preference shares.
There are various forms of financial instruments of time valuation. These can be in the form of bonds, equity and preference shares. Bonds is generally consider as safe and fixed money market instrument. Equity is considered as a capital market instrument and yields a high rate of interest. On the other hand, preference shares also entitles a shareholder to get a fixed percentage of dividend over a period of time (Faccio, Marchica and Mura 2016). There are several advantages and disadvantages of these financial instruments which can further evaluated with the help of the following table:-
Instruments |
Advantages |
Disadvantages |
Equity |
1. High rate of return 2. Limited liability |
1. High risk 2. Depends on market fluctuation 3. High volatility |
Bonds |
1. Low volatility 2. Liquidity is high 3. Less risky investment |
1. Reinvestment risk is there 2. Fixed rate of interest which can be lower than market prices 3. The investors will lose their money if the company is declared bankrupt 4. Exchange rate risk is also there |
Preference shares |
1. Fixed rate of dividend 2. Less risky |
1. No voting rights 2. Low rate of return |
Table: Advantages and disadvantages of financial instruments
From the above table, it can be inferred that all the given financial instruments have several advantages and disadvantages. It will solely depend upon the investor in which financial instrument he/she will invest. Apart from this, it is choice of the investor whether he will choose risk prone investments and risk free requirements according to the respective aims and objectives (Finnerty 2013).
- Capital budgeting and time value.
Delaney, Rich and Rose (2016) defined capital budgeting as the process in which business organizations, especially large business organizations determine the potential expenditure and return on investments which they can face in the future.
Time value of money is important for capital budgeting. There are various factors which affect capital budgeting like time value, discount rates and converting values. Future value and present value is critical in case of capital budgeting.
Using time value of money, an investor can understand the decision of investment in a project in a better manner.
Discounting rate vs. Compounding rate
The graph above compares the values of GBP. EU and JPY against USD. It shows that though GBP and EU value fell in April, both the currencies are showing rising trends compared to USD. JPY is showing also showing an upward trend, but of a higher than EU and GBP. This means firms would have to allocate more amount of money for purchasing products from these markets after May 14, 2015 than they would have incurred around May 8 when all the three currencies showed downward trends against USD. The multinational firms have to take into account factors like exchange rates and future value of as shown in figure 1 and figure 2 while forming budget (Goyat and Nain 2016). From the above analysis, it can be inferred that capital budgeting and time value of money goes side by side.
- The other issues
There are various issues or disadvantages associated with time value of money. These can be as follows:-
- Calculation of Net Present value is sensitive with discounting rates-Net present value is based on summation of all the respective discounted cash flow of any particular given project. Therefore, any considerable percentage of increase or decrease of discounted cash flows can reflect a wrong value of Net present Value (Brooks 2015).
- Cannot use different rates of discounted cash flows-It is true that market rates cannot be same for entire time horizon. It may happen that the risk is more in first year in comparison with the second year. However, capital budgeting techniques of NPV, IRR keeps the discounting rate same for the entire time horizon. This can be considered as another issue of these methods.
- Real options are excluded- The calculations of NPV or any capital budgeting technique do not include real options which are there in a respective project. This can be considered as a disadvantage of capital budgeting methods.
These are the disadvantages which are associated with time value of money.
Financial goals of Studebaker
There are several financial goals of Studebaker which are as follows:-
- He wants to accumulate as much additional money as he could as he is planning an early retirement in next 20 years or by 2038 at the age of 60.
- He had a mortgage which he had to clear within next 20 years
- He wanted to accumulate all the funds of the money market into one single life insurance policy.
However, it is not a correct goal. There are few reasons behind it. These reasons are as follows:-
- Opportunity costs are not taken into consideration
- The annual costs will be 47,145.31 if the excess amount of money market is introduced into one single life insurance policy.
- Life insurance would give him only 6 percent interest, however, any long term investment will give him around 7 percent rate of interest.
- He should invest in safety funds and try to avoid market risks.
Therefore, the financial goals of Studebaker cannot be considered as effective.
The given return has been calculated by assuming 6 percent return on the total amount invested $550,000. This return is calculated on the basis of accumulation. With the help of this, total accumulated value of the single insurance premium has been calculated.
The below table shows the annual repayment for the given 20 years The total mortgage amount is taken to be $705,000 mortgage and the rate of interest is 9 percent. The annual repayment has been shown with calculations of every year
Date |
Interest |
Principal |
Balance |
2018 |
$42,075 |
$8,670 |
$696,330 |
Jan, 2019 |
$5,222 |
$1,121 |
$695,210 |
Feb, 2019 |
$5,214 |
$1,129 |
$694,081 |
Mar, 2019 |
$5,206 |
$1,137 |
$692,943 |
Apr, 2019 |
$5,197 |
$1,146 |
$691,797 |
May, 2019 |
$5,188 |
$1,155 |
$690,643 |
Jun, 2019 |
$5,180 |
$1,163 |
$689,480 |
Jul, 2019 |
$5,171 |
$1,172 |
$688,308 |
Aug, 2019 |
$5,162 |
$1,181 |
$687,127 |
Sep, 2019 |
$5,153 |
$1,190 |
$685,937 |
Oct, 2019 |
$5,145 |
$1,199 |
$684,739 |
Nov, 2019 |
$5,136 |
$1,208 |
$683,531 |
Dec, 2019 |
$5,126 |
$1,217 |
$682,315 |
2019 |
$62,101 |
$14,016 |
$682,315 |
Jan, 2020 |
$5,117 |
$1,226 |
$681,089 |
Feb, 2020 |
$5,108 |
$1,235 |
$679,854 |
Mar, 2020 |
$5,099 |
$1,244 |
$678,610 |
Apr, 2020 |
$5,090 |
$1,253 |
$677,356 |
May, 2020 |
$5,080 |
$1,263 |
$676,093 |
Jun, 2020 |
$5,071 |
$1,272 |
$674,821 |
Jul, 2020 |
$5,061 |
$1,282 |
$673,539 |
Aug, 2020 |
$5,052 |
$1,292 |
$672,248 |
Sep, 2020 |
$5,042 |
$1,301 |
$670,946 |
Oct, 2020 |
$5,032 |
$1,311 |
$669,635 |
Nov, 2020 |
$5,022 |
$1,321 |
$668,315 |
Dec, 2020 |
$5,012 |
$1,331 |
$666,984 |
2020 |
$60,786 |
$15,331 |
$666,984 |
Jan, 2021 |
$5,002 |
$1,341 |
$665,643 |
Feb, 2021 |
$4,992 |
$1,351 |
$664,292 |
Mar, 2021 |
$4,982 |
$1,361 |
$662,932 |
Apr, 2021 |
$4,972 |
$1,371 |
$661,561 |
May, 2021 |
$4,962 |
$1,381 |
$660,179 |
Jun, 2021 |
$4,951 |
$1,392 |
$658,787 |
Jul, 2021 |
$4,941 |
$1,402 |
$657,385 |
Aug, 2021 |
$4,930 |
$1,413 |
$655,973 |
Sep, 2021 |
$4,920 |
$1,423 |
$654,549 |
Oct, 2021 |
$4,909 |
$1,434 |
$653,115 |
Nov, 2021 |
$4,898 |
$1,445 |
$651,671 |
Dec, 2021 |
$4,888 |
$1,456 |
$650,215 |
2021 |
$59,348 |
$16,769 |
$650,215 |
Jan, 2022 |
$4,877 |
$1,466 |
$648,749 |
Feb, 2022 |
$4,866 |
$1,477 |
$647,271 |
Mar, 2022 |
$4,855 |
$1,489 |
$645,783 |
Apr, 2022 |
$4,843 |
$1,500 |
$644,283 |
May, 2022 |
$4,832 |
$1,511 |
$642,772 |
Jun, 2022 |
$4,821 |
$1,522 |
$641,250 |
Jul, 2022 |
$4,809 |
$1,534 |
$639,716 |
Aug, 2022 |
$4,798 |
$1,545 |
$638,171 |
Sep, 2022 |
$4,786 |
$1,557 |
$636,614 |
Oct, 2022 |
$4,775 |
$1,568 |
$635,046 |
Nov, 2022 |
$4,763 |
$1,580 |
$633,465 |
Dec, 2022 |
$4,751 |
$1,592 |
$631,873 |
2022 |
$57,775 |
$18,342 |
$631,873 |
Jan, 2023 |
$4,739 |
$1,604 |
$630,269 |
Feb, 2023 |
$4,727 |
$1,616 |
$628,653 |
Mar, 2023 |
$4,715 |
$1,628 |
$627,025 |
Apr, 2023 |
$4,703 |
$1,640 |
$625,385 |
May, 2023 |
$4,690 |
$1,653 |
$623,732 |
Jun, 2023 |
$4,678 |
$1,665 |
$622,067 |
Jul, 2023 |
$4,666 |
$1,678 |
$620,389 |
Aug, 2023 |
$4,653 |
$1,690 |
$618,699 |
Sep, 2023 |
$4,640 |
$1,703 |
$616,996 |
Oct, 2023 |
$4,627 |
$1,716 |
$615,281 |
Nov, 2023 |
$4,615 |
$1,728 |
$613,552 |
Dec, 2023 |
$4,602 |
$1,741 |
$611,811 |
2023 |
$56,054 |
$20,062 |
$611,811 |
Jan, 2024 |
$4,589 |
$1,754 |
$610,056 |
Feb, 2024 |
$4,575 |
$1,768 |
$608,289 |
Mar, 2024 |
$4,562 |
$1,781 |
$606,508 |
Apr, 2024 |
$4,549 |
$1,794 |
$604,714 |
May, 2024 |
$4,535 |
$1,808 |
$602,906 |
Jun, 2024 |
$4,522 |
$1,821 |
$601,085 |
Jul, 2024 |
$4,508 |
$1,835 |
$599,250 |
Aug, 2024 |
$4,494 |
$1,849 |
$597,401 |
Sep, 2024 |
$4,481 |
$1,863 |
$595,538 |
Oct, 2024 |
$4,467 |
$1,877 |
$593,662 |
Nov, 2024 |
$4,452 |
$1,891 |
$591,771 |
Dec, 2024 |
$4,438 |
$1,905 |
$589,867 |
2024 |
$54,172 |
$21,944 |
$589,867 |
Jan, 2025 |
$4,424 |
$1,919 |
$587,947 |
Feb, 2025 |
$4,410 |
$1,933 |
$586,014 |
Mar, 2025 |
$4,395 |
$1,948 |
$584,066 |
Apr, 2025 |
$4,380 |
$1,963 |
$582,103 |
May, 2025 |
$4,366 |
$1,977 |
$580,126 |
Jun, 2025 |
$4,351 |
$1,992 |
$578,134 |
Jul, 2025 |
$4,336 |
$2,007 |
$576,127 |
Aug, 2025 |
$4,321 |
$2,022 |
$574,105 |
Sep, 2025 |
$4,306 |
$2,037 |
$572,068 |
Oct, 2025 |
$4,291 |
$2,053 |
$570,015 |
Nov, 2025 |
$4,275 |
$2,068 |
$567,947 |
Dec, 2025 |
$4,260 |
$2,083 |
$565,864 |
2025 |
$52,114 |
$24,003 |
$565,864 |
Jan, 2026 |
$4,244 |
$2,099 |
$563,765 |
Feb, 2026 |
$4,228 |
$2,115 |
$561,650 |
Mar, 2026 |
$4,212 |
$2,131 |
$559,519 |
Apr, 2026 |
$4,196 |
$2,147 |
$557,372 |
May, 2026 |
$4,180 |
$2,163 |
$555,210 |
Jun, 2026 |
$4,164 |
$2,179 |
$553,031 |
Jul, 2026 |
$4,148 |
$2,195 |
$550,835 |
Aug, 2026 |
$4,131 |
$2,212 |
$548,623 |
Sep, 2026 |
$4,115 |
$2,228 |
$546,395 |
Oct, 2026 |
$4,098 |
$2,245 |
$544,150 |
Nov, 2026 |
$4,081 |
$2,262 |
$541,888 |
Dec, 2026 |
$4,064 |
$2,279 |
$539,609 |
2026 |
$49,862 |
$26,255 |
$539,609 |
Jan, 2027 |
$4,047 |
$2,296 |
$537,313 |
Feb, 2027 |
$4,030 |
$2,313 |
$535,000 |
Mar, 2027 |
$4,012 |
$2,331 |
$532,669 |
Apr, 2027 |
$3,995 |
$2,348 |
$530,321 |
May, 2027 |
$3,977 |
$2,366 |
$527,956 |
Jun, 2027 |
$3,960 |
$2,383 |
$525,572 |
Jul, 2027 |
$3,942 |
$2,401 |
$523,171 |
Aug, 2027 |
$3,924 |
$2,419 |
$520,752 |
Sep, 2027 |
$3,906 |
$2,437 |
$518,314 |
Oct, 2027 |
$3,887 |
$2,456 |
$515,858 |
Nov, 2027 |
$3,869 |
$2,474 |
$513,384 |
Dec, 2027 |
$3,850 |
$2,493 |
$510,892 |
2027 |
$47,399 |
$28,717 |
$510,892 |
Jan, 2028 |
$3,832 |
$2,511 |
$508,380 |
Feb, 2028 |
$3,813 |
$2,530 |
$505,850 |
Mar, 2028 |
$3,794 |
$2,549 |
$503,301 |
Apr, 2028 |
$3,775 |
$2,568 |
$500,733 |
May, 2028 |
$3,755 |
$2,588 |
$498,145 |
Jun, 2028 |
$3,736 |
$2,607 |
$495,538 |
Jul, 2028 |
$3,717 |
$2,627 |
$492,911 |
Aug, 2028 |
$3,697 |
$2,646 |
$490,265 |
Sep, 2028 |
$3,677 |
$2,666 |
$487,599 |
Oct, 2028 |
$3,657 |
$2,686 |
$484,913 |
Nov, 2028 |
$3,637 |
$2,706 |
$482,207 |
Dec, 2028 |
$3,617 |
$2,727 |
$479,480 |
2028 |
$44,706 |
$31,411 |
$479,480 |
Jan, 2029 |
$3,596 |
$2,747 |
$476,733 |
Feb, 2029 |
$3,576 |
$2,768 |
$473,966 |
Mar, 2029 |
$3,555 |
$2,788 |
$471,177 |
Apr, 2029 |
$3,534 |
$2,809 |
$468,368 |
May, 2029 |
$3,513 |
$2,830 |
$465,538 |
Jun, 2029 |
$3,492 |
$2,852 |
$462,686 |
Jul, 2029 |
$3,470 |
$2,873 |
$459,813 |
Aug, 2029 |
$3,449 |
$2,894 |
$456,919 |
Sep, 2029 |
$3,427 |
$2,916 |
$454,003 |
Oct, 2029 |
$3,405 |
$2,938 |
$451,065 |
Nov, 2029 |
$3,383 |
$2,960 |
$448,105 |
Dec, 2029 |
$3,361 |
$2,982 |
$445,122 |
2029 |
$41,759 |
$34,358 |
$445,122 |
Jan, 2030 |
$3,338 |
$3,005 |
$442,118 |
Feb, 2030 |
$3,316 |
$3,027 |
$439,091 |
Mar, 2030 |
$3,293 |
$3,050 |
$436,041 |
Apr, 2030 |
$3,270 |
$3,073 |
$432,968 |
May, 2030 |
$3,247 |
$3,096 |
$429,872 |
Jun, 2030 |
$3,224 |
$3,119 |
$426,753 |
Jul, 2030 |
$3,201 |
$3,142 |
$423,611 |
Aug, 2030 |
$3,177 |
$3,166 |
$420,445 |
Sep, 2030 |
$3,153 |
$3,190 |
$417,255 |
Oct, 2030 |
$3,129 |
$3,214 |
$414,041 |
Nov, 2030 |
$3,105 |
$3,238 |
$410,804 |
Dec, 2030 |
$3,081 |
$3,262 |
$407,541 |
2030 |
$38,536 |
$37,581 |
$407,541 |
Jan, 2031 |
$3,057 |
$3,287 |
$404,255 |
Feb, 2031 |
$3,032 |
$3,311 |
$400,944 |
Mar, 2031 |
$3,007 |
$3,336 |
$397,608 |
Apr, 2031 |
$2,982 |
$3,361 |
$394,247 |
May, 2031 |
$2,957 |
$3,386 |
$390,861 |
Jun, 2031 |
$2,931 |
$3,412 |
$387,449 |
Jul, 2031 |
$2,906 |
$3,437 |
$384,012 |
Aug, 2031 |
$2,880 |
$3,463 |
$380,549 |
Sep, 2031 |
$2,854 |
$3,489 |
$377,060 |
Oct, 2031 |
$2,828 |
$3,515 |
$373,545 |
Nov, 2031 |
$2,802 |
$3,541 |
$370,003 |
Dec, 2031 |
$2,775 |
$3,568 |
$366,435 |
2031 |
$35,011 |
$41,106 |
$366,435 |
Jan, 2032 |
$2,748 |
$3,595 |
$362,840 |
Feb, 2032 |
$2,721 |
$3,622 |
$359,219 |
Mar, 2032 |
$2,694 |
$3,649 |
$355,570 |
Apr, 2032 |
$2,667 |
$3,676 |
$351,893 |
May, 2032 |
$2,639 |
$3,704 |
$348,190 |
Jun, 2032 |
$2,611 |
$3,732 |
$344,458 |
Jul, 2032 |
$2,583 |
$3,760 |
$340,698 |
Aug, 2032 |
$2,555 |
$3,788 |
$336,910 |
Sep, 2032 |
$2,527 |
$3,816 |
$333,094 |
Oct, 2032 |
$2,498 |
$3,845 |
$329,249 |
Nov, 2032 |
$2,469 |
$3,874 |
$325,376 |
Dec, 2032 |
$2,440 |
$3,903 |
$321,473 |
2032 |
$31,154 |
$44,962 |
$321,473 |
Jan, 2033 |
$2,411 |
$3,932 |
$317,541 |
Feb, 2033 |
$2,382 |
$3,962 |
$313,579 |
Mar, 2033 |
$2,352 |
$3,991 |
$309,588 |
Apr, 2033 |
$2,322 |
$4,021 |
$305,567 |
May, 2033 |
$2,292 |
$4,051 |
$301,516 |
Jun, 2033 |
$2,261 |
$4,082 |
$297,434 |
Jul, 2033 |
$2,231 |
$4,112 |
$293,322 |
Aug, 2033 |
$2,200 |
$4,143 |
$289,178 |
Sep, 2033 |
$2,169 |
$4,174 |
$285,004 |
Oct, 2033 |
$2,138 |
$4,206 |
$280,799 |
Nov, 2033 |
$2,106 |
$4,237 |
$276,562 |
Dec, 2033 |
$2,074 |
$4,269 |
$272,293 |
2033 |
$26,937 |
$49,180 |
$272,293 |
Jan, 2034 |
$2,042 |
$4,301 |
$267,992 |
Feb, 2034 |
$2,010 |
$4,333 |
$263,659 |
Mar, 2034 |
$1,977 |
$4,366 |
$259,293 |
Apr, 2034 |
$1,945 |
$4,398 |
$254,895 |
May, 2034 |
$1,912 |
$4,431 |
$250,463 |
Jun, 2034 |
$1,878 |
$4,465 |
$245,999 |
Jul, 2034 |
$1,845 |
$4,498 |
$241,501 |
Aug, 2034 |
$1,811 |
$4,532 |
$236,969 |
Sep, 2034 |
$1,777 |
$4,566 |
$232,403 |
Oct, 2034 |
$1,743 |
$4,600 |
$227,803 |
Nov, 2034 |
$1,709 |
$4,635 |
$223,169 |
Dec, 2034 |
$1,674 |
$4,669 |
$218,499 |
2034 |
$22,323 |
$53,794 |
$218,499 |
Jan, 2035 |
$1,639 |
$4,704 |
$213,795 |
Feb, 2035 |
$1,603 |
$4,740 |
$209,055 |
Mar, 2035 |
$1,568 |
$4,775 |
$204,280 |
Apr, 2035 |
$1,532 |
$4,811 |
$199,469 |
May, 2035 |
$1,496 |
$4,847 |
$194,622 |
Jun, 2035 |
$1,460 |
$4,883 |
$189,739 |
Jul, 2035 |
$1,423 |
$4,920 |
$184,819 |
Aug, 2035 |
$1,386 |
$4,957 |
$179,862 |
Sep, 2035 |
$1,349 |
$4,994 |
$174,868 |
Oct, 2035 |
$1,312 |
$5,032 |
$169,836 |
Nov, 2035 |
$1,274 |
$5,069 |
$164,767 |
Dec, 2035 |
$1,236 |
$5,107 |
$159,660 |
2035 |
$17,277 |
$58,840 |
$159,660 |
Jan, 2036 |
$1,197 |
$5,146 |
$154,514 |
Feb, 2036 |
$1,159 |
$5,184 |
$149,330 |
Mar, 2036 |
$1,120 |
$5,223 |
$144,107 |
Apr, 2036 |
$1,081 |
$5,262 |
$138,844 |
May, 2036 |
$1,041 |
$5,302 |
$133,543 |
Jun, 2036 |
$1,002 |
$5,341 |
$128,201 |
Jul, 2036 |
$962 |
$5,382 |
$122,820 |
Aug, 2036 |
$921 |
$5,422 |
$117,398 |
Sep, 2036 |
$880 |
$5,463 |
$111,935 |
Oct, 2036 |
$840 |
$5,504 |
$106,431 |
Nov, 2036 |
$798 |
$5,545 |
$100,887 |
Dec, 2036 |
$757 |
$5,586 |
$95,300 |
2036 |
$11,758 |
$64,359 |
$95,300 |
Jan, 2037 |
$715 |
$5,628 |
$89,672 |
Feb, 2037 |
$673 |
$5,671 |
$84,001 |
Mar, 2037 |
$630 |
$5,713 |
$78,288 |
Apr, 2037 |
$587 |
$5,756 |
$72,532 |
May, 2037 |
$544 |
$5,799 |
$66,733 |
Jun, 2037 |
$501 |
$5,843 |
$60,891 |
Jul, 2037 |
$457 |
$5,886 |
$55,004 |
Aug, 2037 |
$413 |
$5,931 |
$49,074 |
Sep, 2037 |
$368 |
$5,975 |
$43,099 |
Oct, 2037 |
$323 |
$6,020 |
$37,079 |
Nov, 2037 |
$278 |
$6,065 |
$31,014 |
Dec, 2037 |
$233 |
$6,110 |
$24,904 |
2037 |
$5,720 |
$70,397 |
$24,904 |
Jan, 2038 |
$187 |
$6,156 |
$18,747 |
Feb, 2038 |
$141 |
$6,202 |
$12,545 |
Mar, 2038 |
$94 |
$6,249 |
$6,296 |
Apr, 2038 |
$47 |
$6,296 |
$0 |
2038 |
$469 |
$24,904 |
$0 |
In this case, 9 percent mortgage has been taken to find out the loan balance for year 19 and 20. In this case, the 1st year or the base year has been assumed as 2018. It has been evaluated that at the end of 20th year, the amount will be zero, while at the end of 19th Year, the amount will be $474,265 and balance after 20th year will be $447,804.
Date |
Interest |
Principal |
Balance |
Jan, 2018 |
$5,288 |
$385 |
$704,615 |
Feb, 2018 |
$5,285 |
$388 |
$704,227 |
Mar, 2018 |
$5,282 |
$391 |
$703,836 |
Apr, 2018 |
$5,279 |
$394 |
$703,442 |
May, 2018 |
$5,276 |
$397 |
$703,045 |
Jun, 2018 |
$5,273 |
$400 |
$702,646 |
Jul, 2018 |
$5,270 |
$403 |
$702,243 |
Aug, 2018 |
$5,267 |
$406 |
$701,837 |
Sep, 2018 |
$5,264 |
$409 |
$701,428 |
Oct, 2018 |
$5,261 |
$412 |
$701,017 |
Nov, 2018 |
$5,258 |
$415 |
$700,602 |
Dec, 2018 |
$5,255 |
$418 |
$700,183 |
2018 |
$63,255 |
$4,817 |
$700,183 |
Jan, 2019 |
$5,251 |
$421 |
$699,762 |
Feb, 2019 |
$5,248 |
$424 |
$699,338 |
Mar, 2019 |
$5,245 |
$428 |
$698,910 |
Apr, 2019 |
$5,242 |
$431 |
$698,480 |
May, 2019 |
$5,239 |
$434 |
$698,046 |
Jun, 2019 |
$5,235 |
$437 |
$697,608 |
Jul, 2019 |
$5,232 |
$441 |
$697,168 |
Aug, 2019 |
$5,229 |
$444 |
$696,724 |
Sep, 2019 |
$5,225 |
$447 |
$696,277 |
Oct, 2019 |
$5,222 |
$451 |
$695,826 |
Nov, 2019 |
$5,219 |
$454 |
$695,372 |
Dec, 2019 |
$5,215 |
$457 |
$694,915 |
2019 |
$62,803 |
$5,268 |
$694,915 |
Jan, 2020 |
$5,212 |
$461 |
$694,454 |
Feb, 2020 |
$5,208 |
$464 |
$693,990 |
Mar, 2020 |
$5,205 |
$468 |
$693,523 |
Apr, 2020 |
$5,201 |
$471 |
$693,051 |
May, 2020 |
$5,198 |
$475 |
$692,577 |
Jun, 2020 |
$5,194 |
$478 |
$692,098 |
Jul, 2020 |
$5,191 |
$482 |
$691,617 |
Aug, 2020 |
$5,187 |
$485 |
$691,131 |
Sep, 2020 |
$5,183 |
$489 |
$690,642 |
Oct, 2020 |
$5,180 |
$493 |
$690,149 |
Nov, 2020 |
$5,176 |
$496 |
$689,653 |
Dec, 2020 |
$5,172 |
$500 |
$689,153 |
2020 |
$62,309 |
$5,763 |
$689,153 |
Jan, 2021 |
$5,169 |
$504 |
$688,649 |
Feb, 2021 |
$5,165 |
$508 |
$688,141 |
Mar, 2021 |
$5,161 |
$512 |
$687,629 |
Apr, 2021 |
$5,157 |
$515 |
$687,114 |
May, 2021 |
$5,153 |
$519 |
$686,595 |
Jun, 2021 |
$5,149 |
$523 |
$686,072 |
Jul, 2021 |
$5,146 |
$527 |
$685,545 |
Aug, 2021 |
$5,142 |
$531 |
$685,014 |
Sep, 2021 |
$5,138 |
$535 |
$684,479 |
Oct, 2021 |
$5,134 |
$539 |
$683,940 |
Nov, 2021 |
$5,130 |
$543 |
$683,396 |
Dec, 2021 |
$5,125 |
$547 |
$682,849 |
2021 |
$61,768 |
$6,303 |
$682,849 |
Jan, 2022 |
$5,121 |
$551 |
$682,298 |
Feb, 2022 |
$5,117 |
$555 |
$681,743 |
Mar, 2022 |
$5,113 |
$560 |
$681,183 |
Apr, 2022 |
$5,109 |
$564 |
$680,620 |
May, 2022 |
$5,105 |
$568 |
$680,052 |
Jun, 2022 |
$5,100 |
$572 |
$679,479 |
Jul, 2022 |
$5,096 |
$576 |
$678,903 |
Aug, 2022 |
$5,092 |
$581 |
$678,322 |
Sep, 2022 |
$5,087 |
$585 |
$677,737 |
Oct, 2022 |
$5,083 |
$590 |
$677,147 |
Nov, 2022 |
$5,079 |
$594 |
$676,553 |
Dec, 2022 |
$5,074 |
$598 |
$675,955 |
2022 |
$61,177 |
$6,894 |
$675,955 |
Jan, 2023 |
$5,070 |
$603 |
$675,352 |
Feb, 2023 |
$5,065 |
$607 |
$674,745 |
Mar, 2023 |
$5,061 |
$612 |
$674,133 |
Apr, 2023 |
$5,056 |
$617 |
$673,516 |
May, 2023 |
$5,051 |
$621 |
$672,895 |
Jun, 2023 |
$5,047 |
$626 |
$672,269 |
Jul, 2023 |
$5,042 |
$631 |
$671,638 |
Aug, 2023 |
$5,037 |
$635 |
$671,003 |
Sep, 2023 |
$5,033 |
$640 |
$670,363 |
Oct, 2023 |
$5,028 |
$645 |
$669,718 |
Nov, 2023 |
$5,023 |
$650 |
$669,068 |
Dec, 2023 |
$5,018 |
$655 |
$668,414 |
2023 |
$60,530 |
$7,541 |
$668,414 |
Jan, 2024 |
$5,013 |
$659 |
$667,754 |
Feb, 2024 |
$5,008 |
$664 |
$667,090 |
Mar, 2024 |
$5,003 |
$669 |
$666,420 |
Apr, 2024 |
$4,998 |
$674 |
$665,746 |
May, 2024 |
$4,993 |
$679 |
$665,067 |
Jun, 2024 |
$4,988 |
$685 |
$664,382 |
Jul, 2024 |
$4,983 |
$690 |
$663,692 |
Aug, 2024 |
$4,978 |
$695 |
$662,997 |
Sep, 2024 |
$4,972 |
$700 |
$662,297 |
Oct, 2024 |
$4,967 |
$705 |
$661,592 |
Nov, 2024 |
$4,962 |
$711 |
$660,881 |
Dec, 2024 |
$4,957 |
$716 |
$660,165 |
2024 |
$59,822 |
$8,249 |
$660,165 |
Jan, 2025 |
$4,951 |
$721 |
$659,444 |
Feb, 2025 |
$4,946 |
$727 |
$658,717 |
Mar, 2025 |
$4,940 |
$732 |
$657,985 |
Apr, 2025 |
$4,935 |
$738 |
$657,247 |
May, 2025 |
$4,929 |
$743 |
$656,504 |
Jun, 2025 |
$4,924 |
$749 |
$655,755 |
Jul, 2025 |
$4,918 |
$754 |
$655,001 |
Aug, 2025 |
$4,913 |
$760 |
$654,241 |
Sep, 2025 |
$4,907 |
$766 |
$653,475 |
Oct, 2025 |
$4,901 |
$772 |
$652,703 |
Nov, 2025 |
$4,895 |
$777 |
$651,926 |
Dec, 2025 |
$4,889 |
$783 |
$651,143 |
2025 |
$59,049 |
$9,022 |
$651,143 |
Jan, 2026 |
$4,884 |
$789 |
$650,354 |
Feb, 2026 |
$4,878 |
$795 |
$649,559 |
Mar, 2026 |
$4,872 |
$801 |
$648,758 |
Apr, 2026 |
$4,866 |
$807 |
$647,951 |
May, 2026 |
$4,860 |
$813 |
$647,138 |
Jun, 2026 |
$4,854 |
$819 |
$646,319 |
Jul, 2026 |
$4,847 |
$825 |
$645,494 |
Aug, 2026 |
$4,841 |
$831 |
$644,663 |
Sep, 2026 |
$4,835 |
$838 |
$643,825 |
Oct, 2026 |
$4,829 |
$844 |
$642,981 |
Nov, 2026 |
$4,822 |
$850 |
$642,131 |
Dec, 2026 |
$4,816 |
$857 |
$641,274 |
2026 |
$58,202 |
$9,869 |
$641,274 |
Jan, 2027 |
$4,810 |
$863 |
$640,411 |
Feb, 2027 |
$4,803 |
$870 |
$639,542 |
Mar, 2027 |
$4,797 |
$876 |
$638,666 |
Apr, 2027 |
$4,790 |
$883 |
$637,783 |
May, 2027 |
$4,783 |
$889 |
$636,894 |
Jun, 2027 |
$4,777 |
$896 |
$635,998 |
Jul, 2027 |
$4,770 |
$903 |
$635,095 |
Aug, 2027 |
$4,763 |
$909 |
$634,186 |
Sep, 2027 |
$4,756 |
$916 |
$633,270 |
Oct, 2027 |
$4,750 |
$923 |
$632,347 |
Nov, 2027 |
$4,743 |
$930 |
$631,417 |
Dec, 2027 |
$4,736 |
$937 |
$630,480 |
2027 |
$57,277 |
$10,794 |
$630,480 |
Jan, 2028 |
$4,729 |
$944 |
$629,536 |
Feb, 2028 |
$4,722 |
$951 |
$628,585 |
Mar, 2028 |
$4,714 |
$958 |
$627,626 |
Apr, 2028 |
$4,707 |
$965 |
$626,661 |
May, 2028 |
$4,700 |
$973 |
$625,688 |
Jun, 2028 |
$4,693 |
$980 |
$624,708 |
Jul, 2028 |
$4,685 |
$987 |
$623,721 |
Aug, 2028 |
$4,678 |
$995 |
$622,727 |
Sep, 2028 |
$4,670 |
$1,002 |
$621,724 |
Oct, 2028 |
$4,663 |
$1,010 |
$620,715 |
Nov, 2028 |
$4,655 |
$1,017 |
$619,697 |
Dec, 2028 |
$4,648 |
$1,025 |
$618,673 |
2028 |
$56,264 |
$11,807 |
$618,673 |
Jan, 2029 |
$4,640 |
$1,033 |
$617,640 |
Feb, 2029 |
$4,632 |
$1,040 |
$616,600 |
Mar, 2029 |
$4,624 |
$1,048 |
$615,552 |
Apr, 2029 |
$4,617 |
$1,056 |
$614,496 |
May, 2029 |
$4,609 |
$1,064 |
$613,432 |
Jun, 2029 |
$4,601 |
$1,072 |
$612,360 |
Jul, 2029 |
$4,593 |
$1,080 |
$611,280 |
Aug, 2029 |
$4,585 |
$1,088 |
$610,192 |
Sep, 2029 |
$4,576 |
$1,096 |
$609,096 |
Oct, 2029 |
$4,568 |
$1,104 |
$607,992 |
Nov, 2029 |
$4,560 |
$1,113 |
$606,879 |
Dec, 2029 |
$4,552 |
$1,121 |
$605,758 |
2029 |
$55,156 |
$12,915 |
$605,758 |
Jan, 2030 |
$4,543 |
$1,129 |
$604,629 |
Feb, 2030 |
$4,535 |
$1,138 |
$603,491 |
Mar, 2030 |
$4,526 |
$1,146 |
$602,344 |
Apr, 2030 |
$4,518 |
$1,155 |
$601,189 |
May, 2030 |
$4,509 |
$1,164 |
$600,026 |
Jun, 2030 |
$4,500 |
$1,172 |
$598,853 |
Jul, 2030 |
$4,491 |
$1,181 |
$597,672 |
Aug, 2030 |
$4,483 |
$1,190 |
$596,482 |
Sep, 2030 |
$4,474 |
$1,199 |
$595,283 |
Oct, 2030 |
$4,465 |
$1,208 |
$594,075 |
Nov, 2030 |
$4,456 |
$1,217 |
$592,858 |
Dec, 2030 |
$4,446 |
$1,226 |
$591,632 |
2030 |
$53,945 |
$14,126 |
$591,632 |
Jan, 2031 |
$4,437 |
$1,235 |
$590,397 |
Feb, 2031 |
$4,428 |
$1,245 |
$589,152 |
Mar, 2031 |
$4,419 |
$1,254 |
$587,898 |
Apr, 2031 |
$4,409 |
$1,263 |
$586,635 |
May, 2031 |
$4,400 |
$1,273 |
$585,362 |
Jun, 2031 |
$4,390 |
$1,282 |
$584,079 |
Jul, 2031 |
$4,381 |
$1,292 |
$582,787 |
Aug, 2031 |
$4,371 |
$1,302 |
$581,486 |
Sep, 2031 |
$4,361 |
$1,311 |
$580,174 |
Oct, 2031 |
$4,351 |
$1,321 |
$578,853 |
Nov, 2031 |
$4,341 |
$1,331 |
$577,522 |
Dec, 2031 |
$4,331 |
$1,341 |
$576,181 |
2031 |
$52,620 |
$15,451 |
$576,181 |
Jan, 2032 |
$4,321 |
$1,351 |
$574,829 |
Feb, 2032 |
$4,311 |
$1,361 |
$573,468 |
Mar, 2032 |
$4,301 |
$1,372 |
$572,096 |
Apr, 2032 |
$4,291 |
$1,382 |
$570,715 |
May, 2032 |
$4,280 |
$1,392 |
$569,322 |
Jun, 2032 |
$4,270 |
$1,403 |
$567,920 |
Jul, 2032 |
$4,259 |
$1,413 |
$566,506 |
Aug, 2032 |
$4,249 |
$1,424 |
$565,083 |
Sep, 2032 |
$4,238 |
$1,434 |
$563,648 |
Oct, 2032 |
$4,227 |
$1,445 |
$562,203 |
Nov, 2032 |
$4,217 |
$1,456 |
$560,747 |
Dec, 2032 |
$4,206 |
$1,467 |
$559,280 |
2032 |
$51,170 |
$16,901 |
$559,280 |
Jan, 2033 |
$4,195 |
$1,478 |
$557,802 |
Feb, 2033 |
$4,184 |
$1,489 |
$556,313 |
Mar, 2033 |
$4,172 |
$1,500 |
$554,813 |
Apr, 2033 |
$4,161 |
$1,511 |
$553,301 |
May, 2033 |
$4,150 |
$1,523 |
$551,778 |
Jun, 2033 |
$4,138 |
$1,534 |
$550,244 |
Jul, 2033 |
$4,127 |
$1,546 |
$548,698 |
Aug, 2033 |
$4,115 |
$1,557 |
$547,141 |
Sep, 2033 |
$4,104 |
$1,569 |
$545,572 |
Oct, 2033 |
$4,092 |
$1,581 |
$543,991 |
Nov, 2033 |
$4,080 |
$1,593 |
$542,398 |
Dec, 2033 |
$4,068 |
$1,605 |
$540,794 |
2033 |
$49,585 |
$18,486 |
$540,794 |
Jan, 2034 |
$4,056 |
$1,617 |
$539,177 |
Feb, 2034 |
$4,044 |
$1,629 |
$537,548 |
Mar, 2034 |
$4,032 |
$1,641 |
$535,907 |
Apr, 2034 |
$4,019 |
$1,653 |
$534,254 |
May, 2034 |
$4,007 |
$1,666 |
$532,589 |
Jun, 2034 |
$3,994 |
$1,678 |
$530,910 |
Jul, 2034 |
$3,982 |
$1,691 |
$529,220 |
Aug, 2034 |
$3,969 |
$1,703 |
$527,516 |
Sep, 2034 |
$3,956 |
$1,716 |
$525,800 |
Oct, 2034 |
$3,943 |
$1,729 |
$524,071 |
Nov, 2034 |
$3,931 |
$1,742 |
$522,329 |
Dec, 2034 |
$3,917 |
$1,755 |
$520,574 |
2034 |
$47,851 |
$20,220 |
$520,574 |
Jan, 2035 |
$3,904 |
$1,768 |
$518,805 |
Feb, 2035 |
$3,891 |
$1,782 |
$517,024 |
Mar, 2035 |
$3,878 |
$1,795 |
$515,229 |
Apr, 2035 |
$3,864 |
$1,808 |
$513,421 |
May, 2035 |
$3,851 |
$1,822 |
$511,599 |
Jun, 2035 |
$3,837 |
$1,836 |
$509,763 |
Jul, 2035 |
$3,823 |
$1,849 |
$507,914 |
Aug, 2035 |
$3,809 |
$1,863 |
$506,050 |
Sep, 2035 |
$3,795 |
$1,877 |
$504,173 |
Oct, 2035 |
$3,781 |
$1,891 |
$502,282 |
Nov, 2035 |
$3,767 |
$1,905 |
$500,376 |
Dec, 2035 |
$3,753 |
$1,920 |
$498,457 |
2035 |
$45,954 |
$22,117 |
$498,457 |
Jan, 2036 |
$3,738 |
$1,934 |
$496,522 |
Feb, 2036 |
$3,724 |
$1,949 |
$494,574 |
Mar, 2036 |
$3,709 |
$1,963 |
$492,611 |
Apr, 2036 |
$3,695 |
$1,978 |
$490,632 |
May, 2036 |
$3,680 |
$1,993 |
$488,640 |
Jun, 2036 |
$3,665 |
$2,008 |
$486,632 |
Jul, 2036 |
$3,650 |
$2,023 |
$484,609 |
Aug, 2036 |
$3,635 |
$2,038 |
$482,571 |
Sep, 2036 |
$3,619 |
$2,053 |
$480,518 |
Oct, 2036 |
$3,604 |
$2,069 |
$478,449 |
Nov, 2036 |
$3,588 |
$2,084 |
$476,365 |
Dec, 2036 |
$3,573 |
$2,100 |
$474,265 |
2036 |
$43,879 |
$24,192 |
$474,265 |
Jan, 2037 |
$3,557 |
$2,116 |
$472,149 |
Feb, 2037 |
$3,541 |
$2,131 |
$470,018 |
Mar, 2037 |
$3,525 |
$2,147 |
$467,870 |
Apr, 2037 |
$3,509 |
$2,164 |
$465,707 |
May, 2037 |
$3,493 |
$2,180 |
$463,527 |
Jun, 2037 |
$3,476 |
$2,196 |
$461,331 |
Jul, 2037 |
$3,460 |
$2,213 |
$459,118 |
Aug, 2037 |
$3,443 |
$2,229 |
$456,889 |
Sep, 2037 |
$3,427 |
$2,246 |
$454,643 |
Oct, 2037 |
$3,410 |
$2,263 |
$452,380 |
Nov, 2037 |
$3,393 |
$2,280 |
$450,101 |
Dec, 2037 |
$3,376 |
$2,297 |
$447,804 |
2037 |
$41,610 |
$26,461 |
$447,804 |
As per exhibit 3, it has been seen that accumulated funds after 20 years insurance policy will grew to $1,763,925. However, this amount does not reflect actual accumulated amount of investment. The total amount of annual cost of insurance is $26,145.31. The total costs incurred will be $522,906.22. Due to this reason, the debt position of Studebaker will be ($1,241,018.78) at the end of the 20th year. However, since the excess amount of $300000 is invested, then the figure of annual costs cannot be considered true. Apart from this, in that case, the annual costs will also increase. Therefore, the correct accumulated table is as follows:-
Increase in Accumulation Value |
|||||
Policy Payment |
Accumulation Value |
Annual Cost” |
Cumulative Cost |
||
End of Year |
|||||
0 |
$550,000 |
||||
1 |
$588,500 |
$38,500 |
$47,145.31 |
$47,145.31 |
|
2 |
$629,695 |
$41,195 |
$47,145.31 |
$94,290.62 |
|
3 |
$673,774 |
$44,079 |
$47,145.31 |
$141,435.93 |
|
4 |
$720,938 |
$47,164 |
$47,145.31 |
$188,581.24 |
|
5 |
$771,403 |
$50,466 |
$47,145.31 |
$235,726.55 |
|
6 |
$825,402 |
$53,998 |
$47,145.31 |
$282,871.86 |
|
7 |
$883,180 |
$57,778 |
$47,145.31 |
$330,017.17 |
|
8 |
$945,002 |
$61,823 |
$47,145.31 |
$377,162.48 |
|
9 |
$1,011,153 |
$66,150 |
$47,145.31 |
$424,307.79 |
|
10 |
$1,081,933 |
$70,781 |
$47,145.31 |
$471,453.10 |
|
11 |
$1,157,669 |
$75,735 |
$47,145.31 |
$518,598.41 |
|
12 |
$1,238,705 |
$81,037 |
$47,145.31 |
$565,743.72 |
|
13 |
$1,325,415 |
$86,709 |
$47,145.31 |
$612,889.03 |
|
14 |
$1,418,194 |
$92,779 |
$47,145.31 |
$660,034.34 |
|
15 |
$1,517,467 |
$99,274 |
$47,145.31 |
$707,179.65 |
|
16 |
$1,623,690 |
$106,223 |
$47,145.31 |
$754,324.96 |
|
17 |
$1,737,348 |
$113,658 |
$47,145.31 |
$801,470.27 |
|
18 |
$1,858,963 |
$121,614 |
$47,145.31 |
$848,615.58 |
|
19 |
$1,989,090 |
$130,127 |
$47,145.31 |
$895,760.89 |
|
20 |
$2,128,326 |
$139,236 |
$47,145.31 |
$942,906.20 |
Types of discounting rates
Therefore, from the above table, it can be inferred that the excess amount earned is $1,578,326 and the considering the costs, the total accumulated funds earned is $635,420.25.
Excess amount |
$1,578,326 |
Fund Value less costs |
$635,420.25 |
However, considering the hidden costs, the net present value is coming to be ($8,723.59), which is negative.
- If the excess $300,000 is invested, then the calculation of the accumulated value can be evaluated with the help of the following table:-
Increase in Accumulation Value |
|||
Policy Payment |
Accumulation Value |
||
End of Year |
|||
0 |
$300,000 |
||
1 |
$321,000 |
$21,000 |
|
2 |
$343,470 |
$22,470 |
|
3 |
$367,513 |
$24,043 |
|
4 |
$393,239 |
$25,726 |
|
5 |
$420,766 |
$27,527 |
|
6 |
$450,219 |
$29,454 |
|
7 |
$481,734 |
$31,515 |
|
8 |
$515,456 |
$33,721 |
|
9 |
$551,538 |
$36,082 |
|
10 |
$590,145 |
$38,608 |
|
11 |
$631,456 |
$41,310 |
|
12 |
$675,657 |
$44,202 |
|
13 |
$722,954 |
$47,296 |
|
14 |
$773,560 |
$50,607 |
|
15 |
$827,709 |
$54,149 |
|
16 |
$885,649 |
$57,940 |
|
17 |
$947,645 |
$61,995 |
|
18 |
$1,013,980 |
$66,335 |
|
19 |
$1,084,958 |
$70,979 |
|
20 |
$1,160,905 |
$75,947 |
From the above table, it can be inferred the total accumulated value will be $1,160,905 and the excess amount earned will be $860,905 and the Net Present Value will be $52,323.04.
The total amount of Accumulated fund by placing $26,145.31in 8 percent for 20 years can be evaluated with the help of the following table:-
Increase in Accumulation Value |
|||
Policy Payment |
Accumulation Value |
||
End of Year |
|||
0 |
26,145.31 |
||
1 |
$27,975 |
$1,830 |
|
2 |
$29,934 |
$1,958 |
|
3 |
$32,029 |
$2,095 |
|
4 |
$34,271 |
$2,242 |
|
5 |
$36,670 |
$2,399 |
|
6 |
$39,237 |
$2,567 |
|
7 |
$41,984 |
$2,747 |
|
8 |
$44,923 |
$2,939 |
|
9 |
$48,067 |
$3,145 |
|
10 |
$51,432 |
$3,365 |
|
11 |
$55,032 |
$3,600 |
|
12 |
$58,884 |
$3,852 |
|
13 |
$63,006 |
$4,122 |
|
14 |
$67,417 |
$4,410 |
|
15 |
$72,136 |
$4,719 |
|
16 |
$77,185 |
$5,050 |
|
17 |
$82,588 |
$5,403 |
|
18 |
$88,369 |
$5,781 |
|
19 |
$94,555 |
$6,186 |
|
20 |
$101,174 |
$6,619 |
The total amount of accumulate fund will be $101,174 and total amount of increase value will be $75,028.79
If 7 percent return is assumed to be earned, in that case, total accumulated value will be $2,128,326. Apart from this, the exact amount of increase in accumulated value will be $139,236.
Increase in Accumulation Value |
|||||
Policy Payment |
Accumulation Value |
Annual Cost” |
Cumulative Cost |
||
End of Year |
|||||
0 |
$550,000 |
||||
1 |
$588,500 |
$38,500 |
$26,145.31 |
$26,145.31 |
|
2 |
$629,695 |
$41,195 |
$26,145.31 |
$52,290.62 |
|
3 |
$673,774 |
$44,079 |
$26,145.31 |
$78,435.93 |
|
4 |
$720,938 |
$47,164 |
$26,145.31 |
$104,581.24 |
|
5 |
$771,403 |
$50,466 |
$26,145.31 |
$130,726.56 |
|
6 |
$825,402 |
$53,998 |
$26,145.31 |
$156,871.87 |
|
7 |
$883,180 |
$57,778 |
$26,145.31 |
$183,017.18 |
|
8 |
$945,002 |
$61,823 |
$26,145.31 |
$209,162.49 |
|
9 |
$1,011,153 |
$66,150 |
$26,145.31 |
$235,307.80 |
|
10 |
$1,081,933 |
$70,781 |
$26,145.31 |
$261,453.11 |
|
11 |
$1,157,669 |
$75,735 |
$26,145.31 |
$287,598.42 |
|
12 |
$1,238,705 |
$81,037 |
$26,145.31 |
$313,743.73 |
|
13 |
$1,325,415 |
$86,709 |
$26,145.31 |
$339,889.04 |
|
14 |
$1,418,194 |
$92,779 |
$26,145.31 |
$366,034.36 |
|
15 |
$1,517,467 |
$99,274 |
$26,145.31 |
$392,179.67 |
|
16 |
$1,623,690 |
$106,223 |
$26,145.31 |
$418,324.98 |
|
17 |
$1,737,348 |
$113,658 |
$26,145.31 |
$444,470.29 |
|
18 |
$1,858,963 |
$121,614 |
$26,145.31 |
$470,615.60 |
|
19 |
$1,989,090 |
$130,127 |
$26,145.31 |
$496,760.91 |
|
20 |
$2,128,326 |
$139,236 |
$26,145.31 |
$522,906.22 |
|
Net present Value |
$158,529.24 |
From the above analysis, it can be inferred that single-premium life insurance policy is an unattractive investment for Studebaker. There are several reasons behind it. Firstly, if the excess $300,000 is invested into the insurance policy, then the total annual costs will increase to $47,145.31. In that case, the total savings of Studebaker at the end of 20 years will be $635,420.25. On the other hand, if the excess amount of $300,000 is invested, then the excess of accumulated value will be more than which is $860,905.
Increase in Accumulation Value |
||||||
Policy Payment |
Accumulation Value |
Annual Cost” |
Cumulative Cost |
|||
End of Year |
||||||
0 |
$300,000 |
|||||
1 |
$324,000 |
$24,000 |
$26,145.31 |
$26,145.31 |
($2,145.31) |
|
2 |
$346,680 |
$22,680 |
$26,145.31 |
$52,290.62 |
($3,465.31) |
|
3 |
$370,948 |
$24,268 |
$26,145.31 |
$78,435.93 |
($1,877.71) |
|
4 |
$396,914 |
$25,966 |
$26,145.31 |
$104,581.24 |
($178.98) |
|
5 |
$424,698 |
$27,784 |
$26,145.31 |
$130,726.56 |
$1,638.67 |
|
6 |
$454,427 |
$29,729 |
$26,145.31 |
$156,871.87 |
$3,583.54 |
|
7 |
$486,237 |
$31,810 |
$26,145.31 |
$183,017.18 |
$5,664.56 |
|
8 |
$520,273 |
$34,037 |
$26,145.31 |
$209,162.49 |
$7,891.25 |
|
9 |
$556,692 |
$36,419 |
$26,145.31 |
$235,307.80 |
$10,273.81 |
|
10 |
$595,661 |
$38,968 |
$26,145.31 |
$261,453.11 |
$12,823.15 |
|
11 |
$637,357 |
$41,696 |
$26,145.31 |
$287,598.42 |
$15,550.94 |
|
12 |
$681,972 |
$44,615 |
$26,145.31 |
$313,743.73 |
$18,469.68 |
|
13 |
$729,710 |
$47,738 |
$26,145.31 |
$339,889.04 |
$21,592.73 |
|
14 |
$780,790 |
$51,080 |
$26,145.31 |
$366,034.36 |
$24,934.40 |
|
15 |
$835,445 |
$54,655 |
$26,145.31 |
$392,179.67 |
$28,509.97 |
|
16 |
$893,926 |
$58,481 |
$26,145.31 |
$418,324.98 |
$32,335.84 |
|
17 |
$956,501 |
$62,575 |
$26,145.31 |
$444,470.29 |
$36,429.53 |
|
18 |
$1,023,456 |
$66,955 |
$26,145.31 |
$470,615.60 |
$40,809.76 |
|
19 |
$1,095,098 |
$71,642 |
$26,145.31 |
$496,760.91 |
$45,496.62 |
|
20 |
$1,171,755 |
$76,657 |
$26,145.31 |
$522,906.22 |
$50,511.55 |
|
21 |
$1,253,778 |
$82,023 |
$26,145.31 |
$522,906.22 |
$55,877.53 |
|
22 |
$1,341,542 |
$87,764 |
$26,145.31 |
$522,906.22 |
$61,619.13 |
|
23 |
$1,435,450 |
$93,908 |
$26,145.31 |
$522,906.22 |
$67,762.64 |
|
24 |
$1,535,932 |
$100,482 |
$26,145.31 |
$522,906.22 |
$74,336.20 |
|
25 |
$1,643,447 |
$107,515 |
$26,145.31 |
$522,906.22 |
$81,369.91 |
|
26 |
$1,758,488 |
$115,041 |
$26,145.31 |
$522,906.22 |
$88,895.97 |
|
27 |
$1,881,582 |
$123,094 |
$26,145.31 |
$522,906.22 |
$96,948.86 |
|
28 |
$2,013,293 |
$131,711 |
$26,145.31 |
$522,906.22 |
$105,565.45 |
|
29 |
$2,154,224 |
$140,931 |
$26,145.31 |
$522,906.22 |
$114,785.21 |
|
30 |
$2,305,019 |
$150,796 |
$26,145.31 |
$522,906.22 |
$124,650.34 |
|
Savings annually |
a |
$4,155.01 |
||||
Savings till 1-12 years |
b |
$10,387.53 |
From the above table, it can be inferred that, the total annual savings need to be $4,155.01. It has been seen that, the annual cost of insurance is fixed to $26,145.31. However, there is variable increase in accumulated value of the investment. Total increase of accumulated value is $150,796 and total annual costs is $522,906.22. Therefore, total savings needs to be $124,650.34. Therefore, per year savings will be coming to be $4,155.01.
The below table shows that the monthly payments on the new 30-year of $705,000.
Date |
Interest |
Principal |
Balance |
Jan, 2018 |
$5,720 |
$330 |
$704,670 |
Feb, 2018 |
$5,717 |
$333 |
$704,338 |
Mar, 2018 |
$5,715 |
$335 |
$704,002 |
Apr, 2018 |
$5,712 |
$338 |
$703,664 |
May, 2018 |
$5,709 |
$341 |
$703,324 |
Jun, 2018 |
$5,706 |
$343 |
$702,980 |
Jul, 2018 |
$5,704 |
$346 |
$702,634 |
Aug, 2018 |
$5,701 |
$349 |
$702,285 |
Sep, 2018 |
$5,698 |
$352 |
$701,933 |
Oct, 2018 |
$5,695 |
$355 |
$701,578 |
Nov, 2018 |
$5,692 |
$358 |
$701,220 |
Dec, 2018 |
$5,689 |
$361 |
$700,860 |
2018 |
$68,457 |
$4,140 |
$700,860 |
Jan, 2019 |
$5,686 |
$363 |
$700,496 |
Feb, 2019 |
$5,683 |
$366 |
$700,130 |
Mar, 2019 |
$5,680 |
$369 |
$699,760 |
Apr, 2019 |
$5,677 |
$372 |
$699,388 |
May, 2019 |
$5,674 |
$375 |
$699,013 |
Jun, 2019 |
$5,671 |
$378 |
$698,634 |
Jul, 2019 |
$5,668 |
$382 |
$698,253 |
Aug, 2019 |
$5,665 |
$385 |
$697,868 |
Sep, 2019 |
$5,662 |
$388 |
$697,480 |
Oct, 2019 |
$5,659 |
$391 |
$697,089 |
Nov, 2019 |
$5,656 |
$394 |
$696,695 |
Dec, 2019 |
$5,653 |
$397 |
$696,298 |
2019 |
$68,036 |
$4,562 |
$696,298 |
Jan, 2020 |
$5,649 |
$400 |
$695,898 |
Feb, 2020 |
$5,646 |
$404 |
$695,494 |
Mar, 2020 |
$5,643 |
$407 |
$695,087 |
Apr, 2020 |
$5,639 |
$410 |
$694,676 |
May, 2020 |
$5,636 |
$414 |
$694,263 |
Jun, 2020 |
$5,633 |
$417 |
$693,846 |
Jul, 2020 |
$5,629 |
$420 |
$693,425 |
Aug, 2020 |
$5,626 |
$424 |
$693,002 |
Sep, 2020 |
$5,623 |
$427 |
$692,574 |
Oct, 2020 |
$5,619 |
$431 |
$692,144 |
Nov, 2020 |
$5,616 |
$434 |
$691,709 |
Dec, 2020 |
$5,612 |
$438 |
$691,272 |
2020 |
$67,571 |
$5,026 |
$691,272 |
Jan, 2021 |
$5,609 |
$441 |
$690,830 |
Feb, 2021 |
$5,605 |
$445 |
$690,386 |
Mar, 2021 |
$5,601 |
$448 |
$689,937 |
Apr, 2021 |
$5,598 |
$452 |
$689,485 |
May, 2021 |
$5,594 |
$456 |
$689,029 |
Jun, 2021 |
$5,590 |
$459 |
$688,570 |
Jul, 2021 |
$5,587 |
$463 |
$688,107 |
Aug, 2021 |
$5,583 |
$467 |
$687,640 |
Sep, 2021 |
$5,579 |
$471 |
$687,169 |
Oct, 2021 |
$5,575 |
$475 |
$686,694 |
Nov, 2021 |
$5,571 |
$478 |
$686,216 |
Dec, 2021 |
$5,567 |
$482 |
$685,734 |
2021 |
$67,059 |
$5,538 |
$685,734 |
Jan, 2022 |
$5,564 |
$486 |
$685,247 |
Feb, 2022 |
$5,560 |
$490 |
$684,757 |
Mar, 2022 |
$5,556 |
$494 |
$684,263 |
Apr, 2022 |
$5,552 |
$498 |
$683,765 |
May, 2022 |
$5,548 |
$502 |
$683,263 |
Jun, 2022 |
$5,544 |
$506 |
$682,757 |
Jul, 2022 |
$5,539 |
$510 |
$682,246 |
Aug, 2022 |
$5,535 |
$515 |
$681,732 |
Sep, 2022 |
$5,531 |
$519 |
$681,213 |
Oct, 2022 |
$5,527 |
$523 |
$680,690 |
Nov, 2022 |
$5,523 |
$527 |
$680,163 |
Dec, 2022 |
$5,518 |
$531 |
$679,632 |
2022 |
$66,495 |
$6,102 |
$679,632 |
Jan, 2023 |
$5,514 |
$536 |
$679,096 |
Feb, 2023 |
$5,510 |
$540 |
$678,556 |
Mar, 2023 |
$5,505 |
$544 |
$678,011 |
Apr, 2023 |
$5,501 |
$549 |
$677,463 |
May, 2023 |
$5,496 |
$553 |
$676,909 |
Jun, 2023 |
$5,492 |
$558 |
$676,351 |
Jul, 2023 |
$5,487 |
$562 |
$675,789 |
Aug, 2023 |
$5,483 |
$567 |
$675,222 |
Sep, 2023 |
$5,478 |
$571 |
$674,651 |
Oct, 2023 |
$5,474 |
$576 |
$674,075 |
Nov, 2023 |
$5,469 |
$581 |
$673,494 |
Dec, 2023 |
$5,464 |
$586 |
$672,908 |
2023 |
$65,874 |
$6,723 |
$672,908 |
Jan, 2024 |
$5,460 |
$590 |
$672,318 |
Feb, 2024 |
$5,455 |
$595 |
$671,723 |
Mar, 2024 |
$5,450 |
$600 |
$671,123 |
Apr, 2024 |
$5,445 |
$605 |
$670,518 |
May, 2024 |
$5,440 |
$610 |
$669,909 |
Jun, 2024 |
$5,435 |
$615 |
$669,294 |
Jul, 2024 |
$5,430 |
$620 |
$668,675 |
Aug, 2024 |
$5,425 |
$625 |
$668,050 |
Sep, 2024 |
$5,420 |
$630 |
$667,420 |
Oct, 2024 |
$5,415 |
$635 |
$666,785 |
Nov, 2024 |
$5,410 |
$640 |
$666,145 |
Dec, 2024 |
$5,405 |
$645 |
$665,500 |
2024 |
$65,190 |
$7,408 |
$665,500 |
Jan, 2025 |
$5,399 |
$650 |
$664,850 |
Feb, 2025 |
$5,394 |
$656 |
$664,194 |
Mar, 2025 |
$5,389 |
$661 |
$663,533 |
Apr, 2025 |
$5,383 |
$666 |
$662,867 |
May, 2025 |
$5,378 |
$672 |
$662,195 |
Jun, 2025 |
$5,373 |
$677 |
$661,518 |
Jul, 2025 |
$5,367 |
$683 |
$660,835 |
Aug, 2025 |
$5,362 |
$688 |
$660,147 |
Sep, 2025 |
$5,356 |
$694 |
$659,453 |
Oct, 2025 |
$5,350 |
$699 |
$658,754 |
Nov, 2025 |
$5,345 |
$705 |
$658,049 |
Dec, 2025 |
$5,339 |
$711 |
$657,338 |
2025 |
$64,435 |
$8,162 |
$657,338 |
Jan, 2026 |
$5,333 |
$717 |
$656,622 |
Feb, 2026 |
$5,327 |
$722 |
$655,899 |
Mar, 2026 |
$5,322 |
$728 |
$655,171 |
Apr, 2026 |
$5,316 |
$734 |
$654,437 |
May, 2026 |
$5,310 |
$740 |
$653,697 |
Jun, 2026 |
$5,304 |
$746 |
$652,950 |
Jul, 2026 |
$5,298 |
$752 |
$652,198 |
Aug, 2026 |
$5,292 |
$758 |
$651,440 |
Sep, 2026 |
$5,285 |
$764 |
$650,676 |
Oct, 2026 |
$5,279 |
$771 |
$649,905 |
Nov, 2026 |
$5,273 |
$777 |
$649,128 |
Dec, 2026 |
$5,267 |
$783 |
$648,345 |
2026 |
$63,604 |
$8,993 |
$648,345 |
Jan, 2027 |
$5,260 |
$790 |
$647,555 |
Feb, 2027 |
$5,254 |
$796 |
$646,759 |
Mar, 2027 |
$5,247 |
$802 |
$645,957 |
Apr, 2027 |
$5,241 |
$809 |
$645,148 |
May, 2027 |
$5,234 |
$815 |
$644,332 |
Jun, 2027 |
$5,228 |
$822 |
$643,510 |
Jul, 2027 |
$5,221 |
$829 |
$642,682 |
Aug, 2027 |
$5,214 |
$836 |
$641,846 |
Sep, 2027 |
$5,208 |
$842 |
$641,004 |
Oct, 2027 |
$5,201 |
$849 |
$640,155 |
Nov, 2027 |
$5,194 |
$856 |
$639,299 |
Dec, 2027 |
$5,187 |
$863 |
$638,436 |
2027 |
$62,688 |
$9,909 |
$638,436 |
2047 |
$3,688 |
$68,910 |
$0 |
From the above analysis, it can be inferred that none of the monthly payments will be equal to $68,622. However, in case of 1st year, the total year payment is coming to be $68,457, which is summation of all the monthly for that particular year.
The total annual of $47,145.31in year 1 and $170,502.31 by year 20 is coming while considering the excess of $300,000. The loss amount considering 7 percent of $300,000 is added to the amount $26,145.31 is taken into consideration. In this manner, it was determined.
The strategies undertaken by Morton can be evaluated with the help of the following points:-
- Separate amount of $300,000 of money market will be invested at 7 percent interest
- Safety long term policy is completely ignored
- Tax sheltered investment has also been ignored
These loopholes are there in the strategies undertaken by Morton
There are several recommendations that can be given based on the information. These are as follows:-
- The excess amount of $300,000 needs to be invested in bonds which can be considered as a fixed income policy and safe as well. The average return is expected to be more than 6 percent as well. This investment is of long term purpose and will serve the requirements of
- Few portion of equity amount can be deposited to savings account for safety purpose
- Studebaker needs to invest more amount in money market instruments for safety purpose.
These are the recommendations that can be given to Studebaker.
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